The objective function z=f(x, y) that represents the total cost for spaying x female cats and neutering y male cats is f(x, y) = 83x + 49y
How to determine the objective function?From the question, we have the following parameters that can be used in our computation:
Cost of spay on a female cat = 83Cost of neuter on a male cat = 49Represent the female cat with x and the male cat with y
So, we have the following equation
Total amount = 83x + 49y
Express as a function
z = 83x + 49y
Hence, the objective function is z = 83x + 49y
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What is the surface area of a rectangular prism that has a length of 4 cm, a height of 14 cm, and a width of 15 cm?
Answer:
the surface area of the rectangular prism is 572cm².
Step-by-step explanation:
The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:
2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²
So the surface area of the rectangular prism is 572 square centimeters.
Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
Evaluate when a=4 and b=9: 5ab-b
Answer:
171Step-by-step explanation:
\(\tt 5ab-b, \: when\: a=4\: and \:b=9\)
\(\tt 5(4)(9)-(9)\)
\(\tt \:5\times 4\times 9-9\)
\(\tt 180-9\)
\(\tt 171\)
Hope it helps! :)
What’s 6 and 2/3 divided by 8
Answer: 5/6
Step-by-step explanation:
Answer:
6 divided by 8 is 3/4 (.78)
2/3 divided by 8 is 1/12 (0.083)
6 2/3 divided by 8 is 5/6 (0.83)
Represent 1/3 of 1/4
Answer:
1/12
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
the word 'of' in math means to multiply so 1/3 of 1/4 means to multiply them together
1/3 x 1/4 = 1/12
which one is bigger 9/10 or 19/20
Answer:
19/20
Step-by-step explanation:
9/10=18/20
18/20≤19/20
i need the measurement of angle a
Angle B = 90°
Angle C = 67°
To find:-Angle A.
Solution:-\({\boxed{\mathcal{\red{Angle\: A \:=\: 23° \:}}}}\)✅
Step-by-step explanation:-We know that,
\(\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)
➪ ∠ A + ∠ B + ∠ C = 180°
➪ ∠ A + 90° + 67° = 180°
➪ ∠ A + 157° = 180°
➪ ∠ A = 180° - 157°
➪ ∠ A = 23°
\(\sf\red{Therefore, \:the\: value \:of \:∠\: A\: is \:23°.}\)
To verify:-∠ A + ∠ B + ∠ C = 180°
✒ 23° + 90° + 67° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
\(\boxed{Hence\:verified.}\)
Note:-
Please refer to the attached file.
\(\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆\)
Calc II Question
Find the volume of the solid obtained by rotating the region bonded bt the given curves about the specified line.
Y = e^-x
Y = 1
X = 2
About the Y = 2
Answer:
\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Step-by-step explanation:
This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution. I'll show how to do it with both:
Shell Method (Horizontal Axis)
\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)
Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)
Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))
Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)
Plugging in our integral, we get:
\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Washer Method (Parallel to x-axis)
\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)
Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))
Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))
Bounds: \([a,b]=[0,2]\)
Plugging in our integral, we get:
\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)
\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)
Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!
Melanie has $1.80 worth of nickels and dimes. She has 12 more nickels than dimes. Graphically solve a system of equations in order to determine the number of nickels, , and the number of dimes, y, that Melanie has. y Click twice to not each line Click linn to doloto it
Let's begin by listing out the information given to us:
Let nickel be represented as n, and dimes as d
Melanie has $1.80 worth of nickels and dimes:
\(n+d=1.80\)She has 12 more nickels than dimes:
\(\begin{gathered} n=12d \\ n=12(0.05)=0.6 \\ n=0.06 \end{gathered}\)The point of intersection of the graph is (0.6, 1.74). Therefore, the number of nickels is 0.6 while the number of dimes is 1.74
What are the outputs of the function below?
-6, -3, 1, 5
-6, -3, 4, 6
-8, 2, 4, 6
-8, 2, 1, 5
Answer:
\(5 { \times 54}^{2} \)
samuel is buying a bicycle with a price of $ 60 . The sales tax is 8 % of the price. The total price of the bicycle including sales tax is how much money?
Answer: 64.80
Step-by-step explanation:
The sales tax is 8% of the price, which means the tax amount is:
Tax = 8% of $60 = 0.08 * $60 = $4.80
To find the total price of the bicycle including sales tax, we need to add the tax amount to the original price:
Total price = $60 + $4.80 = $64.80
Therefore, the total price of the bicycle including sales tax is $64.80.
Select the correct answer. What is the solution to this equation? 9^x-1=2
Answer: 1/2
Step-by-step explanation:
Which equation has no solution?
3k - 20 = 12
8+15g=15+8g
12x+6=3(4x+2)
9р +7 =6р- 2+ Зр
Answer:
9р +7 =6р- 2+ Зр
Step-by-step explanation:
Answer:
9p+7=6p-2+3p your answer is
Zander bought 3 hats for $7 each and 2 shirts for $9 each. How much did Zander spend
Answer: 16
Step-by-step explanation: because you add $7 and $9 together
Answer:
39
Step-by-step explanation:
If Zander bought 3 shirts you are multiplying 7 and 3 which gives you 21 so he bought 3 hats for $21 and then he spent 9 dollars on 2 shirts so 9 times 2 which gets you $18 so then you do $21+$18 which gives you the answer which is 39
What is the size of ZACB?
Answer:
b
Step-by-step explanation:
The record low temperature in Houston for November 12th is -3 degrees. The record high temperature is 83 degrees. What is the difference between the record high temperature and the record low temperature?
Answer:
80 degrees
Step-by-step explanation:
-3 + 83 is the same as 83 -3.
How to solve adjacent angles?
Answer:
D
Step-by-step explanation:
1 + 4x and 57° are corresponding angles and are congruent , so
1 + 4x = 57 ( subtract 1 from both sides )
4x = 56 ( divide both sides by 4 )
x = 14
m.
4.96)2,9.76
Need Answer to how much does 4.96 go into 2976
Answer:600
Step-by-step explanation:2,976/4.96=600
The diameter of a circle is 8cm. Find its circumference to the nearest tenth.
Answer:
\(C = 25.1 \text{ cm}\)
Step-by-step explanation:
We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:
\(C = \pi d\)
Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).
↓ plugging in the given radius
\(C = 8\pi \text{ cm}\)
↓ rounding to the nearest tenth
\(\boxed{C = 25.1 \text{ cm}}\)
Adita has 21 flowers.
She wants to split them equally among 7 friends.
How many flowers can Adita give to each friend?
Answer:
3 flowers each
Lauren flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will
show heads, the spinner will land on green, and the cube will show an even number.
Lauren will get 2/25 because the coin only lands on heads or tail
Which of the following values is not an irrational number?
the cube root of 80, pi, 2.8×\(\sqrt{7}\) \(\sqrt{59}\)
20 points.
We can write that -
√80 → rational.π → irrational.2.8 x √7 → rational.√59 → irrational.What are irrational numbers?An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.
Given are the numbers to be verified as rational or irrational.
√80 → Given number is rational as the value is equivalent to 8.94427190999916.π → Given number is irrational.2.8 x √7 → 2.645751311064591 x 2.8 → 7.408103670980854 → Given number is rational.√59 → Given value is Irrational. The value is 7.681145747868608.Therefore, we can write that -
√80 → rational.π → irrational.2.8 x √7 → rational.√59 → irrational.To solve more questions on rational and irrational numbers, visit the link below -
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Select all the correct answers
Select the Scenarios that correctly represent the giving graph
Answer:
Option 1 and option 5.
Step-by-step explanation:
Write a function rule for
Answer:
x^2
Step-by-step explanation:
1^2=1
2^2=4
3^2=9
A copy machine makes 187 copies in 4 minutes and 15 seconds. How many copies does it make per minute?
copies per minute
The copy machine make 44 copies per minute.
What is the unitary method?The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;
We are given that Time copy machine take= 4min 15sec
Number of copies=187
Now, 1min=60sec
4min=240sec
Total time=240+15 =255sec
Therefore, 255sec=187copies
60sec= 187 x 60/255
=44
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5. Match the steps for constructing a congruent line segment to their pictures.
▼
▼
1. Step 2: Draw a second line
segment that is longer than the
first.
2. Step 4: That intersection is the
final endpoint of the copied
segment.
3. Step 1: Put the point of the
compass on one endpoint of the
segment to be copied. Change the
compass setting so that the
pencil end is just touching the
other endpoint, make a small arc
to see this.
4. Step 3: Without changing the
compass setting, put the
compass point on the new
endpoint on a new line. Make a
small arc that intersects the line.
We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:
Step 1 - Picture a
Step 2 - Picture b
Step 3 - Picture c
Step 4 - Picture c.
What is a line segment?Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.
The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.
A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.
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Answer:
Step-by-step explanation:
(e) distance from the x-axis is 2. (f) distance from the y-axis is 7
The question in letter f is:
Find the locus of points whose:
f) distance from the y axis is 7.
To do that we need to remember the cartesian plane,
The black axis is the Y axis, and the blue axis is the X axis. Do you understand??
After that, we need to find all points that has a distance of 7 units from the Y axis... I'm gonna draw in red color.
Finally, all points in the red line has the distace of 7 units from the Y axis.
Which quadratic relation has a y-intercept of 8?
O y = 0.5(x + 2)(x + 4)
O y = 0.5 (x - 2)(+ 8)
O y = 0.5(x2 -2x - 16)
O y = 0.5 (x2 -2x + 16)
Answer:
y = 0.5 (x^2 -2x + 16) has a y-intercept of 8.
Step-by-step explanation:
The x-coordinate of every y-intercept is zero. To determine which of the four quadratics given here has a y-intercept of 8, we need only substitute 0 for x in each; if the result is 8, we've found the desired quadratic.
O y = 0.5(x + 2)(x + 4) becomes y = 0.5(2)(4) = 4 (reject this answer)
O y = 0.5 (x - 2)(x + 8) becomes y = 0.5(-2)(8) = -8 (reject)
O y = 0.5(x2 -2x - 16) becomes y = 0.5(-16) = -8 (reject)
O y = 0.5 (x2 -2x + 16) becomes y = 0.5(16) = 8 This is correct; that '8' represents the y-intercept (0, 8).
Write an equation in slope intercept form given m = 2 and the point (0,-5)
Answer:
y = 2x - 5
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 )
given m = 2 and point where line crosses y- axis (0, - 5 ) , then c = - 5
y = 2x - 5 ← equation of line
Write down the 3rd term in the sequence given by: T(n) = n2 + 4 pls explain how to do It plsss
Answer:
T(3) = 13
Step-by-step explanation:
If we are trying to find the 3rd term of this specific sequence, then we simply plug in 3 as n.
T(3) = (3)² + 4
T(3) = 9 + 4
T(3) = 13
However, this isn't proper notation for an arithmetic or geometric sequence.
Answer:
13
Step-by-step explanation:
T(n) = n² + 4
Put n as 3 to find the third term.
T(3) = (3)² + 4
Solve for the powers.
T(3) = 9 + 4
Add the terms.
T(3) = 13