The average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.
What is average change?
The ratio of "change in the function values" to "change in the interval endpoints" is referred to as the average rate of change of a function f(x) over an interval [a, b].
Here, we have
Sea level changes by -73.5 ft in 3 minutes
So, we apply the average change formula, and we get
= -73.5/3
= - 24.5 ft per minute
And the otter goes deeper because - 24.5 < 0
Hence, the average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.
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Solve the inequality.
3-x≤-19 or -x ≥ 24
x> [?] or x ≤
x≤[
Enter
The solution to the given inequality 3 - x ≤ 19
or - x ≥ 24 is x ≥ -16 or x ≤ -24
What is the solution of the inequality?An inequality is a statement that is of two quantities; one is specifically less than or greater than another. Inequality symbols are:
Less than < Less than or equal to ≤ Greater than > Greater than or equal to ≥ equal to =3 - x ≤ 19
or
- x ≥ 24
3 - x ≤ 19
substract 3 from both sides-x ≤ 19 - 3
- x ≤ 16
divide both sides by -1
x ≤ 16/-1
x ≥ -16
or
- x ≥ 24
divide both sides by -1x ≥ 24/-1
x ≤ -24
In conclusion, the solution to the inequality is given by x ≥ -16 or x ≤ -24
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If A = (1 , 4) and B = ( 7 , 6), then coordinates of the midpoint of AB are
Answer:
(4 , 5)
Step-by-step explanation:
midpoint formula: (x1+x2/2 , y1+y2/2)
so
(1+7/2 , 4+6/2)
(8/2 , 10/2)
4 , 5
What expression has the same value as 2(5x + 2) - (3y)2x – 4x
Answer:
10x+6xy+4
Step-by-step explanation:
2(5x+2)-(3y) 2x-4x
By removing the bracket
10x+4-6xy+12xy
10x+4+6xy
10x+6xy+4
F(x)=3x^4-4x^3+x^2+6x-2
The rational zeros for F(x)=3x^4-4x^3+x^2+6x-2 are x= -1 and x= 1/3 while the linear factors are (x+1) and (3x-1)
How to determine the rational zeros and linear factors?Synthetic division has to do with dividing polynomials.
The process involves:
Step 1: Set up the synthetic division.
Step 2: The leading coefficient should be brought down to the bottom row.
Step 3: Multiply this by the value just written on the bottom row.
Step 4: Then, add the column created in step 3.
This can be illustrated thus:
Given: f(x) = 3x⁴-4x³+x²+6x-2
3x⁴-4x³+x²+6x-2 = 0
We will try x = -1 in f(x). In this case, replace x with -1. This will be:
= 3x⁴-4x³+x²+6x-2 = 0
Since f(-1)= 0 so (x+1) is a factor
Using synthetic division:
-1)....3....-4....1....6....-2
.........3.....-7...8....-2..|..0
Remainder = 0
Quotient = 3x³ -7x² + 8x -2
For 3x³ -7x² + 8x -2, f(1/3) = 0 so (x- 1/3) is a factor
1/3)....3....-7....8....-2
..........3.....-6...6...|..0
Remainder = 0
Quotient = 3x²-6x+6
= 3(x²-2x+2)
Since there are no more rational zeros or linear factors for x²-2x+2. Therefore, the rational zeros are x= -1 and x= 1/3.
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40
100%
Complete the table to show different percentages of the steaming time.
Time (min)
Percentage
100% of 40 min
50% of 40 min
250% of 40 min
The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively
How to complete the table to show different percentages of the steaming time?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min
100% of 40 min:
100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min
50% of 40 min:
50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min
250% of 40 min:
250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min
Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.
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A random sample of 10 subjects have weights with a standard deviation of 10.9508 kg What is the variance of their weights? Be sure to include the appropriate units with the result
Based on the information given the variance of their weights is 119.9200 kg².
What is variance?
The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: σ².
Main body:
n=sample size=10
Standard deviation=10.9508 kg
Using this formula
Variance=(Standard deviation)²
Let plug in the formula
Variance=(10.9508 kg)²
Variance= 119.9200 kg²
Hence the variance of their weights is 119.9200 kg².
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please help 25 points
⇒ ∠AEC is the angle vertical opposite to ∠BEC
reduce 12/16 to simplest terms
Answer: 3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 16 is 4
Divide both the numerator and denominator by the GCD
12 ÷ 4
16 ÷ 4
Reduced fraction: 3/4
Therefore, 12/16 simplified to lowest terms is 3/4.
Answer:.
Step-by-step explanation:
water faucet leaked 3/5 liters of water over the course of 2/5 hours. How many liters would it have leaked in 1 hour please tell me the answer
Answer:
1.5 liters
Step-by-step explanation:
2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.
How to determine the weight?Let x represent the weight of Cooper
Let x +25 represent the weight of Daisy
Let 3x -20 represent the weight of Luna
Hence,
x + (x +25) + (3x -20) = 175
5x +5 =175
Combine like terms
5x = 175 -5
5x =170
Divide both side by 5x
x = 170/5
x =34
Weight of Luna
3x -20 where x= 34
3(32) -20
= 102 -20
= 82 pounds
Therefore the correct option is D.
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Lorna Hall’s real estate tax of $2,010.88 was due on December 14, 2017. Lorna lost her job and could not pay her tax bill until February 27, 2018. The penalty for late payment is 612% ordinary interest. (Use Days in a year table.) a. What is the penalty Lorna must pay? (Round your answer to the nearest cent.) b. What is the total amount Lorna must pay on February 27? (Round your answer to the nearest cent.)
a. The penalty Lorna must pay is $26.86.
b. The total amount Lorna must pay on February 27 is $2037.74.
Given that,
On December 14, 2017, Lorna Hall's $2,010.88 real estate tax was due. Because of her job loss, Lorna was unable to pay her taxes until February 27, 2018. Late payment fees are assessed at a rate of 6 1/2% regular interest.
We have to find
a. What is the fine Lorna is required to pay
b. How much will Lorna owe in total on February 27.
First,
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $2010.88
r is 6 1/2%
t is 17+31+27= 75 days is 75/365
So,
i= 2010.88×6 1/2×75/365
i= $26.86
The penalty Lorna must pay is $26.86.
Second,
We know that,
Total amount= real estate tax due amount+ Penalty pay.
Total amount= $2010.88+$26.86
Total amount= $2037.74
The total amount Lorna must pay on February 27 is $2037.74.
Therefore, a. The penalty Lorna must pay is $26.86.
b. The total amount Lorna must pay on February 27 is $2037.74.
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I need to find the measure
Answer:
x = 147°
Step-by-step explanation:
To find x, we have to find the angle measures in the small triangle.
180 - 61 = 119° (sum of adjacent angles on straight line=180)
The other angle measure in the triangle is 28° because they are vertically opposite angles.
We subtract 119° and 28° to find the angle measure next to x.
180 - 119 - 28 = 33° (sum of angles in a triangle=180)
x = 180 - 33
= 147° (sum of adjacent angles on straight line=180)
Pls help need by today
Answer:
use AAA congurency rule
Step-by-step explanation:
angle a=angle f
angle b=angle e
angle c= angle d(a+b+c=180 when the triangle 2 sides are equal that means 3 is also equal)
Is there a proportional relationship between the area and radius of a circle? Explain.
The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
The area of a circle with radius "r" is given as,
A = πr²
Since,π = constant.
Removing constant by proportionality.
A ∝ r²
Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".
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Using the graph below, determine the employee's hourly wage.
Using the graph, the hourly wage of the employees is: $8 per hour.
How to Determine Hourly Wage From a Graph?Slope of a proportional graph is the unit rate between two variables, x and y, and it is calculated as: k = y/x.
To find the unit rate or slope of the graph, use any point on the graph (x, y).
The unit rate of the graph in the image above is the hourly wage of the employees.
Using any point on the line, say, (13, 104), we can find the slope/unit rate. Therefore:
Unit rate/slope, k = 104/13
Unit rate/slope, k = 8
Therefore, the hourly wage is: $8 per hour.
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Find the slope of the line that contains the points named.
P(1, 2), Q(3, 4)
0-1
01
02
Answer:
If the coordinates of at least two points in the line are given, the slope (m) may be calculated by, m = (y2 - y1) / (x2 - x1
Ms. Jones is comparing two sets of scores. For Test A, the standard deviation is 7, and for Test B, the standard deviation is 12. This means that
The comparison done by Mr Jones means that Test A of standard deviation 7 is closer to the mean scores and Test B of standard deviation 12 is further apart from the mean score
What is standard deviation?The standard deviation is a statistic measure that expresses how much variance or dispersion there is in a group of numbers.
A high standard deviation suggests that the values are dispersed throughout a wider range,
A low standard deviation suggests that the values tend to be close to the established mean.
A positive value means the standard deviation is above the mean while a negative value means the standard deviation is below the mean
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Solve-ns16 Which of the following must be true about the inequality and the resulting graph? Select three
options.
ns<-24
n>-24
The circle is open.
The circle is closed.
The arrow points right.
By using the concept of inequality, the correct options are
2nd, 4th and 5th option
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here,
The given inequation is
[tex]\frac{-2}{3}n \leq 16[/tex]
Now,
[tex]\frac{-2}{3}n \leq 16\\n \geq -16 \times \frac{3}{2}\\n \geq -24\\[/tex]
Since n is greater than or equal to 24, the arrow will point towards right
The circle will be closed as there is an equality
So the correct options are 2nd, 4th and 5th option
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Complete Question
The complete question has been attached here
rita class has 14 girls and 16 boys how does the ratio 14:30 describe ritas class
Answer:
The ratio shows that there are 14 girls to 30 students in total
Step-by-step explanation:
14 + 16 = 30 that mean that there are 30 students in total, therefore, the ratio shows 14 girls : 30 students
2. Draw the image of RST under the dilation with scale factor 5/3 and center of dilation (2, -2) . Label the image R'S'T' .
Answer:
Step-by-step explanation:
what are her monthly payments
The interest she is pay total is $2340.822 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
Given that,
For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
We have to find will she pay interest at all.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $6490
r is 7.26%
t is 5 years
So,
i= 6490×0.0726×5
i= $2355.87
Therefore, the interest she is pay total is $2355.87 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.
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Can someone help pls
Answer:
99
Step-by-step explanation: 99
Please help I need to find X
Answer:
x=17
Step-by-step explanation:
8x+20 is equal to 11x-31 because l parallel to m.
8x+20=11x-31
3x=51
x=17
Answer:
[tex]\sf x=17^o[/tex]Step-by-step explanation:
L || m
[tex]\sf (8x+20)^o=(11x-31)^o[/tex]
[ Corresponding angles]
[tex]\sf 8x+20=11x-31[/tex]
[tex]\sf 8x-11x=-31-20[/tex]
[tex]\sf -3x=-51[/tex]
[tex]\sf \cfrac{-3x}{-3}=\cfrac{-51}{-3}[/tex]
[tex]\sf x=17^o[/tex]
__________________
Hope this helps!
Have a great day!
NO LINKS!! Please help me with this probability question Part 1j
Answer:
[tex]\textsf{b)} \quad \text{P}(A\;\text{and}\;B)=\dfrac{1}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\text{P}(A)=\dfrac{1}{4}[/tex]
[tex]\text{P}(B)=\dfrac{1}{4}[/tex]
[tex]\text{P}(A|B)=\dfrac{4}{5}[/tex]
Conditional Probability Formula
[tex]\text{P}(A \cap B)=\text{P}(B)\;\text{P}(A|B)[/tex]
Substitute the given values into the formula:
[tex]\begin{aligned}\implies \text{P}(A \cap B)&=\dfrac{1}{4} \cdot \dfrac{4}{5}\\\\&=\dfrac{4}{20}\\\\&=\dfrac{1}{5}\end{aligned}[/tex]
Adam has a goal to hike
70 miles. If he hikes 8
miles per day, how
long will it take him to
hike all 70 miles?
Answer:
9 days (round up)
Step-by-step explanation:
70 ÷ 8 = 8.75
≈ 9 (round up)
My friend is hoping to move to your town but is concerned because she doesn’t have a car. Do you think this will present a big problem for her? Use the distance formula in some way to justify your response.
There are many things obstructing the route so yes. I cannot give a detailed answer as I have not been given the "distance formula" sorry
You can add and subtract fractions with different denominators. trite or false
Answer:
False
Step-by-step explanation:
The denominators have to be the same for you to be able to add or subtract a fraction.
How many legs do 40 cows have if 3 cows only have 2
Answer:
154 legs
Step-by-step explanation:
40-3=37
37 times 4 = 148
3 times 2 ° 6
148+6= 154
Answer: 154 legs
Step-by-step explanation: First, multiply 37×4 because there are 37 cows with 4 legs, which gets you 148. Since there are 3 cows with only 2 legs, do 3×2=6. Finally, add 148 and 6 to get 154 legs.
please give brainliest!
Graph the solution set to the inequality: 8x - 7y ≥ 42
Answer:
How do I show you the graph because I have it
Step-by-step explanation:
log x + 5 log y -4 log z rewrite as a single logarithm
Solution :
[tex]\qquad \sf \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]
[tex]\qquad \sf \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]
( a log(x) = log(x^a) )
[tex]\qquad \sf \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]
( log (a) + log (b) = log (ab) )
[tex]\qquad \sf \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]
( log (a) - log (b) = log (a/b) )