Answer:
The independent variable is time.
Step-by-step explanation:
Given,
The original number of pigs on the island = 20,
Also, the number of pigs doubled each year,
After 1 year the pigs = 20(2),
After 2 years = 20(2)²,
After 3 years = 20(2)³,
......................., so on...
Similarly, the number of pigs after t years would be,
[tex]y=20.2^t[/tex]
⇒ The value of y depends upon t,
⇒ The number of pigs depends upon the time ( in years ),
Since, the variable in which the other variable depends is called independent variable,
Hence, the independent variable must be time.
The measure of an inscribed angle is 110°. What is the measure of the intercepted arc? 55° 110° 220°
the measurement of an inscribed angle is half of the measure of the intercepted arc.
the inscribed angle is 110 degrees, so we multiply 110 by 2.
110*2 = 220 degrees
The measure of the intercepted arc is 220 degrees
220° is the measure of the intercepted arc
A line passes through the point (-8,3) and has a slope of 5/4.
Write an equation in slope-intercept form for this line.
In the diagram below, what is the approximate length of the minor arc ?
arc length = given angle/360 x 2 x PI x radius
120/450 x 2 x 3.14 x 23 = 48.17
round to 48 cm
Answer:
Option A is correct
the approximate length of the minor arc is, 48 cm
Step-by-step explanation:
Length of an arc is given by:
[tex]l = r \theta[/tex] .....[1]
here r is the radius of the circle from the center and [tex]\theta[/tex] is the angle in radian.
From the given figure, we have;
r = 23 cm
Use conversion:
1 degree = 0.0174533 radian
then
120 degree = 2.094396
[tex]\theta = 2.094396[/tex] radian.
Substitute these in [1] we have;
[tex]l = 23 \cdot 2.094396 = 48.171108[/tex] cm
Therefore, the approximate length of the minor arc is, 48 cm
HELP! Type the correct answer in each box. Use numerals instead of words, if necessary, use / for the fractions bar(s)
The piecewise function is:
[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]
To determine the piecewise function represented by the given coordinates, let's examine the points and their corresponding intervals.
The coordinates are (-1, 4), (1, 4), (3, 2), and (5, 4).
The points (-1, 4) and (1, 4) have the same y-coordinate, indicating that on the interval [tex]\(-1 \leq x \leq 1\)[/tex], the function has a constant value of 4. Therefore, the piecewise function for this interval is f(x) = 4 for [tex]\(-1 \leq x \leq 1\).[/tex]
The points (3, 2) and (5, 4) indicate that on the interval [tex]\(3 \leq x \leq 5\)[/tex], the function is a line passing through these two points. We can find the slope (m) and y-intercept (b) for this line.
[tex]\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{4 - 2}{5 - 3} = \frac{2}{2} = 1 \][/tex]
Using the point (3, 2), we can find the y-intercept:
2 = 1(3) + b
b = -1
Therefore, the equation for the line on the interval [tex]\(3 \leq x \leq 5\) is \(f(x) = x - 1\) for \(3 \leq x \leq 5\).[/tex]
Putting it all together, the piecewise function is:
[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]
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A surface on which all points are at the same potential is referred to as
Using the graph, find this information about the child’s movement in the vertical (y) direction:
1. the best trigonometric function to start with
2. the amplitude
3. the period
4. any horizontal displacement of the graph.
5. any vertical displacement of the graph.
Type your response here:
Quadrilateral ABCD is a parallelogram. ,  bisects , and . What is the best name for quadrilateral ABCD?
A.
rectangle
C.
isosceles trapezoid
B.
rhombus
Find the greatest common factor of the following monomials 28g5h2 12g6h5
Also explain step by step how to solve these problems please
3. Simplify log3 20 - log3 5
There are (72)3 ⋅ 70 lambs on a farm. What is the total number of lambs on the farm?
Heyyy guys just thought I’d let y’all know the answer is *117649* if you (7^2)^3 that’s the answer and 7^0 is 0 soooo yeah!
Which equation is not equivalent to the formula m = ca?
A: [tex]c = \frac{m}{a} [/tex]
B: [tex]a = \frac{c}{m} [/tex]
C: [tex]a = \frac{m}{c} [/tex]
D: m = ac
Answer:m=ca i remember my teacher telling me how to do this.
Step-by-step explanation:
Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area of triangle $acb$ to the area of the trapezoid $abcd$? express your answer as a common fraction.
Help with these three problems? Please
6. add the averages then take that average
50+74 = 124, 124/2 = 62
answer: 62
8. first put all the numbers in order
4, 5 ,6 ,8 11, 12,14, 15, 23 ,23
Find the middle number, since there are 10 numbers find the average of the 2 middle numbers
11+12 =23/2 =11.5
Lower half data = 4, 5, 6, 8, 11
The middle number of that set is Q1,
Q1=6
9
9, find q3
1, 2, 3, 5, 5, 6, 9
Find middle number (5)
upper half data = 5, 6, 9
Q3= 5 , 6, 9 = 5+10 +15 = 30
so answer is $30
How many 3 digit numbers can be made if no digit is repeated and the number can not begin with a zero?
digit #1 - 9 numbers (1-9)
digit #2 = 9 numbers (0-9 minus the first digit)
digit #3 = 8 numbers ( 0-9 minus the first 2 digits)
9*9*8 = 648 combinations
A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row.What is the greatest possible number of pansies in each row?
Determine the common ratio and find the next three terms of the geometric sequence.
3/4,3/10,3/25,...
The next three terms of the sequence are 6/125, 12/625 and 24/3125
Geometric sequenceThe nth term of a geometric sequence is given as:
Tn = ar^n-1
Given the geometric sequence
3/4,3/10,3/25,...
Find the common ratio
r = 3/10 * 4/3
r = 2/5
Find the 4th, 5th and 6th terms
T4 = (3/4)(2/5)^3
T4 = 3/4 * 8/125
T4 = 6/125
T5 = (3/4)(2/5)^4
T5 = 3/4 * 16/625
T5 = 12/625
T6 = (3/4)(2/5)^5
T6 = 3/4 * 32/3125
T6 = 24/3125
Hence the next three terms of the sequence are 6/125, 12/625 and 24/3125
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The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Applying Newton's cooling model, the temperature of the tea after 2 hours will be ___
ºF. round to the nearest integer.
Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
Answer:
109 degrees
Step-by-step explanation:
Parallel to the line 2x-3y=9 and having a y intercept of 3
The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
Find the exact values of sin A and cos A. Write fractions in lowest terms. A right triangle ABC is shown. Leg AC has length 15, leg BC has length 20, and hypotenuse AB has length 25.
In the right triangle with sides 15, 20, and 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.
In the right triangle ABC, we can use the given side lengths to find the trigonometric ratios for angle A. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the legs (AC and BC).
Let's denote the angle A as angle A:
Find sin A:
sin A = (opposite / hypotenuse) = BC / AB = 20 / 25 = 4/5.
Find cos A:
cos A = (adjacent / hypotenuse) = AC / AB = 15 / 25 = 3/5.
So, the exact values are sin A = 4/5 and cos A = 3/5.
In summary, in the right triangle ABC with side lengths AC = 15, BC = 20, and AB = 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.
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The velocity of a train, measured in meters per second, is described by vector t=(-1,-4). Find the direction the train is traveling using standard position
Answer:
inverse tangent 4/1
75.96 + 180 bc 3rd quadrant which equals 255.96 degrees.
Step-by-step explanation:
round 256 degrees
A caterer expects a minimum of 160 but no more than 192 people at a wedding. One fruit tray serves 16 people. The compound inequality represents x, the number of fruit trays the caterer should bring to the wedding.
160 ≤ 16x≤ 192
Which is a possible number of fruit trays the caterer might bring to the wedding?
A. 8
B. 10
C. 14
D. 16
Answer:
b. 10
Step-by-step explanation:
I did the test
Three out of four students in a school said they would vote for nuncio for class president. Predict how many of the 340 students would vote for nuncio
Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?
Answer:
ASA only
Step-by-step explanation:
Given is a picture of two triangles with one side and one angle congruent.
Comparison of these two triangles given
side = side
one angle = one angle (given)
Second angle = second angle (Vertically opposite angles)
Thus we find here that two angles and one corresponding side are congruent.
HEnce we say that these two triangles are congruent by ASA theorem
ASA theorem can be applied here because the equal side is between the two congruent angles.
Instead if the side is not between the congruent angles but corresponding side then we can only use AAS
SO here ASA is correct.
Answer:
ASA only
Step-by-step explanation:
We are given that two triangles in which
An angle of triangle is equal to its corresponding angle of second triangle.
One side of a triangle is equal to one side of other triangle.
ASA postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.
AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.
In triangle AOB and COD
[tex]\angle AOB= \angle COD[/tex] (Vertical angles are equal )
[tex]\angle ABO=\angle CDO[/tex] ( Given )
[tex]OB=OD[/tex] (Given )
[tex]\triangle AOB\cong \triangle COD[/tex] ( ASA Postulate )
Answer: ASA only
Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
^ Please use the template above to answer ^
To solve the quadratic equation x^2 - 10x + 15 = 0 by completing the square, we manipulate it to the form (x - 5)^2 = 10, then solve for x to get two solutions: x = 8.16 and x = 1.84.
Explanation:To solve the quadratic equation by completing the square, we need to manipulate the equation x^2 - 10x + 15 = 0 so it takes the form of (x - a)^2 = b, where a is half of the coefficient of x, and b is a constant.
First, we move the constant to the other side of the equation:
x^2 - 10x = -15
Next, we find the value that completes the square. This value is (10/2)^2 = 25.
Adding 25 to both sides, we get:
x^2 - 10x + 25 = 25 - 15
Now the equation is a perfect square:
(x - 5)^2 = 10
To find the solution for x, we take the square root of both sides:
x - 5 = ±10√10
x = 5 ± √10
Thus, the solutions rounded to the nearest hundredth are:
x = 5 + √10 ≈ 8.16
x = 5 - √10 ≈ 1.84
The complete answer in the template is:
Form:
( x - 5 )^2 = 10
Solution:
x = 8.16, 1.84
The end points of AB are A(-2,-3) , B(3,2) point C lies on AB and is 2/5 of the way from A to . What is the coordinates of point C? Explain how you find your answer
To find the coordinates of point C which divides line AB into a 2:5 ratio, use the section formula. Therefore, the coordinates are (-4/7, -11/7). This provides point C's location on the line segment AB.
Explanation:The coordinates of C are determined through the section formula, which finds the coordinates of a point dividing a line segment into a specific ratio. In this case, the ratio is 2:5. To solve for the x-coordinate of C, the formula [(m*x2) + (n*x1)] / (m+n) is used, where m and n are the ratio values, x1 and x2 are the x-coordinates of points A(-2, -3) and B(3, 2). Using these, the x-coordinate of C is found to be (2*3 + 5*(-2)) / (2+5) = -4/7.
Similar calculations apply to solving for the y-coordinate of C: [(m*y2) + (n*y1)] / (m+n) = (2*2 + 5*(-3)) / (2+5) = -11/7.
Therefore, the coordinates of point C are (-4/7, -11/7). This is the point C on the line segment AB that is 2/5 of the way from point A to point B.
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PLEASE ANSWER ASAP!!! WORTH 13 POINTS! I need help D:
Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories (c) she actually burns in one hour varies no more than 45 calories. Which inequality below represents this scenario?
A) |c − 450| less than or equal to 45
B) |c + 450| greater than or equal to 45
C) |c − 45| less than or equal to 450
D) |c − 45| greater than or equal to 450
I need help with #18 c-i
Two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters
If four times a number plus 3 is 11, what is the number