a. The inequality that models the possible change in the number of feet, r, of the whale's elevation is: 35 - r ≤ 17.
This inequality represents the starting depth of 35 feet below the surface (35), minus the possible change in elevation (r), which should be less than or equal to the maximum height the whale jumps, which is nearly 17 feet above the surface (17).
b. By solving the inequality 35 - r ≤ 17, we can find the range of possible values for r.
First, subtract 35 from both sides of the inequality: -r ≤ 17 - 35. Simplifying further, we have -r ≤ -18. Then, multiply both sides by -1, remembering to reverse the inequality direction: r ≥ 18.
The solution to the inequality is r ≥ 18, meaning that the possible change in the number of feet of the whale's elevation must be equal to or greater than 18. This implies that the whale's jump cannot be less than 18 feet above the surface.
Therefore, the whale's elevation can change by any value equal to or greater than 18 feet, allowing it to jump to a height of nearly 17 feet above the surface.
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a) The inequality can be written as 35 - r ≤ 17. b) The solution to the inequality is r ≥ 18, which means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.
a.
Since the whale swims upward and jumps to a height of nearly 17 feet above the surface, we can represent the change in elevation as r.
The inequality can be written as:
35 - r ≤ 17
Here, 35 represents the starting depth below the surface, and 17 represents the height above the surface that the whale reaches.
By subtracting r from the starting depth, we account for the possible decrease in elevation as the whale swims upward.
b. To solve the inequality, we can isolate r on one side of the equation:
35 - r ≤ 17
Adding r to both sides of the inequality:
35 - r + r ≤ 17 + r
35 ≤ 17 + r
Subtracting 17 from both sides:
35 - 17 ≤ 17 + r - 17
Simplifying further:
18 ≤ r
Therefore, the solution to the inequality is r ≥ 18.
In terms of the situation, the inequality r ≥ 18 means that the change in the number of feet, r, of the whale's elevation must be greater than or equal to 18.
This indicates that as the whale swims upward and jumps to a height of nearly 17 feet above the surface, the whale's elevation can increase by at least 18 feet from its starting depth of 35 feet below the surface.
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-8|4k-10|=-48 okay y'all can you help me out with this?
Answer:
k = 4
Step-by-step explanation:
-8|4k-10|=-48
|4k-10|=-48/-8
|4k-10|= 6
4k = 6+10
4k = 16
k = 4
You invest $15,000 to start a hot dog stand at the local sports complex. It costs you $.65 to produce each hot dog. How many hot dogs must you sell before your average cost per hot dog is $1.15?
The answer should be 30,000. I just do not understand how to get to it.
Thank you in advance!
Answer:
Below is the procedure to find the answer: 30,000 hot dogs.
Explanation:
The average cost is found dividing the total cost by the number of hot dogs:
[tex]Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs[/tex]
The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:
[tex]Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog[/tex]
Substitute the values:[tex]Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15[/tex]
Where x is the number of hot dogs.
Solve for x from the equation:[tex](15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000[/tex]
Which shows you how you can find that the answer is 30,000 hot dogs.
Final answer:
To find the number of hot dogs needed to achieve an average cost of $1.15, including a fixed investment of $15,000 and a variable cost of $.65 per hot dog, the calculation reveals that 30,000 hot dogs must be sold to reach this target.
Explanation:
The question asks how many hot dogs must be sold before the average cost per hot dog is $1.15, given an initial investment of $15,000 and a production cost of $.65 per hot dog. To find the break-even point in terms of units sold to reach the target average cost, we use the formula to calculate average cost: Average Cost = (Fixed Costs + Variable Costs) / Quantity. Here, the fixed cost is the initial investment of $15,000, and the variable cost is $.65 per hot dog.
To find the number of hot dogs needed to achieve an average cost of $1.15, we set up the equation: $1.15 = ($15,000 + $.65Q) / Q. Solving for Q gives us 30,000 hot dogs as the break-even point where the average cost per hot dog would be $1.15.
This calculation allows the business owner to understand how many units need to be sold to overcome the initial investment and start making a profit on each hot dog sold at or above $1.15.
Please help!! question is in the picture
Answer:
C
Step-by-step explanation:
Total number of rolls = 96
There are three even numbers: 2, 4 and 6.
Number 2 was rolled 13 times
Number 4 was rolled 17 times
Number 6 was rolled 20 times
Hence, even number was rolled [tex]13+17+20=50[/tex] times.
The experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.
Therefore,
[tex]P=\dfrac{50}{96}=\dfrac{25}{48}[/tex]
Which equation has the solutions x = StartFraction 5 plus-or-minus 2 StartRoot 7 EndRoot Over 3 EndFraction?
3x2 – 5x + 7 = 0
3x2 – 5x – 1 = 0
3x2 – 10x + 6 = 0
3x2 – 10x – 1 = 0
Answer:
3x^2 - 10x - 1 = 0 $OPTION D ON EDGE$
Step-by-step explanation:
Answer:
3x2 – 10x + 6 = 0
Step-by-step explanation:
Givena general quadratic equation
ax²+bx+c = 0
The general formula for finding x is;
x = -b±√b²-4ac/2a
Where a,b and c are the coefficient of x², x and x° respectively
Given the solution in question to be;
x = 5±2√7/3
The quadratic equation that has thw above general solution will be;
3x²-10x+6 = 0
From the equation, a = 3, b= -10 and c = 6
Substituting this value in the general formula to get x we have;
x = -(-10)±√(-10)²-4(3)(6)/2(3)
x = 10±√100-72/6
x = 10±√28/6
x = 10±√7×4/6
x = 10±2√7/6
Dividing through by 2 gave;
x = 2(5±2√7)/6
x = 5±2√7/3 (which gives the solution in question)
The diagonals of a rhombus are 14 and 48 cm Find the length of a side of the rhombus
What number represents an elevation of 80 feet below sea level
Answer:
-80
Step-by-step explanation:
The answer is -80 because 80 feet below sea level would be a negative number. So you just add a negative sign to 80 and voila! You get the answer. Your welcome, by the way!
Elevation 80 feet below sea level can be represented by the negative number -80 in mathematics. This is because negative numbers are used to represent depths or locations below sea level.
Explanation:In mathematics, when we talk about locations below sea level, we represent them with negative numbers. So, an elevation of 80 feet below sea level will be represented as -80. This numerical representation helps us have an accurate and easy understanding of above and below sea level elevations. Such as, 0 represents sea level, positive numbers represent elevations above sea level, and negative numbers represent depths below sea level.
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At the beginning of the year,
Shelby could run 2 miles. Now
she can run 3.5 miles. What is
the percent increase in the
distance she can run?
Answer:
175% increase
Step-by-step explanation:
(3.5 / 2) * 100 = 175%
What is the value of x?
Answer: x = 15
Step-by-step explanation: The first thing to note is that what we have here are two similar triangles. First we have triangle ABC and secondly we have triangle EDC. Line BD is a transversal that cuts line AE at point C. Hence we can deduce that angle ACB is equal in measurement to angle ECD (opposite angles). Next we also observe that the other two angles are right angles, that is, 90° in size. Therefore we can conclude that the other two angles (angle ABC and angle EDC) are also of the same measurement.
We can now establish the ratio of the similar sides.
Line AB = Line ED
Line AC = Line EC
AB/ED = AC/EC
24/40 = 2x/3x + 5
3/5 = 2x/3x + 5 {the left hand side has been reduced to it's simplest form}
Next we cross multiply and that gives us
3(3x + 5) = 5(2x)
9x + 15 = 10x
Subtract 9x from both sides of the equation
15 = 10x - 9x
15 = x
simpilfy -19+4k-15k+k-9
Answer:
-10k-28
Step-by-step explanation:
-19+4k-15k+k-9
-28-11k+k
-10k-28
Answer:
12k+ -10
im not truely sure if this is correct... but i went off my knowlage
Does anyone know this?
Use this formula to get the total angle measurement of the figure:
T=180(n-2)
Since there are 7 sides, the total measurement must be:
180(7-2)
180(5)
900 degrees
Set up an equation and solve for x:
123+121+127+128+139+125+x=900
763+x=900
x=137
So the missing angle is 137 degrees.
Hope this helped!
Y = -1/3 x + 2
Y= x + 2
What is the solution to the system of equations?
A. (0, 2)
B. (2, 0)
C. (-1, 3)
D. (0, -2)
Answer:
X = 0
Y = 2
so Option A (0,2) IS CORRECT
Step-by-step explanation:
Y = -1/3 x + 2 equation 1
Y = x+ 2 equation 2
from equation 2 we have
y = x+ 2 Put in equation 1
x + 2 = -1/3 x + 2
x +1/3x = 2 -2
0.67 x = 0
X = 0
so put x =0 in equation 2 then we have
y = x +2
Y = 0+ 2
Y = 2
I NEED HELP ASAP The base of a triangle is 21 in. The height is 14 in. What is the area of the triangle?
A) 35 in2
B) 98 in2
C) 147 in2
D) 294 in2
Answer:
C 147in2
Step-by-step explanation:
Formula: [tex]\frac{bh}{2}[/tex]
b=base
h=height
21*14=294
294/2=147
How to do 2(x+1.25)=3.5 by dividing both sides first.
Answer:
1/2
Step-by-step explanation:
2(x+1.25)=3.5
2x+2.5=3.5
2x=3.5-2.5
2x=1
x=1/2
Show how to add 24+9 by making 10s
If you add 10 and then subtract 1, you get the same result as if you just added 9.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to add 24+9 by making 10s.
As per the given question, the required solution would be as:
24 + 10 - 1 = 33
Therefore, if you add 10 and then subtract 1, you get the same result as if you just added 9.
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Final answer:
To add 24 and 9 using tens, break 9 into 6 and 3, add 6 to 24 to get 30, and then add the remaining 3 to reach 33.
Explanation:
To add 24 and 9 by making 10s, you can first break down the number 9 into 6 and 3.
Add 6 to 24 to make a round number, which is 30.
Now you have made a '10' because 30 is a multiple of 10.
Next, add the remaining 3 to get 33.
So, 24 + 9 = 33.
ƒ(x) = 18x + 8, find x when ƒ(x) = 14.
Answer:
Step-by-step explanation:
18x+8=14
18x=6
x=1/3
When ƒ(x) is equal to 14, the value of x is 1/3.
To find the value of x when f(x) is equal to 14, we can set up the equation:
f(x) = 18x + 8
We know that f(x) is equal to 14, so we substitute that into the equation:
14 = 18x + 8
We isolate the variable x by subtracting 8 from both sides of the equation:
14 - 8 = 18x
6 = 18x
To solve for x, we divide both sides of the equation by 18:
6/18 = x
1/3 = x
Therefore, when f(x) is equal to 14, the value of x is 1/3.
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A blue rope is three times as long as the red rope. A green rope is five times as long as the blue rope. If the total length is 508.25 meters, what is the length of the blue rope?
Answer:
The length of the blue rope is 80.25 meters.
Step-by-step explanation:
B = Blue Rope
G = Green Rope
R = Red Rope
B=3R (Blue is 3 x as long as Red)
G=5B (Green is 5 x as long as Blue)
B+G+R = 508.25 (The three ropes together are 508.25 meters)
Since B=3R, I will rewrite the equation above
3R + G + R = 508.25
Now, I will write G in terms of R:
G=5B
B=3R, so 5B = 15R (multiply both sides by 5) which means that G=5B=15R, so G=15R.
Rewrite the equation again in terms of R:
3R + 15R + R = 508.25
19R = 508.25 (combine like terms)
R = 26.75 (divide both sides by 19 to solve for R)
Now, use the value 26.75 (R, which is the length of the red rope) to solve for B (the length of the blue rope):
B=3R
B=3(26.75)
B=80.25 meters
Write two fractions that are equivalent to 5
Answer:
5/1, 25/5
Step-by-step explanation:
Need help ASAP please
Which choice is equivalent to the expression below ?
The answer is B, 7i.
sqrt(-49)
Pull out an i.
i*sqrt(49)
Take the square root to get 7i.
⭐ Answered by Hyperrspace (Ace) ⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Find the circumference of this figure. Show your calculations.
Answer:
Circumference of circle= 37.68 units
Circumference of sector= 6.28 units
Step-by-step explanation:
The given figure is a circle with given radius OB= 6 units.
The circumference of a circle is the total length of its boundary.
For the complete circle its circumference can be calculated by;
Circumference= [tex]2\pi r[/tex]
[tex]=2*3.14*6\\=37.68[/tex] units
For the circumference of the Sector with 60° in the figure, the circumference can be calculate by:
[tex]=\frac{60}{360}* 2*\pi*6\\\\=\frac{1}{6}*12*3.14\\\\ =2*3.14\\\\=6.28[/tex] units
So, the circumference of the full circle is 37.68 units and the circumference of the sector is 6.28 units.
how do you solve 17- ||-16|-9|
Evaluate the inside absolute values first:
17-|16*9|
17-|144|
17-144
-127
Hope this helped!
You have 8 gallons of lemonade to sell. You use cone-shaped cups that are 9 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
You will need 119 cups to sell all of the lemonade.
Step-by-step explanation:
Given,
Diameter of cups = 9 cm
Radius of cup = [tex]\frac{Diameter}{2}=\frac{9}{2}=4.5\ cm[/tex]
Height of cups = 12 cm
We will find volume of cup.
[tex]Volume = \frac{1}{3}\pi r^2h\\[/tex]
Putting all the values
[tex]Volume=\frac{1}{3}(3.14)(4.5)^2(12)\\\\Volume=\frac{1}{3}(3.14)(20.25)(12)\\\\Volume= \frac{763.02}{3}\\\\Volume= 254.34\ cm^3[/tex]
Therefore;
Each cup can hold 254.34 cubed centimeter of lemonade.
Number of gallons = 8
1 gallon = 3785 cm³
8 gallons = 3785*8 = 30280 cm³
Let,
x = Number of cups
Volume of lemonade in one cup * Number of cups = Volume of 8 gallons
254.34x=30280
Dividing both sides by 254.34
[tex]\frac{254.34x}{254.34}=\frac{30280}{254.34}\\x=119.05[/tex]
Rounding off to nearest whole number
x = 119
You will need 119 cups to sell all of the lemonade.
Keywords: volume, division
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Find the minimum value of the
parabola
y = x2 − 4x − 5 .
Answer:
-2x-5
Step-by-step explanation:
Boyle’s law states that the volume of gas varies inversely with applied pressure. Suppose the pressure on 60 cubic meters of gas is raised from 1 atomsphere to 3 atmospheres. What new volume does the gas occupy?
Answer: 20m³
Step-by-step explanation:
From the statement
V <> 1/p --------------------- 1
V = k/p --------------------- 2
K. = VP ---------------------- 3
V = 60 , p = 1
To find k which is a constant, we put those values in equation 3
K = 60 x 1
= 60.
Now from the second statement
V = k/p where p is 3
Therefore,
V = 60/3
= 20m³
Select and place the symbol that will make the statement true.
6 ? 8
Answer:
6<8
Step-by-step explanation:
This is actually simple since the 6 is less than 8 the thing will face away from the 6 and towards the 8.
A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours
Answer:
d
Step-by-step explanation:
Answer:
24 hours
24 hours is the solution to 300=10(2)^t/15
Of the 40 students in Ms. Carr's class, 87.5% live less than 10 miles from school. How many of the students in Ms. Carr's class live less than 10 miles from school.
Answer:
35
Step-by-step explanation:
Total number of students in class is 40
87.5% of the class = 87.5/100 *40 =35
The students in Ms. Carr's class that live less than 10 miles from school are 35 students.
To find out how many students in Ms. Carr's class live less than 10 miles from school, we can use the percentage provided in the question.
1. Identify the total number of students in the class:
Ms. Carr has a total of 40 students in her class.
2. Determine the percentage of students living less than 10 miles from school:
We know that 87.5% of these students live less than 10 miles from school.
3. Convert the percentage to a decimal for calculation:
To convert 87.5% to a decimal, we divide by 100:
[tex]\[ 87.5\% = \frac{87.5}{100} = 0.875 \][/tex]
4. Calculate the number of students:
Now, multiply the total number of students by the decimal:
Number of students = 0.875 × 40 = 35
5. Conclusion:
Therefore, 35 students in Ms. Carr's class live less than 10 miles from school.
The width of a rectangular painting is 3in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
Question:
A width of a rectangular painting is 3 in. More than twice the height. A frame that is 2.5 in. Wide goes around the painting
a. write an expression for the combined area of the painting and frame.
b. use the expression to find the combined area when the height of the painting is 12 in.
c. use the expression to find the combined area when the height of the the painting is 15 in.
Answer:
a) (h + 5)(2h + 8) is the expression for the combined area of the painting and frame
b) The combined area when h = 12 is 544 square inches
c) The combined area when h = 15 is 760 square inches
Solution:
Given that,
A frame that is 2.5 inches wide goes around the painting
The frame will go around all 4 sides of the painting.
That means that the length of each side of the painting will increase by 2.5 inches
Therefore,
The height of painting and frame is:
h = h + 2.5 + 2.5
h = h + 5
(2.5 inches on the top and the bottom)
Also given that,
Width of a rectangular painting is 3 inches more than twice the height
w = 3 + 2h
Now the width of painting and frame is:
w = 3 + 2h + 2.5 + 2.5
(Again, 2.5 inches on the top and the bottom)
w = 2h + 8
Thus the combined area of the painting and frame is:
[tex]Combined\ area = (h+5)(2h+8)[/tex]
B) Substitute h = 12 inches
[tex]Combined\ area = (12+5)(2(12)+8)\\\\Combined\ area = 17 \times (24+8) = 17 \times 32\\\\Combined\ area = 544[/tex]
Thus the combined area when h = 12 is 544 square inches
C) Substitute h = 15 inches
[tex]Combined\ area = (15+5)(2(15)+8)\\\\Combined\ area = 20 \times (30+8) = 20 \times 38\\\\Combined\ area = 760[/tex]
Thus combined area when h = 15 is 760 square inches
calculus 1 limits and derivatives chapter help. delta and epsilon proof
Answer:
[tex]\delta=\frac{\epsilon}{3}[/tex]
The proof is in the explanation.
Step-by-step explanation:
Compare [tex]\lim_{x\rightarrow 7}(3x-2)=19[/tex] to [tex]\lim_{x\rightarrow a}f(x)=L[/tex].
We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-a|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].
We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|3x-2-19|<\epsilon[/tex].
[tex]|3x-2-19|<\epsilon[/tex]
Simplify:
[tex]|3x-21|<\epsilon[/tex]
Factor on left side inside the | |:
[tex]|3(x-7)|<\epsilon[/tex]
|ab|=|a||b|:
[tex]|3||x-7|<\epsilon[/tex]
|3|=3:
[tex]3|x-7|<\epsilon[/tex]
Divide both sides by 3:
[tex]|x-7|<\frac{\epsilon}{3}[/tex]
So we will need to choose [tex]\delta=\frac{\epsilon}{3}[/tex].
We want to prove there exists a [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].
Proof:
Let [tex]\epsilon>0[/tex]. We will choose [tex]\delta=\frac{\epsilon}{3}[/tex] such that [tex]0<|x-7|<\delta[/tex] will give us [tex]|f(x)-L|<\epsilon[/tex].
[tex]|f(x)-L|=|(3x-2)-19|[/tex]
[tex]=|3x-21|[/tex]
[tex]=|3||x-7|[/tex]
[tex] =3|x-7|<3\delta=3\frac{\epsilon}{3}=\epsilon[/tex].
Therefore, we have for all [tex]\epsilon>0[/tex], [tex]\delta=\frac{\epsilon}{3}[/tex] is the number that satisfies the definition.
the amount in a savings account increased from $200 to $216. what was the percent increase?
Answer:
7.41%
Step-by-step explanation:
16/216 =
16 ÷ 216 =
0.074074074074074 =
0.074074074074074 × 100/100 =
0.074074074074074 × 100% =
(0.074074074074074 × 100)% ≈
7.407407407407% ≈
7.41%;