A farmer owns pigs, chickens, and ducks. When all her animals are together, she has 30 feathered animals, and the animals all together have a total of 120 legs and 90 eyes. (All the animals have the expected number of parts.) How many of each animal might she have?
She has 18 pigs, 13 chickens, and 17 ducks.
She has 10 pigs, 15 chickens, and 15 ducks.
She has 15 pigs, 12 chickens, and 18 ducks.
She has 12 pigs, 15 chickens, and 15 ducks.
To solve this problem, let us first assign some variables. Let us say that:
x = pigs
y = chickens
z = ducks
From the problem statement, we can formulate the following equations:
1. y + z = 30 ---> only chicken and ducks have feathers
2. 4 x + 2 y + 2 z = 120 ---> pig has 4 feet, while chicken and duck has 2 each
3. 2 x + 2 y + 2 z = 90 ---> each animal has 2 eyes only
Rewriting equation 1 in terms of y:
y = 30 – z
Plugging this in equation 2:
4 x + 2 (30 – z) + 2 z = 120
4 x + 60 – 2z + 2z = 120
4 x = 120 – 60
4 x = 60
x = 15
From the given choices, only one choice has 15 pigs. Therefore the answers are:
She has 15 pigs, 12 chickens, and 18 ducks.
what's the exact circumference of the circle
a. 7p cm
b. 5p cm
c. 10p cm
d. 4p cm
Answer:
B
Step-by-step explanation:
not sure
According to the chart, from 1996-2006, unintentional drug overdose deaths per 100,000 population rose dramatically. The numbers for each year are, roughly, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 9. What is the mean of these statistics?
Answer: 5.36
Step-by-step explanation: i got it right on my test
Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can?
The diagonals of parallelogram DEFG intersect at H. What congruence statements can you make about the parallelogram?
3 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible?
When rolling three different dice, the number of possible outcomes can be calculated by performing 6*6*6, which equals 216, as there are 6 possible results on each die.
Explanation:The question pertains to the count of distinct outcomes when rolling three differently colored dice. Each die has 6 possible outcomes (numbered 1 to 6). Since these are independent events, you multiply the number of outcomes of each event (or the number of outcomes of each die's roll) to get the total number of different outcomes for all the events combined. Hence, the total different outcomes would be 6*6*6 = 216
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Which of the following polynomials corresponds to the subtraction of the multivariate polynomials 19x^3+44x^2y+17 and y^3-11xy^2+2x^2y-13x^3
A. y^3-6x^3+33x^2y+2x^2y+17
B. 20x^3-y^3+33x^2y+2x^2y+17
C. 31x^3-6x^3+44x^2y+11x^2y+17
D. 32x^3-y^3+42x^2y+11x^2y+17
Evaluate the expression for the given value of the variable(s).
5a + 5b; a = -6, b = -5
A.
-55
B.
55
C.
5
D.
-5
In order to evaluate the given expression 5a + 5b, we need to substitute the given values of a and b into the expression. The evaluated value of the expression 5a + 5b for a = -6 and b = -5 is -55.
Explanation:In order to evaluate the given expression 5a + 5b, we need to substitute the given values of a and b into the expression. The value given for a is -6 and for b is -5.
So, the expression becomes: 5*(-6) + 5*(-5) = -30 - 25 = -55.
Therefore, the evaluated value of the expression 5a + 5b with a = -6 and b = -5 is -55.
The evaluated value of the expression 5a + 5b for a = -6 and b = -5 is -55.
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Find the critical value of t for a sample size of 23 and a 99% confidence level. choose the correct value from below:
To find the critical t-value for a sample size of 23 at a 99% confidence level, you need to use the degrees of freedom (df=22) and locate the t-value that corresponds to the 0.995 area in the t-distribution, which can be found using tables or a calculator's invT() function.
Explanation:The question pertains to finding the critical t-value for a sample size of 23 at a 99% confidence level. To determine this, you need to take into account the degrees of freedom (df), which is the sample size minus one (n-1). In this case, df = 23 - 1 = 22. Since the confidence level is 99%, there is 1% left for the two tails combined in a two-tailed test. This means that for each tail, the area is 0.5%. Therefore, you look for the t-value that corresponds to the area to the left, which is 1 - 0.005 = 0.995. Using a t-distribution table or a calculator function such as invT(), you find the critical t-value that would place an area of 0.995 to the left of it.
Remember that you might not directly find the exact degrees of freedom in some t-distribution tables, and you may need to interpolate between the provided values. The exact critical value would typically be found using statistical software or a graphing calculator that can output precise t-values for non-standard degrees of freedom and confidence levels.
A square has sides 5.3cm long. Work out the area of the square
Answer:
Area of square = 28.09 square cm.
Step-by-step explanation:
Given : A square has sides 5.3 cm long.
To find : Work out the area of the square.
Solution : We have given
Side of square = 5 .3 cm .
Area of square = side * side .
Area of square = 5.3 * 5.3 .
Area of square = 28.09 square cm.
Therefore, Area of square = 28.09 square cm.
How many unique ways are there to arrange the letters in the word APE
The number of unique ways that are there to arrange the letters in the word APE is 6 ways
Factorial experimentFrom the question, we are to determine the number of ways the word APE can be arranged.
Since there are 3 letters in the word APE, the number of ways it can be arranged is expressed as:
3! = 3 * 2 * 1
3! = 6 ways
Hence the number of unique ways that are there to arrange the letters in the word APE is 6 ways
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What is 784 in expanded form, using exponents?
What would the answer be?
Find s(2t - 4) for s(t) = 3t - 7
A. 6t - 19
B. 6t - 18
C. 5t - 11
D. 5t - 19
Answer:
A. 6t - 19
Step-by-step explanation:
Put the function argument into the function definition and evaluate:
s(2t -4) = 3(2t -4) -7 = 6t -12 -7 = 6t -19
Factor: 216+8d^3
d^3 is d to the third power
Order these decimals form greatest to least 3.6; 0.36; 36; 0.036
Find the area of the circle.
Round to the nearest hundredth.
Which equation results from isolating a radical term and squaring both sides of the equation for the equation sqrt(c-2) - sqrt(c) = 5
A) c-2=25+c
B) c-2=25-c
C) c-2 = 25+c-10sqrt(c)
D) c-2 = 25-c+10sqrt(c)
Answer:
D) c - 2 = 25 + c + 10√c
Step-by-step explanation:
The given equation is sqrt(c-2) - sqrt(c) = 5
Taking square on both sides, we get
Here we used ( a+ b)^2 = a^2 + b^2 + 2ab formula.
c - 2 = 5^2 + (√c)^2 + 2(5)√c
c - 2 = 25 + c +10√c
Hope this helps!! Have a great day!! ❤
The correct equation resulting from isolating a radical term and squaring both sides of the original equation is D) [tex]\( c-2 = 25-c+10\sqrt{c} \)[/tex].
To arrive at this result, let's start with the original equation and isolate one of the radical terms:
[tex]\[ \sqrt{c-2} - \sqrt{c} = 5 \][/tex]
Now, isolate the radical on one side:
[tex]\[ \sqrt{c-2} = 5 + \sqrt{c} \][/tex]
Next, square both sides to eliminate the radical:
[tex]\[ (\sqrt{c-2})^2 = (5 + \sqrt{c})^2 \] \[ c-2 = 25 + 2 \cdot 5 \cdot \sqrt{c} + (\sqrt{c})^2 \] \[ c-2 = 25 + 10\sqrt{c} + c \][/tex]
Now, we want to isolate the term with the radical on one side and the rest on the other side:
[tex]\[ c-2 = 25 + 10\sqrt{c} + c \][/tex]
Subtract c from both sides to get:
[tex]\[ c-2-c = 25 + 10\sqrt{c} \] \[ -2 = 25 + 10\sqrt{c} \][/tex]
Finally, add 2 to both sides to isolate the radical term:
[tex]\[ -2 + 2 = 25 + 10\sqrt{c} + 2 \] \[ 0 = 25 + 10\sqrt{c} - 2 \] \[ c-2 = 25 - c + 10\sqrt{c} \][/tex]
This matches option D, confirming that the correct equation is:
[tex]\[ c-2 = 25-c+10\sqrt{c} \][/tex]
WILL GIVE A BRAINLIEST!! PLEASE HELP
Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence.
3, 1, 1/3, 1/9, …
A.
a(n)=3x(1/3)n-1
B.
a(n)=1/3(3)n-1
C.
a(n)=3x(n-1)^3
D.
The sequence is not a geometric sequence.
Assuming that the equations define x and y implicitly as differentiable functions x=f(t),y=g(t) find the slope of the curve x=f(t), y=g(t) at the given value of t x(t+1)-4tsqrt(x)=9, 2y+4y^3/2=t^3+t , t=0
Final answer:
To find the slope of the curve at a given value of t, differentiate the implicit equations x=f(t) and y=g(t) with respect to t, then substitute the given t value into the derivatives to find the slopes.
Explanation:
Slope of the curve at the given value of t:
Given equations: x(t+1)-4tsqrt(x)=9 and 2y+4y^3/2=t^3+t, t=0Differentiate the equations x and y with respect to t to find dx/dt and dy/dtSubstitute t=0 into the derived dx/dt and dy/dt to find the slopes at the given value of tp=2L+2w solve for w helppppp
What percent of 400 is 260
Mrs. Patil bought 4 packs of pencils for her class. Then she bought 3 more packs of pencils. There are 12 pencils in a pack. How many pencils did she buy?
The number of pencils from 7 packs is 84.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Mrs. Patil bought 4 packs of pencils for her class. Then she bought 3 more packs of pencils.
Now, 4+3 =7 packs
There are 12 pencils in a pack.
Here, number of pencils =12×7
= 84 pencils
Therefore, the number of pencils from 7 packs is 84.
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Line segment SU is dilated to create S'U' using point Q as the center of dilation.
The scale factor of the dilation is:
I hope that helps!
If a point divides any line segment into two equal parts, then the point is the mid-point of that line. The ratio of the whole line segment and the distance from mid-point to any end point of the line segment is always 2:1, hence the scale factor of the dilation is 2.
To find the scale factor of the dilation, we need to find the ratio from initial point of the line segment to the distance from the point that is lie on that line segment.
Following points can be concluded from the given conditions.
It is shown in the figure that the distance from Q to S is 4 unit, and the distance from Q to S' is 8 unit.The distance from Q to U is 5 unit and the distance from Q to U' is 10 unit.U and S both are the mid-points of the line segment QU' and QS' respectively.The ratio of the whole line segment and the distance from mid-point to any end point of the line segment is always 2:1, hence the scale factor of the dilation is 2.
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Help please! The grades received by 200 students follow a normal distribution. The mean of the grades is 70%, and the standard deviation is 7%. The number of students who received a grade greater than 70% is about? and the number of students who got a grade higher than 84% is about?
Find z so that 6% of the standard normal curve lies to the left of z. remember that this means you are looking for the area (which means you need to find the 4 digit number in the area portion of table 3 that is closet to 6%).
We can solve this problem by referring to the standard normal probabilities table for z statistic.
At P = 0.06 to the left of z, this corresponds to a value of approximately z = -1.55
Answer: z = - 1.55 (P = 0.0606 ~ 0.06)
If x and y are two nonnegative numbers and the sum of twice the first ( x ) and three times the second ( y ) is 60, find x so that the product of the first and cube of the second is a maximum.
To find the value of x such that the product of the first number and the cube of the second number is a maximum, we need to solve the equations and find the critical points. From the critical points, we can determine the maximum value of the product.
Explanation:To find the value of x such that the product of the first number and the cube of the second number is a maximum, we need to use the given condition that the sum of twice the first number and three times the second number is 60. Let's solve this step-by-step.
Let the first number be x and the second number be y.According to the given condition, 2x + 3y = 60.We need to maximize the product xy^3.To maximize the product, we can use the method of substitution.From step 2, we have 2x = 60 - 3y.Substituting the value of 2x from step 5 into the product xy^3, we get (60 - 3y)y^3.To find the maximum value, we need to find the critical points, which are the points where the derivative is equal to zero or does not exist.Find the derivative of (60 - 3y)y^3, which is -9y^2 + 180y - 3y^4.Set the derivative equal to zero and solve for y.From the values of y, find the corresponding values of x using the equation 2x = 60 - 3y.Compare the values of xy^3 for different y values to find the maximum.Learn more about Maximum Product here:https://brainly.com/question/35486509
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Select all the numbers that are multiples of 9.
9
21
27
45
54
78
81
38
Answer: 9, 27, 45, 54, 81,
Hope this helps! :)
HELP PLEASE!!
graph A
graph B
graph C
graph D
Which graph is defined by f(x) = x2 + 5|x| + 6?
(each graph is in order)
X/x+2 = 4/5. Solve for x.