Answer:
$120
Step-by-step explanation:
Suppose the woman had x dollars in her purse at the beginning of the shopping.
First, she spent 4/5 of all the money she had, therefore she had 1-4/5=1/5 left
1/5 of x = (1/5)x or 0.2x
Then she lost 2/3 of what was remaining, which is 2/3 * (1/5)x= (2/15)x
What will be left will be (1-2/3) or 1/3 of that 1/5x left after shopping.
This will be 1/3*(1/5)x=(1/15)x
It is given from the problem statement that this is $10 left.
Therefore, (1/15)x= 10
Multiplying through by 15 and simplifying,
x= $150.
Now she spent 4/5 of this $150, which is
(4/5)*150=$120
To find out how much money the woman spent, we need to determine the amount she had in her purse and then calculate the difference after spending and losing some. We can solve this using a step-by-step approach.
Explanation:To calculate how much money the woman spent, we need to follow these steps:
First, she spent 4/5 of all the money she had in her purse. Let's call this amount X.After spending 4/5 of X, she lost 2/3 of what was remaining. This means she has 1/3 of what was remaining left. Let's call this amount Y.We know that Y is equal to $10. So, we can set up the equation Y = $10 and solve for X.Once we find X, we can calculate how much money the woman spent by subtracting X from the original amount she had in her purse.Let's solve this step-by-step:
Step 1: X = Amount she had in her purse
Step 2: Y = (4/5) * X * (1/3)
Step 3: Y = $10
Step 4: Calculate X - Y to find how much money she spent.
Need some help with this
Answer:
Step-by-step explanation:
The total number of outcomes the two fair number cubes are thrown is 36. This can be seen by counting the outcomes shown on the table.
a) for a sum of 4, there are only 3 possible outcomes. They are 3,2 2,2 and 1,3
Therefore, the probability of getting a sum of 4 will be
3/36 = 1/12
b) for a sum of 5, there are only 4 possible outcomes. They are 4,1 3,2 2,3 and 1,4
Therefore, the probability of getting a sum of 4 will be
4/36 = 1/9
c)for a sum of 6, there are only 5 possible outcomes. They are 5,1 4,2 3,3 2,4 and 1,5
Therefore, the probability of getting a sum of 6 will be
5/36 = 5/36
The probability that the sum of the results of the throw is 4,5 or 6 would be
1/12 + 1/9 + 5/36 = (3 + 4 + 5)/36 = 12/36 = 1/3
If a current mortgage payment of $792 per month can be reduced to $578 per month by refinancing, how many months would you need to remain in the house to recoup refinancing charges of $3,784? (Round up to the nearest month.)
Answer:
[tex]Months =\frac{3784}{214 /month}=17.682months\approx 18 months[/tex]
As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months
Step-by-step explanation:
Notation
[tex]P_f =792[/tex] current mortgage payment
[tex]P_i = 578[/tex] reduced mortgage payment
R= 3784 represent the rfinancing charges
Solution to the problem
In order to solve this question we need to find first the difference between the two mortgage payments like this:
[tex]P_f- P_i = 792-578=214[/tex]
And then since the refinancing charges is $3784 we can find the number of months that we will need to remain in the house like this:
[tex]Months =\frac{3784}{214 /month}=17.682months[/tex]
As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months
Suppose 60% of all college professors like tennis, 65% like bridge, and 50% like chess; 45% like any given pair of recreations.
(a) Should you be suspicious if told 20% like all three recreations?
(b) What is the smallest percentage who could like all three recreations?
Answer:
a) yes we should get suspicious
b) smallest percentage to like all three sports= 60
Step-by-step explanation:
Let the total professors be =100
n(tennis) = 60
n( bridge) = 65
n( chess)= 50
n( T U B) = 45, n(BU C) = 45, n(T UC)=45
n( T U B U C)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) + [tex]n(T\cap B\cap C)[/tex]
100 = 60 + 65 + 50 - 45-45-45 + [tex]n(T\cap B\cap C)[/tex]
[tex]n(T\cap B\cap C)[/tex] = 60
Therefore,
a) yes we should get suspicious
b) smallest percentage to like all three sports= 60
Final answer:
The given information suggests that we should be suspicious if told that 20% of all college professors like all three recreations. The smallest percentage who could like all three recreations is 0%.
Explanation:
(a) Yes, we should be suspicious if told that 20% of all college professors like all three recreations. This is because the given information states that 45% of college professors like any given pair of recreations. If 20% of them like all three, it means that the remaining 25% (45% - 20%) would have to like two recreations, which contradicts the given data.
(b) The smallest percentage who could like all three recreations is 0%. Since the information states that 50% of college professors like chess and 65% like bridge, it means that at most, 50% (the percentage who like chess) can like both chess and bridge. Therefore, there is no overlap between those who like chess and bridge, and those who like tennis. Hence, the smallest percentage who could like all three recreations is 0%.
Write an equation of the line containing the given point and perpendicular to the given line:
(4,- 9); 2x+9y=5
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
2x+9y=5
9y = - 2x + 5
y = -2x/9 + 5/9
Comparing with the slope intercept form, slope = -2/9
If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (4,-9) is 9/2
To determine the intercept, we would substitute m = 9/2, x = 4 and y = -9 into y = mx + c. It becomes
- 9 = 9/2×4 + c = 18 + c
c = - 9 - 18 = - 27
The equation becomes
y = 9x/2 - 27
What is the value of cos A?
Answer:
The answer to your question is cos A = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Process
1.- Write the formula
[tex]cos A = \frac{adjacent side}{hypotenuse}[/tex]
2.- Identify the legs of the triangle
opposite side = 12
adjacent side = 9
hypotenuse = 15
3.- Substitute the values in the formula
[tex]cos A = \frac{9}{15}[/tex]
4.- Simplification and result
[tex]cos A = \frac{3}{5}[/tex]
Explanation of finding the value of cos A using trigonometric identities and scalar products.
Cosine function: The value of cos A can be determined using trigonometric identities. For example, from the given expressions like cos 4A=8cos^4A-8cos^2A+1, we can find the value of cos A for specific angles.
Trigonometric identities: By manipulating the given equations and using trigonometric relationships like 1 - cos A = 2sin^2A, you can solve for cos A for different angles.
Scalar products: Understanding the concept of scalar products involving cosine functions like AB cos(θ) will help in applying trigonometry in real-world applications.
Help!!!!!!! Thank you so much
Answer:
18] not a function; (1, 5), (1, -1)
19] is a function
Step-by-step explanation:
The graph of a function will pass the "vertical line test." That is, a vertical line will not intersect the graph at more than one point.
18] There are an infinite number of points where a vertical line will cross the graph twice. Two that are recognizable are the ones at the vertical extremes: (1, 5) and (1, -1). This relation is not a function.
__
19] None of the points on the graph are vertically aligned, so the relation is a function.
Which definition best describes Pythagorean triples? A. Sets of three whole numbers (a, b, and c) that satisfy the equation
B. Pairs of numbers, a and b, such that a2 = b2
C. Any three numbers, each of which is squared
D. Sets of three whole numbers (a, b, and c) that satisfy the equation
Answer:
Option C) Any three numbers, each of which is squared is correct
Step-by-step explanation:
By using Pythagorean Theorem:
Pythagorean theorem is also called as Pythagoras' theorem. It is a fundamental relation among the three sides of a right triangle.
It states that the length of the square of hypotenuse side is equal to the sum of the lengths of the squares of the opposite side and adjacent side.
[tex]a^{2}+b^{2}=c^{2}[/tex]
where c is the length of the hypotenuse side and a and b are the lengths of the opposite and adjacent sides of triangle's.
Therefore Option C) Any three numbers, each of which is squared is correct
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem.
Explanation:Pythagorean triples are sets of three whole numbers (a, b, and c) that satisfy the equation a² + b² = c². This equation is derived from the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse. In a Pythagorean triple, the square of the larger numbers is equal to the sum of the squares of the smaller numbers. For example, the triplet (3, 4, 5) is a Pythagorean triple because 3² + 4² = 5² (9 + 16 = 25).
Yuvraj planned to give a party to 24 people. He ordered food in separate packages for each of the 24 people. But only 15 people turned up and had their food. What percentage of food was left?
someone please help me with this math problem quickly!
Answer:
(fоgоh)(x)=2x³+1
Step-by-step explanation:
Function composition is an operation where two functions, say f(x) and g(x), a new function h(x)=(fоg)(x)=f(g(x)) is generated. In this operation, the function g is applied to the result of the function f. Hence, function f:X→Y and g:Y→Z are joined to form a new function h:X→Z
Given [tex]f(x)=x+1[/tex]
[tex]g(x)=2x[/tex]
[tex]h(x)=x^{3}[/tex]
(fоgоh)(x)=[tex]f(g(h(x)))[/tex]
=[tex]f(g(x^{3}))[/tex]
=[tex]f(2x^{3})[/tex]
=2x³+1
Identify the graphed linear equation.
A) y = 4x + 1
B) y = 4x - 1
C) y = -4x + 1
D) y = -4x - 1
Answer:
The answer to your question is letter C
Step-by-step explanation:
Process
1.- Find two points of the line
A ( 0, 1)
B ( 1, -3)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{-3 - 1}{1 - 0}[/tex]
[tex]m = \frac{-4}{1}[/tex]
m = -4
3.- Find the equation of the line
y - y1 = m (x - x1)
y - 1 = -4( x - 0)
y -1 = -4x
y = -4x + 1
The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution:x: 4 - 5 - 6 - 7 P(X=x): 0.2 - 0.4 - 0.3 - 0.1 (a) Find the mean μ and the variance σ² of X.(b) Find the mean [tex]\mu_{\bar X}[/tex] and the variance [tex]\sigma^2_{\bar X}[/tex] of the mean [tex]\bar X[/tex] for random samples of 36 cherry puffs.(c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 5.5.
Answer:
Step-by-step explanation:
Given is the probability distribution of a random variable X
X 4 5 6 7 Total
P 0.2 0.4 0.3 0.1 1
x*p 0.8 2 1.8 0.7 5.3
x^2*p 3.2 10 10.8 4.9 28.9
a) E(X) = Mean of X = sum of xp = 5.3
[tex]Var(x) = 28.9-5.3^2=0.81[/tex]
Std dev = square root of variance = 0.9
------------------------------------
b) For sample mean we have
Mean = 5.3
Variance = var(x)/n = [tex]\frac{0.81}{{36} } \\=0.0225[/tex]
c) [tex]P(\bar X <5.5)\\= P(Z<\frac{5.5-5.3}{\sqrt{0.0225} } \\= P(Z<1.33)\\=0.908[/tex]
The mean and the variance from the data about the cherries will be 5.3 and 0.81.
How to calculate the mean and variance?The required mean from the information given will be:
= (4 × 0.2) + (5 × 0.4) + (6 × 0.3) + (7 × 0.1)
= 0.8 + 2.0 + 1.8 + 0.7
= 5.3
The variance will be calculated thus:
= (4² × 0.2) + (5² × 0.4) + (6² × 0.3) + (7² × 0.1) - (5.3)²
= 3.2 + 10 + 10.8 + 4.9 - (5.3)²
= 0.81
The variance is 0.81.
The probability that the average number of cherries in 36 cherry puffs will be less than 5.5 will be:
= P(x = 4( + P(x = 5)
= 0.2 + 0.4
= 0.6
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Last year, about 2,400 people participated in a local Fourth of July parade. This year, about 3,200 people participated. What was the approximate percent increase in participation?
Answer:
800 people a year
Step-by-step explanation:
When there is an increment in an observed value, the increment implies that there is a growth or percentage increase in the observed value. The percentage increase in participation is 33%:
Given that:
[tex]Initial = 2400[/tex] --- last year
[tex]New= 3200[/tex] --- this year
The percentage increase is calculated as:
[tex]\%Increase = \frac{New - Initial}{Initial} \times 100\%[/tex]
So, we have:
[tex]\%Increase = \frac{3200 - 2400}{2400} \times 100\%[/tex]
[tex]\%Increase = \frac{800}{2400} \times 100\%[/tex]
[tex]\%Increase = 0.3333 \times 100\%[/tex]
[tex]\%Increase = 33.33 \%[/tex]
Approximate
[tex]\%Increase = 33 \%[/tex]
Hence, the percentage increase in participation from last year to this year is 33%
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Find the Values of k for which the following simultaneous equations have no solutions:
2x - 3ky = 1
4x + (k + 2)y = 5
Answer:
[tex]k=-\frac{2}{7}[/tex]
Step-by-step explanation:
The two equations given represent two straight lines in 2-D graph.
The two lines will not intersect if they are parallel.
Hence the two equations will not have solution if the lines are parallel and not coincident.
The condition for 2 lines given by the equations :
ax+by+c=0
dx+ey+f=0 to be parallel but not coincident is:
[tex]\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}[/tex]
here a=2 b=-3k c=-1 d=4 e=k+2 f=-5
[tex]\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}[/tex]
But also:
[tex]\frac{-3k}{k+2}\neq\frac{1}{5}[/tex]
Hence the value of k is -2/7.
Tim's Tacos sell 57 chicken tacos a night and 89 beef tacos a night for 3 weeks. How many of each kind of taco do they sell when the three weeks are up?
Answer:
see the explanation
Step-by-step explanation:
Remember that
[tex]1\ week=7\ days[/tex]
To convert weeks to days , multiply by 7
so
[tex]3\ weeks=3(7)=21\ days[/tex]
we know that
Each night Tim's Tacos sell 57 chicken tacos and 89 beef tacos
To find out how many of each type of taco sold after three weeks, multiply the number of taco sold daily by 21 (3 weeks)
Chicken tacos
[tex]57(21)= 1,197\ chicken\ tacos[/tex]
Beef tacos
[tex]89(21)= 1,869\ beef\ tacos[/tex]
Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
Answer: it would take 3.1 months
Step-by-step explanation:
Let m represent the number of months that that it will take either of the runners to have the same amount of money in their accounts.
Let y represent the total amount that runner 1 saves for m months
Let z represent the total amount that runner 2 saves for m months
The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. This means that the total amount that he will save for m months would be
y = 112 + 45 + 25m
y = 157 + 25m
The second runner has $50 in savings and will save $60 each month. This means that the total amount that he will save for m months would be
z = 50 + 60m
To determine the number of months before the amount in the account of both runners becomes the same, we would equate y to z. It becomes
157 + 25m = 50 + 60m
157 - 50 = 60m - 25m
35m = 107
m = 107/35
m = 3.06
The auditorium at P.S 104 has 28 rows in all each consists of 95 unfortunately, 30 seats are broken calculate the total number of seats that are broken in the auditorium
Answer:
30 seats
Step-by-step explanation:
The problem statement tells you 30 seats are broken.
___
It does not say 30 seats in each row are broken.
Clara visita the aquarium while on vacation. The aquarium is 2 1/2 miles from her hotel. She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles, and walks the rest of the way to the aquarium. How far did Clara walk after getting off the bus?
Answer:
Step-by-step explanation:
The aquarium is 2 1/2 miles from her hotel. Converting 2 1/2 miles into improper fraction, it becomes 5/2 miles.
She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles. Converting 1 3/4 miles to improper fraction, it becomes 7/4 miles. Therefore the total distance covered by walking and boarding the bus would be
1/4 + 7/4 = 8/4 = 2 miles
She walks the rest of the way to the aquarium. Therefore, the distance that Clara walked after getting off the bus would be
5/2 - 2 = 1/2 miles
In triangle abc, bc=4cm, ad=3cm. The triangle abc moves upward at the speed of 4cm per seconds. What is the area swept by the triangle in three seconds?
Answer:
Step-by-step explanation:
Area Of Triangle And Rectangle
Given a triangle of base b and height h (perpendicular to b), the area can be computed by
[tex]\displaystyle A=\frac{bh}{2}[/tex]
A rectangle of the same dimensions has an area of
[tex]A=bh[/tex]
We have a triangle of base 3 cm and a height of 4 cm. Its area is
[tex]\displaystyle A=\frac{(3)(4)}{2}=6\ cm^2[/tex]
That triangle moves upward at 4 cm per second for 3 seconds. It means that the triangle 'sweeps' upwards three times its height forming a rectangle of base 3 cm and height 12 cm. The area of the swept area is
[tex]A=(3)(12)=36\ cm^2[/tex]
The triangle stays in the top of this rectangle, so its area is part of the total swept area:
Total swept area = 6 + 36 = [tex]42\ cm^2[/tex]
When using your portable radio, you must push the "press to talk" button and wait one second before speaking. This is essential to effective communication because your EMS system must use:
Answer:
Repeaters.
Step-by-step explanation:
This is essential to effective communication because your EMS system must use Repeaters.
These are machines used to carry signals across a great distance. We may be in ambulances or put around an EMS network in different areas. The repeater receives and re transmits signals from lower power systems, such as mobile and handheld phones, to a higher power.
Final answer:
When using portable radios in an EMS system, waiting before speaking is necessary to prevent frequency interference with medical equipment like AEDs. This ensures effective communication and prevents disruptions with critical equipment operations.
Explanation:
When using a portable radio and instructed to push the "press to talk" button and wait one second before speaking, it is essential for effective communication because it ensures that the EMS system has time to establish a clear connection. This waiting period is crucial because communications or medical equipment may use similar radio frequencies. Interruptions and interference on these frequencies can arise from external devices, such as mobile phones operating at 1.9 GHz. Moreover, important medical devices, like automated external defibrillators (AEDs), which provide verbal instructions during cardiac emergencies, rely on these frequencies to function correctly without disruption. Therefore, allowing a small delay ensures that all emergency communication and equipment can operate without interference.
Additionally, speaking slowly and clearly is also vital to ensure that the message is conveyed accurately, especially in situations where there might be wi-fi delays or microphone malfunctions.
Tyrell's SAT math score was in the 64th percentile. If all SAT math scores are normally distributed with a mean of 500 and a standard deviation of 100, what is Tyrell's math score? Round your answer to the nearest whole number
Answer:
[tex]P(x < 535.8) = 0.64[/tex]
[tex]P_{64} = 535.8[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 500
Standard Deviation, σ = 100
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.64
P(X<x) = 0.64
[tex]P( X < x) = P( z < \displaystyle\frac{x - 500}{10})=0.64[/tex]
Calculation the value from standard normal z table, we have, [tex]p(z<0.358) = 0.64[/tex]
[tex]\displaystyle\frac{x - 500}{100} = 0.358\\x = 535.8[/tex]
[tex]P(x < 535.8) = 0.64[/tex]
[tex]P_{64} = 535.8[/tex]
Tyrell's math score is 554.
Explanation:To find Tyrell's math score, we need to use the z-score formula. The z-score formula is given as z = (x - μ)/σ. In this case, we want to find x, so we rearrange the formula to solve for x: x = zσ + μ. Given that Tyrell's score is in the 64th percentile, we can use the z-score table to find the corresponding z-score. The z-score for the 64th percentile is approximately 0.355. Plugging this into the formula, we get: x = 0.355(100) + 500 = 53.55 + 500 = 553.55. Rounding to the nearest whole number, Tyrell's math score is 554.
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A bag of rare spice that weighs pounds will be split equally among people. How much spice will each person get?
Completed question: A bag of rare spice that weighs 3/5 pounds will be split equally among 15 people. How much spice will each person get?
Answer:
0.04 pounds
Step-by-step explanation:
The number of spice received by each person will be equal to the total number of spice divided by the number of people sharing it.
Amount of spice received per person = (3/5) /15
= 0.04 pounds
6. Sue goes to the bakery and purchases cupcakes and cookies for a picnic. She needs to serve 36 people. Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. How many cupcakes did she purchase?
Answer:the number of cupcakes that Sue purchased is 12
Step-by-step explanation:
Let x represent the number of cupcakes that Sue purchased at the bakery.
Let y represent the number of cookies that Sue purchased at the bakery.
She needs to serve 36 people. This means she would purchase a total of 36 people. Therefore,
x + y = 36
Cupcakes cost $2.50 each, cookies cost $1.00 each. She spends $54.00. This means that
2.5x + y = 54 - - - - - - - - - 1
Substituting x = 36 - y into equation 1, it becomes
2.5(36 - y) + y = 54
90 - 2.5y + y = 54
- 2.5y + y = 54 - 90
- 1.5y = - 36
y = - 36/ - 1.5
y = =24
x = 36 - y = 36 - 24 = 12
She purchased 24 cupcakes
Let the number of cupcakes be xLet the number of cookies be yIf she needs to serve 36 people, then;
x + y = 36 .................... 1
if cupcakes cost $2.50 each, cookies cost $1.00 each while she spends $54.00, then;
2.5x + y = 54 ...................... 2
From equation 1, x = 36 - y
Substitute into equation 2;
2.5(36-y) + y = 54
90 - 2.5y + y = 54
-1.5y = - 36
y = 36/1.5
y = 24
Hence she purchased 24 cupcakes
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1. Point A(-5,8) is reflected across the line y = x. What are the coordinates of A'? Show your work and explain.
Need help with this
Answer:
The coordinates of A'(8,-5)
Step-by-step explanation:
we know that
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places
so
The rule of the reflection across the line y=x is
(x,y) -----> (y,x)
we have the point A(-5,8)
Applying the rule of the reflection across the line y=x
A(-5,8) ----> A'(8,-5)
see the attached figure to better understand the problem
The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 500 feet of fencing available, what is the maximum possible area of the corral?
Answer:
[tex]A= 125*250=31250 ft^2[/tex]
Step-by-step explanation:
Let's define some notation first :
w= width , l = length , A= Area, P perimeter
For this case we want to maximize the Area given by this function:
A= l w (1)
With the following restriction P=500 ft
We know that the perimeter on this case is given by:
[tex]P=2w +l[/tex]
Since they are using the creek as one side.
So then we have this:
[tex]500 =2w +l[/tex] (2)
Now we can solve w in terms of l from eqaution (2) and we got:
[tex]w=\frac{500-l}{2}[/tex] (3)
And we can replace this condition into equation (1) like this:
[tex]A= \frac{500-l}{2} l =250l - \frac{1}{2} l^2[/tex]
And we can maximize this function derivating respect to l and we got:
[tex]\frac{dA}{dl}= 250 -l=0[/tex]
And then we got that [tex]l=250[/tex]
And if we solve for w from equation (3) we got:
[tex]w=\frac{500-250}{2}=125[/tex]
And then the dimensions would be:
[tex] l =250ft , w=125ft[/tex]
And the area would be:
[tex]A= 125*250=31250 ft^2[/tex]
To maximize the area of the corral, we can solve a mathematical optimization problem. By expressing the length in terms of the width, we can find the derivative of the area formula and set it to zero. Substituting the resulting value of the width into the area formula gives us the maximum area.
Explanation:To find the maximum area of the corral, we need to determine the dimensions of the rectangle. Let's assume the length of the corral is L and the width is W.
Since one side of the corral is the creek, we only need to use fencing for the other three sides. This implies that 2W + L = 500 (since there are two widths and one length that need fencing).
To maximize the area, we can express L in terms of W using the formula L = 500 - 2W and substitute it into the area formula A = LW. Simplifying, we get A = W(500 - 2W). To find the maximum area, we can take the derivative of A with respect to W, set it equal to zero, and solve for W. The resulting value of W can be substituted back into the equation to find the corresponding value of L. The maximum area is obtained by multiplying these two dimensions together.
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Eight women of different heights are at a party. Each woman decides to only participate in a handshake with women shorter than herself. How many handshakes take place?
Answer:
0 handshakes
Step-by-step explanation:
There are 8 women of different heights.
Let the eight women be A, B, C, D, E, F, G and H
Assume A is taller than B and A decides to shake hands with B, B will refuse because A is taller. If this happens across the eight women then there will be 0 hand shakes.
If this assumption is taken out, we have 7+6+5+4+3+2+1 = 28
Answer:
0
Step-by-step explanation:
There are 0 handshakes because if A is taller than B, then A will want to shake hands with B, but B will not participate because she is shorter.
The speedometer in Kevin's car reads in both miles/hour and kilometers/hour. What information is needed to convert between these two units?a) the number of miles in 1 kilometerb) the number of kilometers that are traveled in 1 hourc) the number of miles that are traveled in 1 hourd) the number of hours per 1 kilometer
Answer:
a) the number of miles in 1 kilometer
Step-by-step explanation:
The car converts from miles/hour to kilometers/hour, if we see the time measurement (hours) it stays the same in both units.
So to make the conversion it is enough to know how many miles are in one kilometer.
For example, lets convert 10miles/hour to kilometers/hour.
there are 0.621371 miles in 1 kilometer, so if we divide 10miles/hour by 0.621371 we get kilometers/hour units:
[tex]\frac{10miles}{hour} (\frac{1kilometer}{0.621371miles} )=16.0934\frac{kilometers}{hour}[/tex]
Thus to make the conversion between the two units is needed the number of miles in 1 kilometer.
The cost c in £ of a monthly phone contract is made up of the fixed line rental l in £ and the price p in £ of the calls made. Enter a formula for the cost and enter the cost if the line rental is £35 and the price of calls made is £12
The cost of the phone contract will be C = 35 + 12m.
From the information given, the fixed line rental is £35 and the price of calls made is £12, therefore the monthly cost will be represented by:
C = 35 + (12 × m)
C = 35 + 12m
Therefore, the cost of the phone contract will be C = 35 + 12m where m represents the number of months.
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The cost of a monthly phone contract is made up of the fixed line rental and the price of the calls made. This can be represented with the formula: c = l + p, where c is the cost, l is line rental, and p is the price of calls. With a line rental of £35 and call price of £12, the total cost of the phone contract is £47.
Explanation:In the scenario presented, the cost, c, of a monthly phone contract is constituted by the fixed line rental or l and the price or p of the calls made. This can be represented with the formula: c = l + p. We can substitute in the provided costs - a line rental of £35 and call price of £12 - into the equation to find the total cost of the phone contract. Thus, c = £35 + £12 = £47.
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A culture increases by 500 bacteria every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be by after 24 hours?
Answer:
6500
Step-by-step explanation:
In 24 hours, there are 12 times 2 hours, so the bacteria count will increase by 500 twelve times. That is, the increase after 24 hours will be ...
12 × 500 = 6000 . . . bacteria
Since the starting number was 500, the total will be ...
500 + 6000 = 6500 . . . . bacteria after 24 hours
_____
If you like, you can compute the rate of change as 500 bacteria / (2 hours) = 250 bacteria/hour. Then the equation for the number is ...
bacteria = 500 + 250h . . . . . where h is the number of hours.
Filling in h=24, we get
bacteria = 500 + 250(24) = 500 +6000 = 6500 . . . . after 24 hours
What is GE ?
Enter your answer in the box.
_____units
Good evening ,
Answer:
GE = 10.Step-by-step explanation:
GE=2×ZE
Since ZE=XY then ZE=5
therefore GE=2×5=10.
:)
Sixty- five percent of men consider themselves knowledgeable football fans.
If 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.
a) 0.65 b) 0.069 c) 0.600 d) 0.238
Answer: d) 0.238
Step-by-step explanation:
We would assume binomial distribution for the number of men sampled. The formula for binomial distribution is expressed as
P(x =r) = nCr × q^(n - r) × p^r
Where
p represents the probability of success.
q represents the probability of failure.
n represents the number of samples.
From the information given,
n = 10
p = 65% = 65/100 = 0.65
q = 1 - p = 1 - 0.65 = 0.35
The probability that exactly six of them will consider themselves knowledgeable fans is expressed as P(x = 6). It becomes
P(x =6) = 10C6 × 0.35^(10 - 6) × 0.65^6
P(x =6) = 10C6 × 0.35^4 × 0.65^6
P(x =6) = 0.238
Final answer:
Option d) 0.238
Explanation:
To find the probability that exactly six out of 10 men consider themselves knowledgeable football fans, we can use the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
n = total number of trials (in this case, 10 men) k = number of successful trials (in this case, 6 knowledgeable fans) p = probability of success (in this case, 0.65) C(n, k) = combination of n items taken k at a time
Using the formula, we get:
P(X=6) = C(10, 6) * 0.65^6 * (1-0.65)^4
Calculating C(10, 6) which is 210, and then raising 0.65 to the power of 6 and (1-0.65) to the power of 4, simplifies to:
P(X=6) = 210 * 0.1160290625 * 0.1502625 = 0.238
After rounding to three decimal places, we get:
P(X=6) = 0.238
Therefore, the correct answer is (d) 0.238.