Answer:
8 Pigs.
Step-by-step explanation:
~ P = the number of pig
~ D = the number of ducks
p + d = 10
4p + 2d = 36
4(10 - d) + 2d = 36
40 - 4d + 2d = 36
40 - 2d = 36
-40 = -40
-2d = -4
-2 -2
d = 2 ducks
p + d = 10
p + 2 = 10
Therefore, 8 pigs. :)) hope this helped you :))
If 5/6 is 180, what is 1/6?
(please explain as well)
Answer: 36
Step-by-step explanation:
If 5/6 = 180
lets find what 1/6 equals
To do this lets divide 180 by 5 to find 1/6
[tex]\frac{180}{5} =36[/tex]
Therefore, 1/6 = 36
We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.
Anyways, we can check our answer by doing:
36*5 = 216 then taking 5/6 of 216, which should equal 180
[tex]216*\frac{5}{6} =180[/tex]
Therefore, we know 36 is the correct answer
If you have a savings account, contact your bank and find out the interest rate on that account. (If you don’t have your own account, contact a local bank to ask what the interest rate would be if you set up a savings account today.)
a. State the interest rate the bank quoted.
b. Write an exponential growth equation that models the yearly growth if you put $625 in the account and left it there for years.
c. What will be the value of the account in 25 years?
d. Which of the following would result in more money: $625 deposited in your bank at the current interest rate for 6 years, or deposit $625 into a money market account with a 5% rate for 1 year? Show how you determined your answer.
Deposit $625 into a money market account with a 5% rate for 1 year would result in more money.
The interest rate of the bankTo do this, we make use of 1.50% interest rate
The exponential growth equationHere, we have:
Initial, a= 625
Rate, r = 1.5%
The exponential growth equation is
A(t) = a * (1 + r)^t
So, we have:
A(t) = 625 * (1 + 1.5%)^t
Evaluate
A(t) = 625 * 1.015^t
Hence, the exponential growth equation is A(t) = 625 * 1.015^t
The value in 25 yearsHere, t = 25.
So, we have:
A(25) = 625 * 1.015^25
Evaluate
A(25) = 906.84
Hence, the value in 25 years is $906.84
The investment with more money#Investment A
a = 625
r = 1.5%
t = 5
So, we have:
A(5) = 625 * 1.015^5
Evaluate
A(5) = 673.3
#Investment B
a = 625
r = 5%
t = 1
So, we have:
A(1) = 625 * 1.5^1
Evaluate
A(1) = 937.5
By comparison, 937.5 is greater than 673.3
Hence, deposit $625 into a money market account with a 5% rate for 1 year would result in more money.
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Solve the congruence 3x=2(mod4)
Answer:
Step-by-step explanation:
jello :
3x=2(mod4)
multiply by ; 5
5×3x=5×2(mod4)
15x=10(mod4)
but : 15= -1 (mod4) and 10= 2 (mod4)
-x=2 (mod4)
now multiply by ; -1 you have : x= -2 (mod4)
-2=2(mod4)
conclusion : x=2 (mod4) means : x=4k+2 k in Z
the sum of three numbers is 78. the third number is 3 times the first. the first number is 7 more than the second. what are the numbers?
Answer:
17
Step-by-step explanation:
x+3x+x-7=78
5x-7=78
5x=78+7
5x=85
x=85/5
x=17
Answer:
The three numbers are 17, 10 and 51.
Step-by-step explanation:
Let the first, second, and third numbers be [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex] respectively.
• From the question, we know:
sum of the numbers is 78.
∴ [tex]x + y + z = 78[/tex] ----------(1st equation)
Let's express both [tex]x[/tex] and [tex]z[/tex] in terms of [tex]\bf y[/tex] :
• We know that:
the third number is 3 times the first.
∴ [tex]z = 3x[/tex]
⇒ [tex]x = \frac{z}{3}[/tex] ----------(2nd equation)
• We also know that:
the first number is 7 more than the second.
∴ [tex]\boxed{x = 7 + y}[/tex]
Substituting [tex]x = \frac{z}{3}[/tex] (from 2nd equation)
⇒ [tex]\frac{z}{3} = 7 + y[/tex]
⇒ [tex]\boxed{z = 21 + 3y}[/tex]
• We can now substitute [tex]x = 7 + y[/tex] and [tex]z = 21 + 3y[/tex] into the first equation:
[tex]x + y + z = 78[/tex]
⇒ [tex](7 + y) + y + (21 + 3y) = 78[/tex]
⇒ [tex]5y + 28 = 78[/tex]
⇒ [tex]5y = 50[/tex]
⇒ [tex]y = \bf 10[/tex]
∴ [tex]x = 7 + 10\\[/tex]
⇒ [tex]x = \bf 17[/tex]
[tex]z = 21 + 3(10)[/tex]
⇒ [tex]z = \bf 51[/tex]
∴ The three numbers are 17, 10 and 51.
In AABC, if AB = 14 and BC = 9, AC may be equal to
A. 13
B. 23
C. 25
D. 5
Answer:
A
Step-by-step explanation:
By the triangle inequality theorem, 5<AC<23.
So, the answer is A.
The volume of a certain right circular cone is 30 cubic inches. What is the volume, in cubic inches, of a second right circular cone with half the radius and twice the height of the first cone
Answer:
V = 15 in.³
Step-by-step explanation:
The original cylinder has radius r and height h.
V = πr²h
Its volume is 30 in.³, so
πr²h = 30 in.³
The new cylinder has radius (1/2)r and height 2h.
Its volume is
V = π(r/2)²(2h)
V = πr² × 2h/4
V = πr²h/2
πr²h is the volume of the original cylinder, and it is 30 in.³.
V = 30 in.³/2
V = 15 in.³
Circadian rhythms are biological processes that oscillate with a period of approximately 24 hours. That is, a circadian rhythm is an internal daily biological clock. Blood pressure appears to follow such a rhythm. For a certain individual the average resting blood pressure varies from a maximum of 100 mmHg at 2:00 P.M. to a minimum of 80 mmHg at 2:00 A.M.
Find a sine function of the form f(t) = a sin(ω(t − c)) + b
that models the blood pressure at time t, measured in hours from midnight.
The equation becomes of the pressure is P = 90 + 10 sin(π/36(t +4 ))
By observation the sine function should be of form P= 90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.
At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg
Substituting it in the equation we get,
100 = 90 + 10 sin(ω(t − c))
10 = 10 sin(ω(14 − c))
1 = sin(ω(14 − c))
ω(14 − c) = π/2 -1)
At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg
80 = 90 + 10 sin(ω(t − c))
-10 = 10 sin(ω(2 − c))
3π/2 = ω(2 − c) -2)
dividing 2) with 1) we get
3 = (14 − c) /(2 − c)
6 - 3c = 14 - c
2c = -8
c = - 4
Substituting the value of c in 1) we get,
ω(14 − (-4)) = π/2
ω18 = π/2
ω = π/36
Thus the equation becomes P = 90 + 10 sin(π/36(t +4 ))
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Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded.
The measure of central angle RST is radians.
What is the area of the shaded sector?
4Pi units squared
8Pi units squared
16Pi units squared
20Pi units squared
The area of the sector in radians is calculated as: B. 8π units squared.
What is the Area of a Shaded Sector?The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:
Area of sector = (1/2) × r²θ; where we have:
θ = the angle subtended at the center/central angle measure in radians
r = the radius of the circle
Given the following:
The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.
Central angle measure in radians (θ) = π
Radius (r) = 4 units
Plug in the values into the area of sector formula
Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)
Area of sector = (1/2) × (16)(π)
Area of sector = (1 × 16 × π)(2)
Area of sector = (16π)(2)
Area of sector = 8π units squared
In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.
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a triangle has two sides of length 2 and 5 and that the angle between these two sides is 60 degrees, what is the length of the third side of the triangle
The length of the third side of the triangle is 4. 33
How to determine the side
We have the length of the two sides to be;
2 and 5
If the angle between them is 60 degrees, then the third side is the opposite side
To find the opposite side, we use the sin ratio, which is
sin 60 = opposite/hypotenuse
sin 60 = x/ 5
Cross multiply
sin 60 × 5 = x
x = 0. 8660 × 5
x = 4. 33
Thus, the length of the third side of the triangle is 4. 33
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sort the sequence according to whether they are arithmetic gemoentic or neither
98.3, 94.1, 89.9, 85.7 (Arithmetic)
1, 0, -1, 0 (Neither)
1.75, 3.5, 7, 14 (Geometric)
-1, 1, -1, 1..... (Geometric)
Determining the type of a sequenceAn arithmetic sequence has a common difference
A geometric sequence has a common ratio
Considering the given sequences one after the other:
For 98.3, 94.1, 89.9, 85.7,..........
The common difference, d = 94.1 - 98.3 = -4.2
Therefore, 98.3, 94.1, 89.9, 85.7 is an arithmetic sequence
For 1, 0, -1, 0......
The sequence does not have a common difference or a common ratio. Therefore, it is neither an arithmetic nor geometric sequence
For 1.75, 3.5, 7, 14,.....
The common ratio = 3/1.75 = 2
Therefore, it is a geometric sequnec
For -1, 1, -1, 1.....
The common ratio = 1/-1 = -1
It is a geometric sequence
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What is the slope of the line that passes through the points ( 8 , − 6 ) (8,−6) and ( 8 , − 9 ) (8,−9)? Write your answer in simplest form
As slope is undefined, then the slope of the line is parallel to the x axis.
How to determine the slope of a line
In this problem we have a line that passes through two points, the slope is determined by definition of secant line:
m = [- 9 - (- 6)]/(8 - 8)
m = - 3/0
As slope is undefined, then the slope of the line is parallel to the x axis.
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If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation? A. g(x) = 3x − 14 B. g(x) = -3x − 14 C. g(x) = 3x + 14 D. g(x) = -3x + 14If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation? A. g(x) = 3x − 14 B. g(x) = -3x − 14 C. g(x) = 3x + 14 D. g(x) = -3x + 14
The following equation represents the function g in function notation,
g(x) = 3x - 14 [Option (A)]
Definition of a Function
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.
Given equation is,
y -3x = -14
⇒ y = -14 + 3x
or y = 3x - 14
Here, y stands for or represents the function g(x) which is a function of independent variable x.
Thus, the correct function notation is as follows,
g(x) = 3x - 14
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Fill in the coefficients for the polynomial with degree 3, roots: x = 2, X =
-1, and x = 3, and with a leading coefficient of 1
The coefficients for the polynomial with degree 3, roots: x = 2, x =
-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.
It is given that the polynomial is of degree 3 and its roots are,
x = 2
x = -1
x = 3
Thus, the factors of the polynomial would be,
(x - 2), (x + 1), and (x - 3)
The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,
(x - 2)(x + 1)(x - 3)
= (x² -2x + x -2)(x - 3)
= (x² -x -2)(x - 3)
= x³ - 3x² - x² + 3x - 2x + 6
= x³ - 4x² + x + 6
= x³ + (-4)x² + x + 6
Hence, the required coefficients of the polynomial are, (-4) and 6.
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How does the volume of a cylinder with a radius of 4 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units
Answer:
The volume of the cylinder is smaller than the rectangular prism.
Step-by-step explanation:
A pyramid with a rectangular base is stacked on top of rectangular prism. The height of the composite figure is 10. The lengths of the rectangular base are 8 and 6 units. The height of the rectangular prism is 4. Which expression represents the volume, in cubic units, of the composite figure
The expression that represents the volume of the composite figure is: 1/3(8)(6)(6) + (8)(6)(4).
What is the Volume of a Composite Figure?The volume for the given composite figure = volume of the rectangular pyramid + volume of rectangular prism.
= 1/3(l)(w)(h) + (l)(w)(h)
Thus, with the given dimensions, plug in the values to get the expression represents the volume of the composite figure:
Volume = 1/3(8)(6)(6) + (8)(6)(4)
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Estimate the product 5.25 × 8.89.
Answer:
47.25
Step-by-step explanation:
8.89 is about 9.
So, we have 9(5.25)=9(5)+9(0.25)=45+2.25=47.25
Questions, are all in picture, please solve
The function represents a cosine graph with axis at y = - 1, period of 6, and amplitude of 2.5.
How to analyze sinusoidal functions
In this question we have a sinusoidal function, of which we are supposed to find the following variables based on given picture:
Equation of the axis - Horizontal that represents the mean of the bounds of the function.Period - Horizontal distance needed between two maxima or two minima.Amplitude - Mean of the difference of the bounds of the function.Type of sinusoidal function - The function represents either a sine or a cosine if and only if trigonometric function is continuous and bounded between - 1 and 1.Then, we have the following results:
Equation of the axis: y = - 1Period: 6Amplitude: 2.5The graph may be represented by a cosine with no angular phase and a sine with angular phase, based on the following trigonometric expression:To learn more on sinusoidal functions: https://brainly.com/question/12060967
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A prism with a heart-shaped base is sliced parallel to the base. What shape is formed?
The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.
We are asked what shape is formed.
From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.
Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
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Answer:
Step-by-step explanation:
Heart Shaped
HELP! 10 POINTS+Braniest
12. The average bowling score of the 5-member in Regional High School bowling team is 128. If all the members of the team get the same score except for one, who bowls a 160, what is the score of the rest of the players? (A) 32 (B) 96 (C) 120 (D) 144
Answer:
C
Step-by-step explanation:
The average is the total of the scores divided by 5.
128 x 5 Gives us the total scores of 640. I know that one bowler had a score of 160. I will subtract that from the total of 640. 640-160 = 480. Since the 4 bowlers left, all had the same score, I will divide 480 by 4 to get 120
Write the following inverse proportion: y is inversely proportional to x, when y = 5 and x = 8.
The inverse proportionality expression is y =40/x
Inverse proportionIf the variable y is inversely proportional to x, this is expressed as;
y = k/x
where
k is the constant of proportionality
If y = 5 and x = 8. then;
5 = k/8
k = 5 * 8
k = 40
Determine the inverse proportionality
Recall that y = k/x
y = 40/x
Hence the inverse proportionality expression is y =40/x
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Can someone help me with these problems having trouble and show work please !!
Answer:
(2x-5)(2x-5), 81 meters
Step-by-step explanation:
All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)
Using this equation we can plug in 7 for x:
(2(7)-5)(2(7)-5) =
(14-5)(14-5) =
9*9 = 81
Consider the three functions:
f(x) = Three-halves(4)x g(x) = Three-halves(4)–x h(x) = –Three-halves(4)x
Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply.
f(x) has a domain of all real numbers.
g(x) has a range of y < 0.
h(x) has a range of y > 0.
g(x) has a domain of all real numbers.
h(x) has a domain of x > 0.
The statements that are true about the domain and range of the functions f(x), g(x), and h(x) include:
f(x) has a domain of all real numbers.g(x) has a domain of all real numbers.What is a function?It should be noted that a function simply means a relation between a set of inputs to a set of possible outputs.
In this case, f(x) has a domain of all real numbers as well as g(x) which also has a domain of all real numbers.
In conclusion, the correct options are A and D.
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Answer:
A and D
Step-by-step explanation:
Edge 2022
The minimum point on the graph of the equation y=f(x) is (−1,−3). What is the minimum point on the graph of the equation y=f(x−5)? A. (4,−3) B. (−1,−8) C. (−1,−3) D. (−7,−3)
Answer:
(4, -3)
Step-by-step explanation:
y = f(x -5) means y = f(x) shifted 5 units to the right. So the minimum point would shift 5 units to the right as well.
Machine A produces 300 bolts less than three times the number machine B produces. If
machine A produces 4,800 bolts, then how many does machine B produce?
Step-by-step explanation:
what is the best definition of luminous
Can someone help me with these problems please!
Answer:
I have just wrote answers
The side lengths of a triangle are 9, 12, and 15. Is this a right triang
O A. Yes, because 9² + 12² > 15².
O B. No, because 9 + 12 ‡ 15.
OC. Yes, because 9² + 12² = 15².
OD. No, because 9² + 12² # 15².
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
27.2
Step-by-step explanation:
V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth
9. shyam travelled 8 km 52 m by bus, 2 km 265 m by car. how much distance did he travel in all
Shyam travel total [tex]10km 317m[/tex] distance ,when he travelled [tex]8 km 52 m[/tex] by bus and [tex]2 km 265 m[/tex] by car .
How to find the total distance travel by Shyam ?
Shyam travelled distance by bus [tex]=8 km 52 m[/tex]
Shyam travelled distance by car [tex]=2 km 265 m[/tex]
Total distance travelled by shyam is
Total distance= distance travelled by car + distance travelled by bus
Total distance
[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]
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If the hypotenuse of a right triangle is 2 [tex]\sqrt{3}[/tex] units long and one of the legs is [tex]\sqrt{3}[/tex] units long, then how long is the other leg?
[tex]\sqrt{3}[/tex]
2[tex]\sqrt{3}[/tex]
3
Answer:
3
Step-by-step explanation:
a = the other leg:
[tex]a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3[/tex]
[tex]a^{2} =9[/tex]
[tex]a=\sqrt{9}[/tex]
[tex]a=3[/tex]
Hope this helps