The spiders and ants in Aunt Mellys attic have a total of 152 legs and 22 heads. Spiders have 8 legs and ants have 6 legs. How many spiders and how many ants are in the attic?
Answers
Answer:
10 spiders and 12 ants
Step-by-step explanation:
You need to create two equations
s = # of spiders
a = # of ants
s + a = 22 heads
since each spider and ant has one head
8s + 6a = 152 legs
since every spider has 8 legs and every ant has 6
s + a = 22 can be turned into s = 22 - a
now use substitution
8(22 - a) + 6a = 152
176 - 8a + 6a = 152
176 - 2a = 152
24 = 2a
a = 12
now that you have the number of ants you can solve for the number of spiders
s + a = 22
s + 12 = 22
s = 10
Related Questions
Find each sum or difference
1. (4a - 5)+(3a + 6)
2. (6x + 9)+ (4x^2 - 7)
3. (6xy + 2y + 6x) + (4xy - x)
Answers
1. (4a - 5)+(3a + 6) = 7a + 1.
To solve, you simply combine the like terms (4a and 3a) to get 7a, and then combine the constants (-5 and 6) to get 1.
2. (6x + 9)+ (4x^2 - 7) = 4x^2 + 6x + 2.
To solve, you combine the like terms (6x and 4x^2) to get 4x^2 + 6x, and then combine the constants (9 and -7) to get 2.
3. (6xy + 2y + 6x) + (4xy - x) = 10xy + 2y + 6x - x = 10xy + 2y + 5x.
To solve, you combine the like terms (6xy and 4xy) to get 10xy, then combine the constants (2y and -x) to get 2y - x, and finally combine the like terms (6x and 5x) to get 11x. The final answer is 10xy + 2y + 5x.
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In this figure, Mangle BDA= ° and Mangle BCA= °
Answers
The missing angles in the figure are not specified. However, using the information provided, we can determine the value of another angle in the figure .
Let's look at the figure below :I n the triangle ABC, there are two angles, Mangle BCA and Mangle BAC, whose measures have not been specified. Let Mangle BAC be x. The sum of the interior angles of a triangle equals 180 degrees. Mangle BCA + Mangle ABC + Mangle BAC = 180 degrees We know Mangle ABC = 90 degrees. Mangle BCA + 90 + x = 180Mangle BCA + x = 90 degree s Mangle BDA = 90 degrees, which means it is a right angle. The sum of the interior angles of a quadrilateral equals 360 degrees. Mangle ABD + Mangle BDA + Mangle BDC + Mangle CDA = 360 degrees We know that Mangle ABD and Mangle BDA are right angles. Mangle BDC = 90 degrees. Mangle CDA = 180 - Mangle BDA = 180 - 90 = 90 degrees .Substituting the values in the equation: Mangle ABD + 90 + 90 + Mangle BDC = 360Mangle ABD + 180 = 360Mangle ABD = 180 degrees .Now we know that Mangle ABD = 180 de g re
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An employee produces 17 parts during an 8-hour shift in which he makes $109 per shift. What is the labor content (abor dollar per unit) of the product
Answers
Labor content (labor dollar per unit) is the total cost of labor required to produce one unit of a product. It can be calculated by dividing the total labor cost by the number of units produced.
In this scenario, we are given that an employee produces 17 parts during an 8-hour shift and earns $109 per shift.
To calculate the labor content, we first determine the labor cost per hour. This is done by dividing the total amount earned in the 8-hour shift by 8.
Labor cost per hour = $109 ÷ 8 = $13 per hour
Next, we calculate the number of parts produced per hour by dividing the total number of parts produced (17) by the duration of the shift (8 hours).
Parts produced per hour = 17 ÷ 8 = 2.125 parts per hour
Finally, we calculate the labor cost per part by dividing the labor cost per hour by the number of parts produced per hour.
Labor cost per part = $13 ÷ 2.125 = $6.12 per part
Therefore, the labor content (labor dollar per unit) of the product is $6.12 per part.
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At the beginning of the year, John had $40 in savings and saved an additional $13 each week thereafter. Isaac started the year with $80 and saved $9 every week. Let 'J' represent the amount of money John has saved tt weeks after the beginning of the year and let 'I' represent the amount of money Isaac has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until John and Isaac have the same amount of money saved.
Answers
Answer:
10 weeks
Step-by-step explanation:
Let’s replace ‘t’ with numbers going up starting from 0 on both sides of the equation. Repeat until you get to 10 and you see that both are equal at $170 has been saved after 10 weeks.
John’s equation: 40 (y intercept) + 13t (saved per week)
Issac’s: 80 (y intercept) + 9t (amount saved per week)
The y-intercept represents the amount of money already saved up.
Around to the nearest tenth.
Answers
Answer:
x ≈ 5.3
Step-by-step explanation:
SOH CAH TOA(tangent = opposite side/ adjacent side)
tan (24°) = x/12
=> x = tan (24°) × 12
=> x ≈ 5.3
Wayne designed the table shown below for an x-ray room. He wants to cover the shaded rectangular surfaces of the table, marked A, B and C, with a sheet of soft foam padding.
What is the total area of the 3 rectangular surfaces to be covered with foam padding?
Answers
The total surface area of surface 3 rectangular surfaces to be covered with foam padding is 36 ft²
What is an area?The area is the amount of space occupied by a two dimensional shape or object.
Area of rectangle = length * width
Area of surface A = 1 ft * 4.5 ft = 4.5 ft²
Area of surface B = 0.5 ft * 4.5 ft = 2.25 ft²
Area of surface C = 6.5 ft * 4.5 ft = 29.25 ft²
Total area = 29.25 + 2.25 + 4.5 = 36 ft²
The total surface area of surface 3 rectangular surfaces to be covered with foam padding is 36 ft²
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Element X decays radioactively with a half life of 9 minutes. If there are 170 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 26 grams?
y = a(.5)t/h
Answers
Answer:
24.4
Step-by-step explanation:
Fiona draws a circle with a diameter of 14 meters. what is the area of fiona's circle? 7 14 28 49
Answers
The required area of Fiona's circle is49π. Option D is correct.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.
The radius of Fiona's circle is half of the diameter, which is 14/2 = 7 meters.
The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Substituting the value of the radius in the formula, we get:
A = π(7)² = 49π
So, the area of Fiona's circle is 154 square meters, if we use the value of π as 3.14.
Therefore, the answer is 49.
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The bake sale sold pies for $5.99 each and cakes for $9.99 each. The total number of pies and cakes sold was 25 for $189.75. How many pies were sold? How many cakes were sold?
Answers
Answer:
15 pies sold and 10 cakes sold.
Step-by-step explanation:
Let p be the number of pies sold. So, the number of cakes sold is 25-p.
5.99p + 9.99(25-p) = 189.75
5.99p + 249.75 - 9.99p = 189.75
4p = 60
p = 15
25 - p = 10
Which sign makes the statement true?
11
20
? 61%
>
<
Submit
ASAP
Answers
11/20 =.55
61% = .61
.55<.61
Solve for x. You must write you answer in fully simplified form. -11 = -8x
Answers
inproper fraction form:
\(x=\frac{11}{8}\)
Decimal form:
\(x=1.375\)
Mixed number form:
\(x=1\frac{3}{8}\)
Hope this helps :)
Answer:
1.375 = x or 1.4 = x
If you need to round it then it would be 1.4 = x
Step-by-step explanation:
Divide both sides by -8
\(\frac{-11}{-8}\) = \(\frac{-8x}{-8}\)
You end up with 1.375 = x
4,-7 -1,5 what’s the midpoint
Answers
Answer:
(4, 5) Midpoint
Step-by-step explanation:
Need- What is a midpoint of the line segment?
Solution:
Midpoint: x,m , y,m = (\(\frac{x {a +x b } }{2}\)) ,( \(\frac{y, a + y b}{2}\))=( \(\frac{0 +8 }{2}\) ) , ( \(\frac{2 + 8 }{2}\)) = \(\frac{8}{2} , \frac{10}{2}\) Midpoint segment - (\(x_{m} , y_{m}\)) = (4,5)The pull of gravity is different on Earth than on the Moon. An object that weighs 25 pounds on Earth weighs about 4 pounds on the Moon. An astronaut, wearing all the necessary gear, weighs 500 pounds on Earth. How many pounds would the astronaut with gear weigh on the Moon?
Answers
Answer:
About 80 pounds
Step-by-step explanation:
25 / 4 = 6.25
500 / 6.25
Answer:
80 pounds
Step-by-step explanation:
indica los monomios semejantes en cada uno de las siguientes series: por favor ayudenmen aaaaaaa D':
Answers
Answer:
Do you have this in english so that I can help :)
Step-by-step explanation:
PLEASE HURRY!! HELP NEED!!
Answers
Answer:10
Step-by-step explanation:
6^2 + 8^2 = c^2
36 + 64 = c^2
Add 36 and 64
100 = c^2
Square root both side to get rid of the square on the letter c and you have to do both side because what you do to one side you must do to the other.
C=10
Can someone plsssssss check my last geometry question
Pleaseeeeeee
Answers
Answer: 24
Step-by-step explanation: Segment CP equals half of what segment JC equals, so in order to find the length of JP, you need to multiply CP by 2, then add 8.
8(2)= 16
16+8 = 24
6. Leah is reading a book that is 646 pages long. She is currently on page
340. If she wishes to finish reading the book in the next 17 days and reads
the same number of pages each day, how many pages per day should she
read in order to meet her goal?
Answers
This is because you need to find the number of pages she didn’t read yet (which you do 646-340) which is 306.
To find the number of pages she need to read in the 17 days you have to do (306 divided by 17) which is 18.
Meaning that she has to read 18 pages each day to meet her goal.
math ridle a 12 hour clock loses 1 minute every hour suppose it shows the correct time now what is the least number of hours from now when it will again show the correct time?
Answers
The least number of hours from now when the clock will again show the correct time is 720 minutes
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
The clock will show the correct time again when it lost 12 hours
As every hour it loses 1 minute, the clock have to lose 12 hours in minutes, so we get:
12 hour * (60 minutes / 1 hour) = 720 minutes
Therefore, the least number of hours from now when the clock will again show the correct time is 720 minutes.
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Andrew is home one winter day studying for an exam. It is lunchtime and he is hungry. Instead of making a sandwich from roast beef in the fridge, he drives to taco bell and spends $5 for 2 tacos, a burrito, and a dr. Pepper. He reasons that he can make $10 per hour cutting lawns so he really saves $5 by going to taco bell rather than preparing his own meal. What's wrong with andrews argument?.
Answers
Answer:
He cannot save $5 when he is buying something instead of making it himself.
Step-by-step explanation:
He makes $10 from lawn mowing and spends $5 on Taco Bell. He has $5 left.
If he made is lunch, He would have had $10 dollars.
Andrew's argument is flawed because he is not considering all of the costs and benefits associated with his decision to go to Taco Bell instead of preparing his own meal.
What is the argument?An argument is a collection of claims, the premises of which are provided in support of another statement, the conclusion.
There are a few problems with Andrew's argument.
First, he is assuming that the only cost of preparing his own meal is the price of the ingredients. However, there are also opportunity costs associated with preparing his own meal, such as the time he spends making it and the opportunity to do something else during that time (such as study for his exam).
Second, Andrew is assuming that he would have spent the same amount of money on ingredients as he did on his meal at Taco Bell. However, it is possible that the ingredients he would have used to make his own meal would have cost less than $5, in which case he would not have saved as much money as he thinks.
Finally, Andrew is assuming that he would have spent the same amount of time preparing his own meal as he did going to Taco Bell. However, it is possible that it would have taken him longer to prepare his own meal, in which case the opportunity cost of his time would have been even higher.
Overall, Andrew's argument is flawed because he does not evaluate all of the expenses and advantages of his decision to eat at Taco Bell instead of cooking his own dinner.
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What is a correlation coefficient and what does it tell you about the scatter plot/ line of best fit?
Answers
A correlation coefficient is a statistical measure that shows the degree of association between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation (as one variable increases, the other decreases), 0 indicates no correlation, and 1 indicates a perfect positive correlation (as one variable increases, the other also increases).
When plotted on a scatter plot, the correlation coefficient can help you determine the strength and direction of the relationship between the variables. If the coefficient is close to -1 or 1, the points on the scatter plot will be more tightly clustered around the line of best fit, indicating a stronger relationship between the variables. On the other hand, if the coefficient is closer to 0, the points will be more spread out, indicating a weaker relationship.
The line of best fit, also known as the regression line, is the line that best approximates the relationship between the variables based on the data points on the scatter plot. It is calculated using a mathematical formula that takes into account the values of both variables. The correlation coefficient can be used to help determine the slope and intercept of the line of best fit, which can be useful for making predictions about future data points. Overall, the correlation coefficient provides valuable information about the strength and direction of the relationship between two variables, which can help inform further analysis and decision making.
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What is the trip fuel cost for a 600 mile trip if the average cost per mile of a car is
$0.19?
A. $67.29
B. $78.50
C. $114
Answers
Answer:
C. $114
Step-by-step explanation:
Take the cost per mile times the miles traveled.
0.19 x 600 Multiply
114
Answer:
114
Step-by-step explanation:
Take the number of miles and multiply by the cost per mile
600*.19
114
What is the perimeter, in units, of ΔABC
Δ
A
B
C
with A(−1,−6)
A
(
−
1
,
−
6
)
, B(7,−6)
B
(
7
,
−
6
)
, and C(3,−3)
C
(
3
,
−
3
)
?
Answers
Answer:
To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).
Applying this formula, we can find the lengths of the sides of the triangle as follows:
AB = sqrt((7 - (-1))^2 + (-6 - (-6))^2) = sqrt(8^2 + 0^2) = sqrt(64) = 8
BC = sqrt((3 - 7)^2 + (-3 - (-6))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
AC = sqrt((-1 - 3)^2 + (-6 - (-3))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
Thus, the perimeter of triangle ABC is 8 + 5 + 5 = 18 units.
Find f[g(x)] and g[f(x)] for the given functions. 3 f(x) = -x³ +3, g(x) = 4x+7 (Simplify your answer. Do not factor.) (Simplify your answer. Do not factor.) f[g(x)] = g[f(x)] =
Answers
The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19
The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7
The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below
f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3
When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343
Then
f[g(x)] = - 64x³ - 336x² - 588x - 340
Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;
g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g
[f(x)] = -4x³ + 19
Therefore,
f[g(x)] = - 64x³ - 336x² - 588x - 340
g[f(x)] = -4x³ + 19
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"What is the image of (-4,2) after a reflection over the y
axis?
Answers
Answer:
(4,2)
Step-by-step explanation:
when reflecting over the y axis you just changed the sign of the x value. (:
Answer:(4,2) just take out the - symbol.
Step-by-step explanation:
PLS HELP I WILL GIVE 100 PTSSSSSSSSSSSSSSSSSSSS fool answers get reported good answers get brainiest
Answers
C) 36 yards 18*6=108
108ft to yards is 36
Answer:C
Step-by-step explanation:
Each jump rope is 6 feet long, so 18 jump ropes would require a total of:
18 x 6 = 108 feet of rope
Since there are 3 feet in a yard, we can convert 108 feet to yards by dividing by 3:
108 ÷ 3 = 36 yards
Therefore, the football coach should buy 36 yards of rope. The answer is (C).
using calculus, find the absolute maximum and absolute minimum of the function f(x)=5x2−10x 1 on the interval [−5,3].
Answers
For the function f(x)=5x2−10x + 1 on the interval [−5,3], absolute maximum 126, and the absolute minimum is -4. The absolute maximum and absolute minimum of a function refer to the largest and smallest values that the function takes on over a given interval, respectively.
To find the absolute maximum and absolute minimum of the function f(x) = 5x² - 10x + 1 on the interval [-5, 3], follow these steps:
Find the critical points by taking the derivative of the function and setting it equal to 0:f'(x) = 10x - 10
10x - 10 = 0
x = 1Check the endpoints of the interval and the critical point:
f(-5) = 5(-5)2² - 10(-5) + 1 = 126
f(1) = 5(1)² - 10(1) + 1 = -4
f(3) = 5(3)² - 10(3) + 1 = 20Compare the values of the function at these points to determine the absolute maximum and absolute minimum:
Absolute maximum: f(-5) = 126
Absolute minimum: f(1) = -4
So, the absolute maximum of the function f(x) = 5x^2 - 10x + 1 on the interval [-5, 3] is 126, and the absolute minimum is -4.
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Xavier earns $___ each time he walks someone's dog. He walks his neighbor's dog each day. He also earned an additional $___ for running with the dog one day.
Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money he could earn in any number of days, d. Make sure that the values you choose make sense for this situation. (1 point)
Part B: Write an algebraic expression from your written description used in Part A. Let d stand for the number of days. (3 points)
Answers
(a) The description after rewriting is " Xavier earns $50 each time he walks someone's dog. He walks his neighbor's dog each day. He also earned additional $10 for running with the dog one day ."
(b) The algebraic expression for the description is 50 + 10d .
In the question ,
a blank description is given ,
which we have to fill the values of our choice that makes sense .
So ,
(a) the description , after filling the values is
Xavier earns $50 each time he walks someone's dog. He walks his neighbor's dog each day. He also earned additional $10 for running with the dog one day .
let the number of days be "d" .
(b) the expression representing the given description is 50 + 10d .
Therefore , (a) The description after rewriting is " Xavier earns $50 each time he walks someone's dog. He walks his neighbor's dog each day. He also earned additional $10 for running with the dog one day ."
(b) The algebraic expression for the description is 50 + 10d .
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3. A CD costs £9.50 in London and
cheaper, in British money, is the CD when bought in the US?
4. An MP3 player costs €20.46 in Spain and £12.60 in the UK. Which is
the cheaper in dollars, and by how much?
in Nou Delhi is 32860 rupees.
Answers
Step-by-step explanation:
Only Q4 has clear details
therefore, solving Question 4,
1 euro = $1.17
then, €20.46 =20.46×1.17 = $23.93.
1 pound =1.28 dollars.
then, £12.60 = 12.60×1.28 =$16.128
therefore, MP3 in pound is cheaper in dollar by $7.81.
what is foci of ellipse calculator?
Answers
An ellipse's form is determined by two locations inside the ellipse known as its foci.
The lengths of the main and minor axes of an ellipse may be used to calculate its foci.
The foci of an ellipse may be calculated using a variety of online calculators.
These calculators normally ask the user to enter the main and minor ellipse axes' lengths before calculating the foci's coordinates. Depending on the calculator in question, some may additionally ask for more details like the ellipse's eccentricity or center of rotation.
Understanding an ellipse's shape and characteristics requires knowing its foci since they are what characterize an ellipse.
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What do we use to replace for an unknown number?
A) A variable
B) A number
C) An Operation
D) An equal sign
Answers
Answer:
A. A variable
Step-by-step explanation: