x3 − 6x2 − 7x + 60 = 0
Ms. Stapleton had 2,600 hens, ducks, and goats on her farm. 35% of them were hens, and 25% of them were goats. How many ducks did she have on her farm ?
Max ran 50 meters in 10 seconds. molly ran 30 meters in 5 seconds. who ran faster
To find who ran faster, we have to find the speed of Max and Molly
The formula for speed is given as Distance/Time
Max's speed
Distance Max ran = 50 meters
Time = 30 seconds
Speed = 50 m/30s
= 1.67 meters/second
Molly's speed
Distance Molly ran = 30 meters
Time = 5 seconds
Speed = 30m/5s
= 6 meters/second
Therefore, Max ran faster than Molly with a speed of 1.67 meters/second.
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The stadium incurs a number of costs to accommodate fans. If the stadium pays $14,000 for labor, $45,000 for leasing parking space, and $57,000 to provide busing to and from the parking areas, what are the percentage costs for labor, leasing, and busing as a percentage of total costs? (Round to the nearest percent.)
Answer:
Percentage of amount paid for labor, parking space and busing are 12%, 39% and 49% respectively.
Step-by-step explanation:
The stadium pays the amount for labor = $14000
Amount paid for leasing a parking space = $45000
and to provide busing to and from the parking space = $57000
Total amount paid = $14000 + $45000 + $57000
= $116000
Percentage of amount paid for labor = [tex]\frac{\text{Amount paid for labor}}{\text{Total amount paid}}\times 100[/tex]
= [tex]\frac{14000}{116000}\times 100[/tex]
=12.06
≈ 12%
Percentage of amount paid for parking space
= [tex]\frac{\text{Amount paid for parking space}}{\text{Total amount paid}}\times 100[/tex]
= [tex]\frac{45000}{116000}\times 100[/tex]
= 38.79%
≈ 39%
Percentage of amount paid for busing = [tex]\frac{\text{Amount paid for busing}}{\text{Total amount paid}}\times 100[/tex]
= [tex]\frac{57000}{116000}\times 100[/tex]
= 49.14%
≈ 49%
Select the correct answer from each drop-down menu.
ABCD is a parallelogram.
M
M
M
Answer:
m∠x = 63°
m∠y =45°
m∠z = 72°
I hope this helps! :)
Answer:
Step-by-step explanation:
It is given that ABCD is a parallelogram, thus by using the properties of parallelogram, we have
∠A=∠C (Opposite angles of parallelogram are equal)
⇒∠x=63°
Thus, the measure of angle A that is x is 63°.
Now, ∠ABC+∠BCD=180°(Corresponding angles of parallelogram)
⇒∠ABD+∠DBC+63=180
⇒∠DBC=180-135
⇒∠DBC=45°
Thus, y=∠DBC=45° (Alternate angles)
and z=∠DBA=72° (Alternate angles)
Hence, the measure of angle x, y and z are 63°, 45° and 72° respectively.
Four hundred grocery store shoppers were surveyed to determine their favorite fruit. How many shoppers prefer bananas? 32%bananas
Answer:
128 Shoppers prefer bananas.
Step-by-step explanation:
In the question it is given that 400 shoppers were surveyed to determine their favorite fruit.
Among all of them 32% people like bananas.
So to find out how many people prefer bananas, we just calculate 32% of 400.
32% of 400
[tex]\frac{32}{100}[/tex] × 400
0.32 × 400 = 128
128 Shoppers prefer bananas.
what else would need to be congruent to show that ABC~XYZ by ASA? given: AB~XY, A~X,
Answer:
Two triangles are said to be congruent by ASA congrency criterion if the two angles and side between them are equal or congruent.
Refer to the image attached.
To prove: [tex]\Delta ABC \sim \Delta XYZ[/tex]
Given: [tex]AB \cong XY, \angle A \cong \angle X[/tex]
Now, we can observe that the side AB is between the angles A and B and the side XY is between the angles X and Y.
Since it is given that [tex]AB \cong XY, \angle A \cong \angle X[/tex], so the condition [tex]\angle B \cong \angle Y[/tex] should be known to shows these triangles congruent.
The perimeter of a rectangle is 42 centimeters.What is the length and width if the width is 3 centimeters more than half the length? Please include work.
The rectangle's length is 12 cm, and the width is 9 cm, calculated by setting up a system of equations using the given perimeter and the relationship between length and width.
Explanation:To find the length and width of the rectangle when given its perimeter and a relationship between its length and width, we can set up a system of equations. First, let's denote the length of the rectangle as L and the width as W. According to the question, the width is 3 centimeters more than half the length, so we have W = ½L + 3.
Since the perimeter (P) of a rectangle is given by P = 2L + 2W, and we know the perimeter is 42 centimeters, we can set up an equation: 42 = 2L + 2(½L + 3). Simplifying this, we get 42 = 2L + L + 6 or 42 = 3L + 6. Subtracting 6 from both sides gives us 36 = 3L or L = 12 centimeters for the length.
Now we can find the width using the previous relationship W = ½L + 3. Substituting the value of L, we get W = ½(12) + 3 = 6 + 3 = 9 centimeters for the width.
Therefore, the length is 12 centimeters and the width is 9 centimeters.
In microeconomics, price helps determine both quantity supplied and quantity demanded. Which other factors also help determine each? Quantity supplied is determined by production costs, and quantity demanded is determined by desire for the product. Quantity supplied is determined by production costs, and quantity demanded is determined by producer behavior. Quantity supplied is determined by consumer behavior, and quantity demanded is determined by aggregate demand. Quantity supplied is determined by producer behavior, and quantity demanded is determined by desire for the product
Answer :- First option is correct.
Microeconomics is the study of psychology of individuals at small scale.
In microeconomics, price of goods helps to determine the quantity supplied and the quantity demanded.
Quantity demanded is determined by
1. Desire of any good 2. Willingness to buy that good 3.Ability to buy a good
Other than that quantity supplied is determined by
1.Production cost [supply can increase with decrease in cost of production]
2. Productivity [supply can increase with increase in number of workers or hard working workers]
3.Technology[supply can increase with increase in the use of new technology related to production]
4.Govt regulation [it can either restrict or advertise the goods that can either increase or decrease the supply of that good respectively.]
5.Taxes and subsidies [implication of taxes can decrease the supply but by implication of subsidies supply can increase]etc.
So, Ist option is correct that the quantity supplied is determined by production cost and quantity demanded is determined by desire for the product.
The table represents a linear function. Which is the slope of the function?
From the table we have the points (-4, -2) and (-2, -10).
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{-10-(-2)}{-2-(-4)}=\dfrac{-10+2}{-2+4}=\dfrac{-8}{2}=-4[/tex]
Answer: The slope = -4.The slope of the linear function is -4. The correct option is B. -4.
How to find the slope of a function?The slope of a function is the rate of change of the dependent variable with respect to the change of the independent variables.
Therefore, the slope is change in the y variable with respect to the change in the x variable.
Let's find the slope of the linear function as follows:
slope = y₂ - y₁ / x₂ - x₁
Therefore,
slope = m = -10 + 2 / -2 + 4
slope = - 8 / 2'
Therefore,
slope = -4
The correct option is B. -4 .
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What is the area of the triangle in the coordinate plane? 26 units² 33 units² 36 units² 66 units²
i am a polygon that connects with the bases of a polyhedron
the perimeter of a rectangle is p units. iF ITS LENGTH AND WIDTH ARE TRIPLED WHAT IS THE PERIMETER OF THE NEW RECTANGLE
Anita divides 1438 by a multiple of 10. Her answer has a 3 in the tenths column. what number did she divide by?
Answer:
40
Step-by-step explanation:
Given that Anita divides 1438 by a multiple of 10
i.e. she might have divided by 10 or 20 or 30 .....
The tenth column is 3
So quotient value would be
30+d for some d in the unit column
It may be 31 or 32.....
Say it is 31, then 1438/31 =46.38 and
1438/39 = 36.87
i.e she must have divided by 40 only
Verify:
1438/40 =35 as quotient and 38 as remainder.
So she divided by 40
A polar bear swims 390 meters at a constant rate in 150 seconds. What is the speed of the polar bear?
The speed of the polar bear is found by dividing the distance swam (390 meters) by the time it took (150 seconds). This results in a speed of 2.6 meters per second.
Explanation:The subject of your question is related to the calculation of speed, which falls under Physics. The polar bear swims 390 meters in 150 seconds. To find the speed, we apply the basic formula which is Speed = Distance/Time. Here, the distance is 390 meters, and the time is 150 seconds.
So if we divide 390 by 150, we get 2.6 meters per second. This means the speed of the polar bear is 2.6 m/s.
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20 PTS! Need help! Please explain! The amount of money a worker makes varies directly with the hourly rate of pay. Worker A earns $168 for an 8 hour period. Worker B earns the same hourly rate as Worker A, but works for only 6 hours. What does Worker B earn?
A) $1008
B) $126
C) $1344
D) $160
On blueprint of a house, 48 millimeters represents 9 meters. The actual length of the living room is 6 meters. What is its length on the blueprint?
The local parts shop buys a machine that costs $500000. Its value depreciates exponentially each year by 10%. What is the machines value after 5 years? Round your answer to the nearest integer.
In triangle JKL and triangle PQR line JK = PQR line KL equals QR angle K equal angle Q then JKL must be congruent triangle PQR
Answer: True
Step-by-step explanation:
I don’t have one I know the answer because I am currently taking the quiz right now.
Find the missing dimension of each triangle described Height: 7 in., area: 21 in2
To find the missing dimension of a triangle given the height and area, we can use the formula for the area of a triangle: Area = 1/2 * base * height. We're given the height as 7 inches and the area as 21 square inches. Plugging these values into the formula, we can solve for the base using algebraic manipulation.
To find the missing dimension of a triangle given the height and area, we can use the formula for the area of a triangle: Area = 1/2 * base * height. We're given the height as 7 inches and the area as 21 square inches. Plugging these values into the formula, we get: 21 = 1/2 * base * 7. Solving for the base, we can multiply both sides of the equation by 2 and divide by 7 to get the base: base = (21 * 2) / 7 = 6 inches.
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Final answer:
By using the area formula for a triangle, A = (b × h) / 2, with the provided height of 7 inches and area of 21 square inches, the base is calculated to be 6 inches.
Explanation:
To find the missing dimension of a triangle, given the height and area, we can use the formula for the area of a triangle A = (b × h) / 2, where A is the area, b is the base, and h is the height. Given that the height h is 7 inches and the area A is 21 square inches, we can rearrange the formula to solve for the base b:
Area = (base × height) / 2 → 21 = (b × 7) / 2 → b = (21 × 2) / 7 → b = 6
The missing dimension, the base of the triangle, is 6 inches, provided height of 7 inches and area of 21 square inches.
Martin says the area of a tile with a length of 1 foot by a width of 1 foot has an area of 1 square foot. And, to find 1/2 of this area, he would need to find 1/2 of the width and 1/2 of the length, and then multiply those two values. Unfortunately, his method is incorrect. Show at least one equation to show why this method would not work, and briefly state a method that will find 1/2 of 1 square foot.
Answer:
His method is incorrect. By finding 1/2 the width and 1/2 the length, if we multiply them , we would get 1/4 of the original area.
Area = 0.5*l*0.5*w = 0.25*l*w = l*w/4
Let us establish
length = l
width = w
Original Area = l*w
Half the area = (a*l)*(b*w) = 0.5*(l*w)
This means that
a*b = 0.5
if b is equal to a, then
a = √0.5 = √2/2 = 0.707
Then, if a factor of a, where to be introduced in the lenght and width of the tile, we would obtain half the area.
Please help with 34 ASAP!!
Prove that the square of an odd number is of the form 8k+1 g
Show that n is odd →∃m∈ℤ,n2=8m+1
Let k be an integer so that n=2k+1. Then n2=(2k+1)2=4k2+4k+1=2(2k2+2k)+1.
But this isn't equal to 8m+1, so can I change that into 4(2m)+1?
Solve the following equation. x + 6 = x + x 2 6 14 72
The solution to the given equation is 6. Therefore, the correct answer is option B.
The given equation is x+6=x+x.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, x+6=2x
Transpose x to other side of the equation, we get
2x-x=6
x=6
Therefore, the correct answer is option B.
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Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.
Answer:
its B
Step-by-step explanation:
what are the mean,median ,mode and range of the data set given the altitude of lakes in feet -11, -28, - 17, -25, -28, -39, -6, and -46
The mean is the sum of data given to the total sample size.. The mean, median, mode, and range are -25, -28.-28, and 40 respectively
How to calculate the mean, median, mode and rangeThe mean is the sum of data given to the total sample size.
Mean = Sum of data/sample size
Mean = -11-28-17-25-28-39-6-46/8
Mean = -200/8
Mean = -25
Calculate the median
Median is the middle number after rearrangement
-46, -39, -28, -28, -25, -17, -11, -6
From the arrangement, the median of the data is -28
Calculate the mode
The mode is the value with the highest frequency. From the data given, the mode is -28
Range:
Range = highest value - lowest value
Range = -6 - (-46)
Range = 40
Hence the mean, median, mode and range are -25, -28.-28 and 40 respectively
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If Sally walked 1⁄2 kilometer in 1⁄4 hour, how fast, in kilometers per hour, was she walking?
Answer:
Sally walks at a speed of 2 kilometers per hour.
Step-by-step explanation:
Given data
Walked distance (d): 1/2 kilometerElapsed time (t): 1/4 hourWe can find the speed (v) of Sally using the following expression
v = d/t = (1/2 km) / (1/4 h) = 2 km/h
Sally walks at a speed of 2 kilometers per hour.
You have $3,750 to deposit. If you deposit the money in a savings account at your local bank, you will earn 1.75% annual interest and will be able to make ATM withdrawals at your bank’s ATMs. If you deposit the money in an online savings account, you will earn 3.25% interest, but you will be charged $4 every time you make an ATM withdrawal. Assuming that your ATM withdrawals do not reduce the amount of interest you earn, roughly how often must you make an ATM withdrawal for the local savings account to be a better deal than the online savings account?
To determine how often ATM withdrawals must be made for the local savings account to be a better deal than the online savings account, we compare the interest earned and ATM fees. By solving the inequality, it is found that more than $14.06 ATM withdrawals must be made in a year.
Explanation:To determine how often you must make ATM withdrawals for the local savings account to be a better deal than the online savings account, we need to compare the interest earned from each account and the fees associated with ATM withdrawals. Let's assume the time period is one year.
For the local savings account, you earn interest of 1.75% annually. So, if you deposit $3,750, you will earn ($3,750 * 1.75%) = $65.63 in interest.
For the online savings account, you earn interest of 3.25% annually. However, each ATM withdrawal incurs a fee of $4. Let's assume you make 'x' withdrawals in a year. So, the total interest earned would be ($3,750 * 3.25%) - ($4 * x).
We need to find the point where the interest earned from the online savings account is less than the interest earned from the local savings account. This can be calculated as:
($3,750 * 3.25%) - ($4 * x) < $65.63
Simplifying this inequality, we get:
0.0325 * $3,750 - $4 * x < $65.63
Adding $4 * x to both sides, we have:
0.0325 * $3,750 < $65.63 + $4 * x
Simplifying further, we get:
$121.87 < $65.63 + $4 * x
Subtracting $65.63 from both sides, we have:
$121.87 - $65.63 < $4 * x
Simplifying again, we get:
$56.24 < $4 * x
Dividing both sides by $4, we find:
$14.06 < x
So, you must make more than $14.06 ATM withdrawals in a year for the local savings account to be a better deal than the online savings account.
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is 20 a perfect square
Martin says the area of a tile with a length of 1 foot by a width of 1 foot has an area of 1 square foot. And, to find 1 2 12 of this area, he would need to find 1 2 12 of the width and 1 2 12 of the length, and then multiply those two values. Unfortunately, his method is incorrect. Show at least one equation to show why this method would not work, and briefly state a method that will find 1 2 12 of 1 square foot.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
If two figures are similar. then the ratio of its areas is equal to the scale factor squared
In this problem we have a tile with a length of 1 foot by a width of 1 foot
The area of the tile is equal to
[tex]A=LW[/tex]
substitute the values
[tex]A=(1)(1)=1\ ft^{2}[/tex]
Let
z-------> the scale factor
x------> the area of 1/2 tile
y------> the area of the original tile
so
[tex]z^{2} =\frac{x}{y}[/tex]
substitute
[tex]z^{2} =\frac{(1/2)}{1}[/tex]
[tex]z=\frac{\sqrt{2}}{2}[/tex] -----> scale factor
therefore
To find the area of 1/2 tile must multiply the dimensions of the tile by the scale factor
so
[tex]L=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]
[tex]W=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]
Calculate the area
[tex]A=\frac{\sqrt{2}}{2}*\frac{\sqrt{2}}{2}=\frac{1}{2}\ ft^{2}[/tex]
Martin's method is incorrect because to find the area of 1/2 tile, he multiplies the dimensions by 1/2
so
[tex]L=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]
[tex]W=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]
the area will be
[tex]A=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\ ft^{2}[/tex]