Answer:
There are several ways to graph a continuous function. I advise you to graph several points that belongs to the function and then join the points.
If the function is linear, two points will be enough to build the graph. If we have functions of higher degree, is better to plot some points, observe the pattern and then join the points.
If the function is extremly difficult to graph by hand, the help of a graphing calculator may be needed.
To graph a continuous function, identify the independent and dependent variables, ensure the values on axes are evenly spaced, plot values as coordinates, and draw a smooth curve connecting the points without lifting the pen. The area under the graph is significant in calculus for representing continuous change, and for continuous probability distributions, it defines the probability as the area under the curve.
To graph a continuous function, first identify your independent and dependent variables. The independent variable is typically placed on the X-axis, while the dependent variable goes on the Y-axis. Ensure the scales for both axes are evenly spaced to accurately represent the continuous values. After setting up the axes, plot the pairs of values that the function defines as x and y coordinates. For a continuous function, you should be able to draw the curve connecting these points without lifting your pen off the paper.
In the context of calculus, the area under the graph represents the aggregation of continuous change over an interval, which differs from discrete sums used for step changes. This is critical when working with functions to determine areas, volumes, or growth over an interval. As such, if you are graphing a function like f(x) = x², you would plot points for x values from the interval and then draw a smooth curve through those points to represent the function continuously.
When considering continuous probability distributions, the graph will depict a curve known as the probability density function (pdf). Probability is calculated as the area under the curve, emphasizing the importance of a continuous, unbroken line in representing these types of distributions.
Suppose BCA is congruent to EDA. Using only the information provided in this problem, can you use the
SSS Postulate or the SAS Postulate to prove triangle ABC is congruent to triangle AED?
Answer:
A. By SAS only
Step-by-step explanation:
Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
In triangles ABC and AED:
sides ACand AD are congruent (from the diagram);angles BCA and EDA are congruent (given);sides BC and ED are congruent (from the diagram).So, SAS postulate can be applied.
SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.
Answer:
ΔABC and ΔAED are congruent to each other by SAS rule.
Step-by-step explanation:
We are given a figure in the question.
The figure shows that:
AC = AD, BC = ED, ∠BAC = ∠EAD
We are also given that triangle BCA is congruent to triangle EDA.
Now, we need to prove that triangle ABC is congruent to triangle AED.
We will use SAS criterion of congruence.
In ΔABC and ΔAED,
AC = AD, ∠BAC = ∠EAD, , BC = ED( all given in the figure)
Hence, the two triangles are congruent to each other by SAS rule.
the chef at a school cafeteria asked students whether they like peas. for the students surveyed, are liking peas and being male independent or dependent events? justify your answer
A.) Dependent;
P(likes peas) =39%
P(male/likes peas) =54%
since these probabilities are not equal, the events are dependent.
B.) Dependent;
P(likes peas) =39%
P(likes peas/male) = 42%
since these probabilities are not equal, the events are dependent.
C.) Independent;
P(likes peas) =39%
P(likes peas/male) =42%
since these probabilities are not equal, the events are independent.
D.) Independent;
P(likes peas) =39%
P(male/likes peas) =54%
since these probabilities are not equal, these events are independent.
Answer:
Option B
Step-by-step explanation:
Given:
total No. of students liking peas= 78
total no. of male students= 100
total number of students= 200
no. of male students liking peas= 42
Now we need to find are liking peas and being male independent or dependent events
P(likes peas)= 78/00
=0.39
=39%
P(likes peas/male) = 42/100
= 42%
as the two probabilities are not equal the two events are dependent.
Hence option B is correct: Dependent;
since these probabilities are not equal, the events are dependent!
Answer:
B
Step-by-step explanation:
In the Dependent case the following relation must be satisfied:
p(a|b) = p(a∩b)/p(b)
Or, in terms of this problem:
p(like peas|male) = p(like peas∩male)/p(male)
The probabilities of this events are:
p(like peas|male) = 42/100 = 42%
p(like peas∩male) = 42/200 = 21%
p(male) = 100/200 = 50%
Therefore, the events are dependent
In the Independent case the following relation must be satisfied:
p(a|b) = p(a)
or
p(like peas|male) = p(like peas)
p(like peas) = 78/200 = 39%
The equation is not satisfied.
A couch advertised for $500 can be purchased
for a down payment of $200 plus 5 equal
monthly installments. What is the amount of
each monthly payment?
How much is it ?
Answer:
$60 a month is the answer
Step-by-step explanation:
$200 down payment leaves you with $300's to pay still. Divide the $300's by 5 and that leaves you with $60 a month.
Select the correct answer from the drop-down menu.
The graph shows a proportional relationship between the distance a car travels and the fuel it consumes.
Answer:
2.5 gallons
Step-by-step explanation:
We need to go 100 miles
Write the proportion
Picking a point on the graph (40 miles, 1 gallon)
100 miles 40 miles
-------------- = -------------
x gallons 1 gallon
Using cross products
100 * 1 = 40 *x
Divide each side by 40
100/40 = 40x/4
2.5 =x
We need 2.5 gallons to go 100 miles
Answer: Based on the graph, the car requires 2.5 gallons of fuel to travel 100 miles.
Look at the picture below for help. The blue dot represents were the two points meet. We are trying to figure out how many gallons are for the 100 miles, 100 miles would be on the side that says distance (miles). That is were you start. Find point 100 on the distance (miles) side and just draw a straight line, stopping when you hit the black line on the graph. Once done, draw another line going straight down from the black line, and you get your answer of 2.5
Answer: 2.5
Hope it helps!
3. Name the plane shown in the figure.
A. Plane GDH
B. Plane FCF
C. Pane EGF
D. Pane ACS
the name of the plane is C. plane EGF
What is the simplified form of the expression?
Answer:
7c^2d-7c+4d-10
Step-by-step explanation:
Start off with the term that has c^2 in it. 5c^2d + 2C = 7c^2d, then since you have multiple choice, the d value differs between the two answer choices that have 7c^2d so you can do +3d +d to get +4d to get the fourth answer choice.
To check your work, you can add/subtract each term to see if you get 7c^2d-7c+4d-10
Which of the following is not a way to represent the solution of the inequality 7 − 9x − (x + 12) less than or equal to 25?
A) x greater than or equal to −3
B) x less than or equal to −3
C) −3 less than or equal to x
D) A number line with a closed circle on negative 3 and shading to the right
Answer:
A) x greater than or equal to −3
Step-by-step explanation:
We have the following inequality:
7 − 9x − (x + 12) ≤ 25
Solving the inequation, we have:
7 − 9x − x - 12 ≤ 25
-10x ≤ 30
-x ≤ 3
x≥-3
Therefore the result is option A) x greater than or equal to −3
Answer:
B.
Step-by-step explanation:
7-9x - (x+12) ≤ 25
7 - 9x - x - 12 ≤ 25
-10x - 5 ≤ 25
-10x ≤ 25 +5
x ≥ 30/-10
x ≥ -3.
So, the incorrect answer is B.
Suppose that a company's annual sales were $1,200,000 in 1999. The annual growth rate of sales from 1999 to 2000 was 16 percent, from 2000 to 2001 it was −5 percent, and from 2001 to 2002 it was 22 percent.
The geometric mean growth rate of sales over this three-year period is calculated as 10.37 percent. Use the geometric mean growth rate and determine the forecasted sales for 2004.
Step-by-step explanation:
A = P (1 + r)^t
Given that P = $1,200,000, r = 0.1037, and t = 5:
A = $1,200,000 (1 + 0.1037)^5
A = $1,965,334.41
Round as needed.
Answer:
The forecasted sales for 2004 is $1965281.
Step-by-step explanation:
The annual sales in 1999 were = $1,200,000
Let geometric mean growth rate = r
we have now p = $1,200,000,
r = 10.37% or 0.1037
t = 5:
We have the formula Amt= [tex]p(1+r)^{t}[/tex]
Amt =[tex]1200000(1+0.1037)^{5}[/tex]
Solving this we get;
[tex]1200000\times1.63777=1965324[/tex]
A = $1,965,324
What are the measures of angles 1 and 2?
m<1 =
m<2=
Answer:
m∠1 = 50°
m∠2 = 130°
Step-by-step explanation:
The measure of the angle formed by 2 chords that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs.
m∠1 = (53+47)/2 = 50°
m∠1 + m∠2 = 180° ⇒ m∠2 = 180 - m∠1 = 180 - 50 = 130°
The measure of angle 2 (θ2) is given as 312°. To determine the measure of angle 1 (θ1), additional information or context is needed as it is not provided directly in the question or accompanying information.
Explanation:The question seems to be about finding the measures of angles angle 1 (θ1) and angle 2 (θ2) in a physics context, possibly related to momentum or forces. Given that Ø2 is provided as 312°, we can infer that this is the measurement of angle 2 (θ2). This angle is said to be in the fourth quadrant, which is consistent with the positive counterclockwise definition of angle measurement. For the measure of angle 1 (θ1), there's not enough direct information provided in the question or the reference information to determine its measure. More context or additional data would be necessary to solve for θ1. If the scenario is about a momentum conservation problem, the relationship between angles might be set by the conservation laws for linear momentum in the x and y directions. However, without additional information or clarification from the student's initial query, we would only be speculating on the measure of θ1.
Examine the equation: 4x = 2 − y Which equation represents the equivalent equation in slope-intercept form?
y = –4x + 2
y = –4x - 2
x = 2 - 4y
x = 8 - 4y
Answer:
[tex]y=-4x+2[/tex]
Step-by-step explanation:
Since, the slope intercept form of a line is,
[tex]y=mx+c[/tex]
Here, the given equation is,
[tex]4x=2-y[/tex]
[tex]4x+y=2[/tex] ( Additive property of equality )
[tex]y=-4x+2[/tex] ( Subtraction property of equality )
Hence, the equation that represents the equivalent equation of the given equation in slope-intercept form is,
[tex]y=-4x+2[/tex]
First option is correct.
Answer:
Step-by-step explanation:
Find m DEF
A. 30
B. 60
C. 90
D.120
The little red lines on each side of the triangle mean that the sides are all equal.
A triangle that has all 3 sides the same is an equilateral triangle.
Because all the sides are identical all 3 inside angles are also identical.
180 / 3 = 60 degrees
The outside angle which is DEF would equal 180 - the inside angle.
DEF = 180 - 60 = 120.
The answer is D.
Answer:
120°
Step-by-step explanation:
It is an equilateral triangle, so all its sides and internal angles measure the same.
The sum of the internal angles of a triangle must be 180°, so each internal angle measures 60°.
The DEF angle is an external angle of that triangle, we can use the next property:
An external angle of a triangle is the sum of the internal angles opposed to it.
The two opposite angles to DEF are DCE and CDE:
DEF = DCE + CDE = 60 ° + 60 ° = 120°
Another way to find this same result is to notice that DEF + DEC total 180° since they form a straight line, and we know that DEC measures 60°
So:
DEF + DEC = 180 °
DEF = 180 ° - DEC
DEF = 180 ° -60 °
DEF = 120 °
may somebody help please me thank you so much
Answer:
45
Step-by-step explanation:
Here are two ways of solving this problem.
Method 1:
Term 1 is 2.
Term 2 is 3.
Term 3 is 4.
Each term is 1 more than the term number.
The 44th term is 45.
Method 2:
Using the hint
Find the common difference: 5 - 4 = 1
The common difference is 1.
1st term + (common difference)(desired term - 1)
2 + 1(44 - 1) = 2 + 43 = 45
Answer: 45
Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F.
0.0833
0.4826
0.3343
0.9826
Final Answer:
The probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.
Explanation:
To find the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large. In this case, we can assume a sample size of 19 is large enough.
Given:
- Population mean (μ) = 98.20°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 19
- Target sample mean (X) = 98.50°F
We need to do the following steps:
1. Calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
SEM = σ / √n
2. Calculate the Z-score for the sample mean of 98.50°F. The Z-score represents how many standard errors the value is away from the population mean.
Z = (X - μ) / SEM
3. Use the Z-score to find the area to the left of it on the standard normal distribution, which represents the probability that the sample mean is less than 98.50°F.
Let's calculate each step:
1. Calculate SEM:
SEM = σ / √n
= 0.62 / √19
≈ 0.62 / 4.3589
≈ 0.1422
2. Calculate Z-score:
Z = (X - μ) / SEM
= (98.50 - 98.20) / 0.1422
≈ 0.30 / 0.1422
≈ 2.1095
3. Lastly, to find the probability that the sample mean is less than 98.50°F, we look up the Z-score in the standard normal distribution table (Z-table), use statistical software, or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.
A Z-score of 2.1095 corresponds to a probability of about 0.9826 (using Z-table or a calculator).
Therefore, the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.
Among the options given, the closest to 0.9826 is 0.9826 itself. Hence, that is the correct answer.
Okay so i really need help anyways soon as possible!
Answer:
Isolate the variables in all cases. Note the equal sign, what you do to one side, you do to the other.
a) 3x = 18
Isolate the variable, x. Divide 3 from both sides:
(3x)/3 = (18)/3
x = 18/3
x = 6
b) 2x = 9
Isolate the variable, x. Divide 2 from both sides:
(2x)/2 = (9)/2
x = 9/2
x = 4.5
c) (x/5) = 7
Isolate the variable, x. Multiply 5 to both sides:
(x/5)(5) = (7)(5)
x = 7 * 5
x = 35
d) x/2 = 6.5
Isolate the variable, x. Multiply 2 to both sides:
(x/2)(2) = (6.5)(2)
x = 6.5 * 2
x = 13
~
a) 3x = 18
x = 6
____________
b) 2x = 9
x = 4.5
____________
c) (x/5) = 7
x = 35
____________
d) x/2 = 6.5
x = 13
____________
Have a great day!
How do you write numbers in scientific notation? 0.0021
Answer: I know you prob don't need this answer anymore but this is for the people who look it up and need it.
Step-by-step explanation:
It's 2.1*10^-3
[tex]2.1 \times 10^{-3[/tex] is the scientific notation of the given number.
To write in scientific notation,
Write the non-zero digits as a decimal number between 1 and 10. In this case, we have 2.1.Count the number of decimal places you moved the decimal point to get the original number. In this case, the decimal point was moved 3 places to the right to get from 0.0021 to 2.1.Write the number in the form of [tex]a \times 10^b[/tex], where a is the decimal number from step 3, and b is the number of decimal places you moved the decimal point in step 4. In this case, the number 0.0021 can be written as [tex]2.1 \times 10^{-3[/tex].So, in scientific notation, 0.0021 is written as [tex]2.1 \times 10^{-3[/tex].
Learn more about Mathematical operations here:
https://brainly.com/question/20628271
#SPJ6
PLEASE ANSWER THIS QUESTION ✔✔
REMEMBER I ADD BRAINLIST AND I UPVOTE ANSWER
Answer:
Its 7.7, 7, 0.6, -0.7
What is the measurement of angle A to the nearest degree? a0degree
Answer:
The measure of angle A is 51 degrees
Answer:
The measure of an angle A=[tex]1^{\circ}[/tex].
Step-by-step explanation:
We are given that an angle [tex]95^{\circ}[/tex] and two sides are 7 in and 9 in in a given figure.
We have to find the value of measurement of angle A.
To find the measurement of angle A we apply sine law.
Sine law:[tex]\frac{a}{sin \alpha}=\frac{b}{sin\beta}=\frac{c}{sin \gamma}[/tex]
Where side a is opposite to angle [tex]\alpha[/tex]
Side b is opposite to angle [tex]\beta[/tex]
Side c is opposite to angle[tex] \gamma[/tex]
We are given an angle 95 degrees and opposite side of given angle is 9 in and the angle A is opposite to side 7 in.
Substituting the values then we get
[tex]\frac{9}{sin 95^{\circ}}=\frac{7}{sin A}[/tex]
[tex]\frac{9}{0.683}=\frac{7}{sin A}[/tex]
[tex] sin A=\frac{7\times 0.683}{9}[/tex]
[tex] sin A=\frac{4.781}{9}=\frac{4781}{9000}[/tex]
[tex] sin A=0.531[/tex]
[tex] A= sin^{-1}(0.531)[/tex]
[tex] A=0.56^{\circ}[/tex]
[tex] A= 1^{\circ}[/tex]
Hence, the measure of an angle A=[tex]1^{\circ}[/tex].
A class trip to a beach has been planned for your senior trip. The resort only allows swimming when the temperature is between 75 degrees and 110 degrees. There is room for 50 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip
A
[tex]0 < x \leqslant 50 \: and \: 75 < y < 110[/tex]
B
[tex]x > 75 \: and \: y < 110[/tex]
C
[tex]75 < x < 110 \: and \: 0 < y \leqslant 50[/tex]
D
[tex]x < 110 \: and \: y > 75[/tex]
Answer:
[tex]\large\boxed{C.\ 75<x<110\ and\ 0<y\leq50}[/tex]
Step-by-step explanation:
x - the temperature
y - the number of people
the temperature is between 75 degrees and 110 degrees:
75 < x < 110
the room for 50 people:
0 < y ≤ 50
Answer:
C
Step-by-step explanation:
We know x is more than 75
75<x
and there is room for 50 people and we have to use y
0<y<110
_^
The only possible answer is C hope this helps :)
Please answer this correctly
Answer:
1) 0.0008306
2) 0.00008306
3) 0.000008306
4) 0.0000008306
Step-by-step explanation:
Please mark me the brainliest... . I am sure the answers are correct.
Answer:
0.0008306
0.00008306
0.000008306
0.0000008306
Step-by-step explanation:
0.008306 ÷ 10 = 0.0008306
0.008306 ÷ 100 = 0.00008306
0.008306 ÷ 1000 = 0.000008306
0.008306 ÷ 10000 = 0.0000008306
to the nearest hundreth, what is the area of a circle with a radius of 5 units?
it's d, since the area of a circle is radius squared times pi
3.14×5^2= 78.4
The graph of which equation has a slope of 4?
(1) y = 4x -3 (3) y = -4x + 3
(2) y = 3x - 4 (4) y=-3x + 4
Please help :( I don’t get it
Answer:
(1)
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
We are looking for an equation of the form
y = 4x ± c ( since slope m = 4)
The only equation which fits the description is
y = 4x - 3 → (1)
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 12, 17, 16, 9, 18, 10, 9
Final answer:
To find the mean absolute deviation (MAD) for the data set, calculate the mean, subtract it from each data value to find deviations, take the absolute values, and then find their mean. The MAD for the data set 12, 17, 16, 9, 18, 10, 9 is approximately 3.43.
Explanation:
To find the mean absolute deviation (MAD) for a given data set, we follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data value to find the deviations.
Take the absolute value of each deviation.
Find the average of these absolute values to determine the MAD.
The data set provided is: 12, 17, 16, 9, 18, 10, 9. First, let's calculate the mean:
(12 + 17 + 16 + 9 + 18 + 10 + 9) / 7 = 91 / 7 = 13
Next, we'll find the absolute deviations from the mean:
|12 - 13| = 1
|17 - 13| = 4
|16 - 13| = 3
|9 - 13| = 4
|18 - 13| = 5
|10 - 13| = 3
|9 - 13| = 4
Lastly, we calculate the mean of these absolute values:
(1 + 4 + 3 + 4 + 5 + 3 + 4) / 7 = 24 / 7 ≈ 3.43
The mean absolute deviation of the data set is approximately 3.43.
Final answer:
The mean absolute deviation of the data set is calculated by finding the mean, determining the absolute deviation of each value from the mean, and then taking the mean of those deviations. For this set, the mean absolute deviation is 3.43.
Explanation:
To find the mean absolute deviation, we follow these steps:
First, we calculate the mean of the data set: (12 + 17 + 16 + 9 + 18 + 10 + 9) ÷ 7 = 91 ÷ 7 = 13.
Next, we find the absolute deviation of each data point from the mean:
Add these absolute deviations: 1 + 4 + 3 + 4 + 5 + 3 + 4 = 24.
Finally, we find the mean of these absolute deviations: 24 ÷ 7 = 3.43 (rounded to the nearest hundredth).
The mean absolute deviation for the data set is 3.43.
What is 1/2 divided by 3?
Answer:
1/6
Step-by-step explanation:
(1/2)/3
To solve, note that there are 2 denominators in all. To solve, multiply the denominators together:
(1/2)/3 = 1/(2 * 3) = 1/6
1/6 is your answer.
~
Answer:
0.16
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Exact form: 1/6
Decimal form: 0.16
write an equation for the line that passes through (-1,4) with a slope of -10
Answer:
y = - 10x - 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here slope m = - 10, hence
y = - 10x + c ← is the partial equation
To find c substitute (- 1, 4) into the partial equation
4 = 10 + c ⇒ c = 4 - 10 = - 6
y = - 10x - 6 ← equation of line
What is the equation of the following line? Be sure to scroll down to see all the answers
Answer:
y = 6x
Step-by-step explanation:
Find slope
Formula
y2 - y1/x2 - x10 - (-3) = 3
0 - (-1/2) = 1/2
Simplify
3/(1/2) = 6
y = 6x
y-intercept
The line crosses the origin, so the y-intercept is 0.
Answer
y = 6x
Obtenha o conjunto das soluçoes racionais de cada sistema:
(a) {x+y=4
{x-y=1
Answer:
(5/2 , 3/2)
or
(2.5 , 1.5)
(These are the same point; just one is in fraction form and the other in decimal)
Step-by-step explanation:
I could be wrong but I think you want to solve the system
x+y=4
x-y=1
The cool thing about this system it is already set up for elimination (some people call it linear combination). This means when you add the equations together, a variable will get eliminated allowing you to solve for the other.
x+y=4
x-y=1
----------Add equations.
2x+0=5
2x =5
x =5/2
x =2.5
So plug in your x into either one of the equations and solve for y.
x+y=4
2.5+y=4
y=4-2.5
y=1.5
So the solution is (2.5 , 1.5) or (5/2, 3/2).
Rosalie takes the bus everyday to school. The ride is 8 minutes long. If she goes to school for 176 days, how many minutes does she spend on the school bus?
Answer:
1408 min.
Step-by-step explanation:
8 × 176 = 1408.
Answer:
1408
Step-by-step explanation:
I need help please help me
Answer:
10 ≥ ⅛c + ¼d
Step-by-step explanation:
They budgeted up to 10 gallons of water, meaning that it CANNOT exceed 10. When turned around, you will see that everything is less than or equal to 10.
I am joyous to assist you anytime.
Complete question:
A small kennel has budgeted to provide 10 gallons of water for its animals. Each cat receive one eight of a gallon per day and each dog receives one fourth of a gallon per day . Which inequality correctly represent the scenario.
a. 10 < -1/8c - 1/4d
b. 10 ≤ 1/8c + 1/4d
c 10 ≥ -1/8c - 1/4d
d. 10 ≥ 1/8c + 1/4d
Answer:
d. 10 ≥ 1/8c + 1/4d
Step-by-step explanation:
The kennel was budgeted to provide 10 gallons of water for its animals. The cat receives 1/8 of a gallon per day and each dog receive 1/4 of a gallon per day.
Since 10 gallons was budgeted for the animals the sum of the a gallon per day for the cat and dog will most likely not exceed 10 gallons. The animals will most likely consume less than the budgeted value or equals to the budgeted value.
note that the sum of 1/8 of a gallon for the cat and 1/4 of a gallon for the dog should be either less than 10 or equals to 10. This means 10 ≥ 1/8c + 1/4d .
What is the exponential form of the following expression
(-5)(-5)(-5) •c•c•c
The expression will be [tex]\[ (-125) \cdot c^3 \][/tex]
The exponential form of the expression [tex]\((-5)(-5)(-5) \cdot c \cdot c \cdot c\)[/tex] can be calculated as follows:
First, simplify the multiplication of the negative numbers:
[tex]\[ (-5)(-5)(-5) = (-125) \][/tex]
Next, simplify the multiplication of the variables:
[tex]\[ c \cdot c \cdot c = c^3 \][/tex]
Now, combine the results:
[tex]\[ (-125) \cdot c^3 \][/tex]
The final exponential form of the expression is:
[tex]\[ (-125) \cdot c^3 \][/tex]
Here's a step-by-step explanation of the calculation:
1. Multiply the negative numbers:
[tex]\[ (-5)(-5) = 25 \][/tex]
Multiply 25 by -5 again:
[tex]\[ 25 \cdot (-5) = -125 \][/tex]
2. Multiply the variables:
[tex]\[ c \cdot c = c^2 \]\\ Multiply \(c^2\) by c again:\\ \[ c^2 \cdot c = c^3 \][/tex]
3. Combine the results:
[tex]\[ (-125) \cdot c^3 \][/tex]
That's the final exponential form of the given expression.
Complete Question:
What is the exponential form of the following expression
(-5)(-5)(-5) •c•c•c
17:44
What is the common ratio of the sequence?
-2, 6, -18,54
OOOO
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Answer:
The common ratio is -3
Step-by-step explanation:
we know that
In a Geometric Sequence each term is found by multiplying the previous term by a constant called the common ratio
In this problem we have
-2,6,-18,54...
Let
a1=-2, a2=6,a3=-18,a4=54
a2/a1=6/-2=-3
a3/a2=-18/6=-3
a4/a3=54/-18=-3
Each term (except the first term) is found by multiplying the previous term by -3
therefore
we have a geometric sequence and the common ratio is -3