Using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The distance travelled = 1176.00 miles
Time taken = 4 hours and 54 minutes = 4*60 + 54 = 294 minutes
The times taken for return flight = 4 hours = 240 minutes
Let,
x = speed of the plane
y = speed of the wind
In a headwind the speed reduces.
So the relative speed of the plane is (x-y)
distance = speed * time
1176 = (x-y) * 294
x-y = 4
Now for the return flight, the wind is tailwind and the speed increases.
So the relative speed of the plane is (x+y).
1176 = (x+y) * 240
x + y = 4.9
Now we have a system of equations.
x - y = 4
x + y = 4.9
Adding,
2x = 8.9
x = 4.45 miles/min = 4.45 * 60 miles/hour = 267 miles/hour
and
y = 4.9 - x = 4.9 - 4.45 = 0.45 miles/min = 0.45*60 = 27 miles/hour
Therefore using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
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A helicopter hovers 500 feet
above a small island. The figure
shows that the angle of
depression from the helicopter
to point P is 48°
How far off
the coast, to the nearest foot, is
the island?
Agriculture: You own an empty one acre lot. (640 acres = 1 mi²; 1 mi = 5,280 ft)
a. If 1 inch of rain fell over your one acre lot, how many cubic inches of water fell on your lot?
b. How many cubic feet of water fell on your lot?
c. If 1 cubic foot of water weighs about 62 pounds, what is the weight of the water that fell on your lot?
d. If the weight of 1 gallon of water is approximately 8.3 pounds, how many gallons of water fell on your lot?
a) 6272640 cubic inches of water fell on the lot
b) 3630 cubic feet of water fell on the lot
c) the weight of the water that fell on the lot = 112.53 tons
d) gallons of water fell on the lot = 27,115.7 gallons
Converting acre into sq ft460 acre=1 [tex]mi^{2}[/tex]
1 acre=1/460 [tex]mi^{2}[/tex]
1 mi=5280 ft
1 mi2=5280×5280[tex]ft^{2}[/tex]
1 acre=(5280×5280)/460
1 acre= 43560 sq ft
Solving the part (a)As one inch is equal to one-twelfth of a foot, one acre of water that is 1 inch deep takes up 3630 cubic feet (43560×(1/12)).
One cubic foot is equal to 12 inches by 12 inches by 12 inches,
or 12×12×12=1728 cubic inches.
6272640 cubic inches are contained in 3630 cubic feet, or 3630 × 728.
Hence, 6272640 cubic inches of water fell on the lot.
Solving the part (b)If 1 inch of rain fell over your one acre lot, 3630 cubic feet of water fell on the lot.
Solving the part (c)3630 times 62 is 225,060 pounds, the weight in pounds.
We are aware that a tons weighs 2000 lb.
225060/2000 = 112.53 tons
Hence, the weight of the water that fell on the lot=112.53 tons.
Solving the part (d)If there are around 8.3 pounds in 1 gallon of water,
Number of gallons of water fell on the lot
=225060/8.3
=27,115.7 gallons
Hence, gallons of water fell on the lot=27,115.7 gallons.
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please help
30 points
The baker can decorate 1.4 or 1 1/3 of cupcakes in a minute.Step-by-step explanation: 42 cupcakes in 30 minutes so if you divide 42 cupcakes in 30 groups you get 1 in each group and 12 left so if make 30 in 3 it makes 4 in each group but it is 30 so you make the four in to a 0.4 or 1/3 which is 1.4.You can also multiply if you make 1.4 into 14 x 3 = 42 same as 1.4 x 30 = 42 so the answer is 1.4.
prove that (sec theta + tan theta - 1)(sec theta - tan theta + 1) = 2tan theta
Answer:
(secΘ+tanΘ-1)(secΘ-tanΘ+1)
=sec²Θ-secΘtanΘ+secΘ+secΘtan-tan²Θ+tanΘ-secΘ+tanΘ-1
=2tanΘ+(sec²Θ-tan²Θ)-1
=2tanΘ+1-1
=2tanΘ
Ellen has three packages of markers. Exactly 10 of the markers in each package are yellow markers. • Package T contains 10 markers. • Package V contains 40 markers. • Package W contains 40 markers.
Ellen will randomly select one marker from each package. Which statements are true?
Select the three that apply.
A. The probability of selecting a yellow marker from Package T is 1.
B. The probability of selecting a yellow marker is equal for packages V and W.
C. The probability of randomly selecting a yellow marker from Package V is 1 / 3 .
D. The probability of selecting a yellow marker is less for Package W than it is for Package T.
E. The probability of selecting a yellow marker from Package V is four times the probability of selecting a yellow marker from Package T.
Answer: B and D
Step-by-step explanation:
Find the missing number 11:15=—:135
Answer:99
Step-by-step explanation:
Answer: 99
Step-by-step explanation:
135 is 9 times of 15
To get the missing number, multiply 11 by 9,
11 x 9 = 99
Please help. I have a test today
A certain company's main source of income is selling socks.
The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:
P(x)=−3(x−5) ^2+12
What is the maximum profit that the company can earn?
____ million dollars
If the company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by P(x)=−3(x−5) ^2+12, the maximum profit is $87 million.
The given profit function is in the form of a quadratic equation with a negative coefficient of the squared term. This means that the graph of the function is a downward-facing parabola, and the vertex of this parabola represents the maximum value of the function.
To find the vertex, we need to convert the given function into vertex form:
P(x) = -3(x - 5)^2 + 12
= -3(x^2 - 10x + 25) + 12
= -3x^2 + 30x - 63
Completing the square, we get:
P(x) = -3(x - 5)^2 + 12 + 75
= -3(x - 5)^2 + 87
The vertex of this parabola is at the point (5, 87), which represents the maximum profit the company can earn.
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100 pts and brainlist for SIMPLE math problem
Stockton lake lost the least amount of water.
What is Denominator?
In mathematics, the denominator is the bottom number in a fraction that indicates the number of equal parts into which a whole is divided.
To compare the amount of water lost by each lake, we need to express the amounts lost in the same units. One way to do this is to find a common denominator for the fractions and percentages involved.
Lake Jensen lost 5/6 of its water, which can be expressed as a fraction with a common denominator of 300:
5/6 = 250/300
Lake Parlow lost 85% of its water, which can be expressed as a fraction with a denominator of 100:
85% = 85/100 = 255/300
Lake Stockton lost 246/300 of its water, which is already in terms of a common denominator of 300.
Now we can compare the amounts lost directly:
Lake Jensen lost 250/300 of its water
Lake Parlow lost 255/300 of its water
Lake Stockton lost 246/300 of its water
To determine which lake lost the least amount of water, we need to find the smallest fraction among these three.
We can see that Lake Stockton lost the least amount of water, since 246/300 is smaller than both 250/300 and 255/300. Therefore, Lake Stockton lost the least amount of water.
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what is this question for math need help
Answer:
A
Step-by-step explanation:
The answer is 2x+2y+2 which is A
Answer: I think its B but I'm not quite sure
Step-by-step explanation:
Let f(x) = √ x − 1 x − 3 .
(i) Evaluate f(4), f(5) and f(a + 1).
(ii) Find the domain of f.
(i) a
(ii) {x | x ∈ R, x ≠ 3, x ≥ 1}
(i) To evaluate f(4), f(5), and f(a + 1), we replace x with 4, 5, and a + 1 in f(x) respectively. We have; f(4) = √ 4 − 1 4 − 3= √ 3 1= √ 3f(5) = √ 5 − 1 5 − 3= √ 4 2= 2f(a + 1) = √ a + 1 − 1 a + 1 − 3= √ a 2= a
(ii) Domain of f:The expression in the denominator cannot be equal to zero, so we must ensure that x − 3 ≠ 0. Therefore, x ≠ 3The expression in the square root must be greater than or equal to zero, so we must ensure that x − 1 ≥ 0. Therefore, x ≥ 1The domain of f is {x | x ∈ R, x ≠ 3, x ≥ 1}.
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what is the value of the expression 9 (5) - X / Y when x= 15 and y= 3
a 5
b 10
c 15
d 20
Answer:
9(5)-/y
9(5)-15/3
45-15/3
45-5
40
Bianca said that if k is a real number, then the solution set of the compound inequality xk is all real numbers. Do you agree? Justify your argument.
Well, I do agree that if k is a real number, then the compound inequality xk's solution set contains only real numbers.
A sentence with two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The word "and" indicates that both claims in the compound sentence are true at the same time. It occurs when the multiple statement's solution sets overlap or intersect. Compound inequalities are those that have the conjunctions "and" or "or" between them. It should be understood that plimb[/[/ofs (Ors Or/ Orss ultras "is larger than -2 and less than or equal to 5" should be translated as 2 x 5. x is greater than or equal to 3 or equal to -4, or "x 3." You'll observe that each of these differences has two inequality signals. Inequality that is compounded by two or more factors.
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i need help with thiss
The only true statement in the following equation are B and D.
How to find true statement?A. When the bacteria population reaches 900, 12 hours have passed since the colony was placed on the petri dish.
To check this statement, we can use the formula for exponential growth:
P(t) = P0 * [tex]3^{(t/6)[/tex]
Where P(t) is the population at time t, P0 is the initial population, and t is the time in hours.
If P(t) = 900, we can solve for t:
900 = [tex]100 * 3^{(t/6)[/tex]
9 = [tex]3^{(t/6)[/tex]
ln(9) = (t/6) * ln(3)
t = 6 * ln(9) / ln(3) ≈ 12.68
So, it takes approximately 12.68 hours for the population to reach 900. Therefore, statement A is false.
B. Three hours after the colony is placed on the petri dish, there are 200 bacteria.
Using the formula above with t=3:
P(3) = [tex]100 * 3^{(3/6) = 200[/tex]
So, statement B is true.
C. Three hours after the colony is placed on the petri dish, there are about 173 bacteria in the colony.
Using the formula above with t=3:
P(3) = [tex]100 * 3^{(3/6) = 200[/tex]
So, statement C is false.
D. In the first hour the colony is placed on the petri dish, the population grows by a factor of [tex]$3^{\frac{1}{6}}$[/tex]
Using the formula above with t=1:
P(1) = [tex]100 * 3^(1/6)[/tex]
So, the population after 1 hour is 100 times the sixth root of 3. We can write this as:
P(1) = [tex]100 * (3^(1/6)) = 100 * 3^{\frac{1}{6}}[/tex]
Therefore, statement D is true.
E. Between 8 a.m. and 9 a.m., the population grows by a factor of [tex]$3^{\frac{2}{3}}$[/tex]
Between 7 a.m. and 8 a.m., the population grows by a factor of 3. Then, between 8 a.m. and 9 a.m., it grows by another factor of 3. So, between 7 a.m. and 9 a.m., the population grows by a factor of [tex]3^2[/tex] = 9. Taking the sixth root of 9 gives:
[tex](3^2)^(1/6) = 3^(1/3) = 3^{\frac{2}{6}} = 3^{\frac{1}{3}}[/tex]
So, the population between 8 a.m. and 9 a.m. grows by a factor of [tex]3^(1/3)[/tex]. Therefore, statement E is false.
In summary, the true statements are B and D.
We can employ the AC approach to factor the quadratic expression seen in the image. To achieve -6 * -15 = 90, we first multiply the coefficients of the first and last terms. The middle term's coefficient, which is -9, is then shown to be two factors of 90. Since -6 * -15 = 90 and -6 + (-15) = -21, which is the same as -9 when we factor out the GCF of 3, these factors are -6 and -15:
[tex]x^2 - 9x - 90 = (x - 15)(x + 6)[/tex]
As a result, the quadratic expression's factored form is (x - 15)(x + 6).
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Q8) What sum of money lent out at 12 per cent p.a. simple interest would produce * 9000 as interest in 2 years?
simple interest would produce ₹ 9000 as interest in 2 years? Rate = 12% p.a. Principal = ? Hence, the required principal amount = ₹ 37500
Answer:
SI=P*R*T/100
SI=9000*12*2/100
SI=2160
TOTAL AMOUNT=2160+9000=11160
What does it mean to construct a triangle inscribed in a circle? (what does the word inscribed mean?)
Answer: A geometric figure which touches only the sides (or interior) of another figure.
Step-by-step explanation:
its inside but does not go past the innner edges
There are 9 teams that are numbered respectively from 1 to 9. Each team member has the group number printed on his/her shirt and each team cannot have more team members then its number. Armen started to add up all the odd numbers he saw on the shirts and asked David to add up all the even ones. What is the greatest possible difference between David's results and Armen's
The greatest possible difference between David's result and Armen's result is 5.
Let's first consider the maximum number of odd shirts Armen can count. Since there are only 5 odd numbers between 1 and 9, the maximum number of odd shirts Armen can count is 1+3+5+7+9 = 25.
Now, let's consider the maximum number of even shirts David can count. Since there are only 4 even numbers between 1 and 9, the maximum number of even shirts David can count is 2+4+6+8 = 20.
Therefore, the greatest possible difference between David's result and Armen's result is
= 25 - 20
Subtract the numbers
= 5
The maximum difference occurs when Armen counts all 5 odd shirts and David counts all 4 even shirts.
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-26 ___ 25
=
<
≤
≠
>
≥ im being timed hurry pls
Answer:25 percent means one fourth. To calculate 25 percent of a number, simply divide it by 4. For example, 25 percent of 12 is 12 divided by 4, or 3
Identify the function in standard form. 3x 2 + 6x - 12 = 0 3x 2 + 2x + 10 = 0 5x 2 - 10x + 5 = 0 2x 2 - 4x + 6 = 0
All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:
ax² + bx + c = 0.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation.
The functions in standard form are:
3x² + 6x - 12 = 0
3x² + 2x + 10 = 0
5x² - 10x + 5 = 0
2x² - 4x + 6 = 0
All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:
ax² + bx + c = 0
where a, b, and c are constants and a ≠ 0.
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According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that .
a. Find the probability that at least 29% of the sample are from poverty-level households, assuming that 22% of all children under the age of 6 in this state live in poverty-level households.
b. Based on your answer to part (a), is there convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%? Explain your reasoning.
a. The resultant probability is 0.17%
b. The resultant statement greater than the national value of 22% is true.
The probability that at least 29% of the sample are from poverty-level households is 0.17% and we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.
According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that at least 29% of the sample are from poverty-level households.
To answer part (a) of the question, we can use the normal approximation to the binomial distribution. The mean of the distribution is np = 300 * 0.22 = 66 and the standard deviation is sqrt(np(1-p)) = sqrt(66 * 0.78) = 7.09. We can use the normalcdf function to find the probability that at least 29% of the sample are from poverty-level households:
normalcdf(87.5, 300, 66, 7.09) = 0.0017
So the probability is 0.17%.
For part (b) of the question, we need to determine if there is convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.
Since the probability that at least 29% of the sample are from poverty-level households is 0.17%, which is very small, we can conclude that there is not convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.
The small probability suggests that the observed sample result is unlikely to occur by chance if the true population proportion is 22%, so we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.
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Solve for x.
a. 4°
b. 4. 5°
c. 6°
d. 11. 5°
The cοrrect answer is d. 11.5°, This is because the equatiοn 4x = 46 can be rearranged tο x = 46/4 = 11.5.
What is equatiοn?An equatiοn is a mathematical statement that describes the relatiοnship between twο values using an equal sign. It cοnsists οf twο expressiοns οn either side οf the equal sign, and the expressiοns must be equal in οrder fοr the equatiοn tο be true. Equatiοns are used tο sοlve prοblems and tο understand hοw different variables interact with each οther.
Fοr example, the equatiοn "2 + 2 = 4" is true because twο plus twο dοes in fact equal fοur. Equatiοns can alsο be used tο represent physical phenοmena, such as the equatiοn F = ma, which describes the relatiοnship between fοrce and mass. Equatiοns can be used tο sοlve many prοblems in mathematics, science, engineering, ecοnοmics, and οther fields.
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A line is breaking a segment into two making two angles, one of the angle is 46° which 4 times the other angle x. Solve for x
a. 4°
b. 4. 5°
c. 6°
d. 11. 5°
Divide 81 into scale 2:1
Answer:
Below
Step-by-step explanation:
You want to divide 81 into (2+1 = 3) parts
81 / 3 = 27 for each part
2 parts would be 2 * 27 = 54
so 2:1 would be 54:27
List all the outcomes when rolling a fair six-sided die. a. What is the probability of getting a 1, 3, or a 6? (ALL ANSWERS SHOULD BE IN FRACTION FORM) b. What is the probability of getting a number less than 5? (ALL ANSWERS SHOULD BE IN FRACTION FORM)
Answer:
The outcomes when rolling a fair six-sided die are: 1, 2, 3, 4, 5, and 6.
a. The probability of getting a 1, 3, or a 6 is 3/6 or 1/2.
b. The probability of getting a number less than 5 is 4/6 or 2/3.
Round this number to the
nearest ten:
801
Answer:
800
Step-by-step explanation:
the answer is 800 as 1 rounds down
i need help please help me
According the question given above the value of n is 21.
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue. The act of substituting a complex mathematical expression with a simpler counterpart is known as simplification (usually shorter).
Here, we have
Given : 7 = n/3
we have to find the value οf n.
We apply simplification here and we get
7 = n/3
n = 7×3
n = 21.
Hence, the value οf n is 21.
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Mr. Shoaf had a birthday a couple weeks ago and his mom took him out to dinner.
The total bill was $76.55. If there was a 5% sales tax and she tipped 25%, what was the total Mr. Shoaf’s mom paid for dinner?
She paid---------------------------------- dollars for the birthday dinner.
The birthday supper cost $94.73 and also the tax rate is $72.72 and was paid by Mr. Shoaf's mother.
What distinguishes VAT from sales tax?A flat charge called valuation tax (VAT) is imposed on a purchase. It resembles a sales tax in the some ways, but unlike with a state taxes, the consumer pays the entire amount due to the government at the moment of sale.
What does Dutch VAT mean?Value added tax is levied by the Dutch government on all products and services. VAT is added by businesses to the sales price to determine the final amount that customers pay. Businesses must pay taxes to the Customs and Tax Administration when goods are sold.
Cost of the meal [tex]= 76.55 -[/tex] (5% of 76.55)
Cost of the meal [tex]= 76.55 - 3.83[/tex]
Cost of the meal [tex]= 72.72[/tex]
calculate tip,
Tip = 25% of the cost of the meal
Tip [tex]= 0.25 *72.72[/tex]
Tip [tex]= 18.18[/tex]
calculate the total amount paid
Total amount paid = cost of the meal + sales tax + tip
Total amount paid [tex]= 72.72 + 3.83 + 18.18[/tex]
Total amount paid [tex]= 94.73[/tex]
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Sean throws the discus at a school meet and the height of the discus is given by the function h=-16+2 + 38t + 5, where h is in feet and t represents the seconds after throwing. A. What is the initial height of the discus? b. After how many seconds does it take for the discus hit the ground?
Hence, in response to the provided question, we can say that As a result, function the discus takes approximately 0.03125 seconds to strike the ground.
what is function?Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.
The supplied function for discus height is as follows:
[tex]h(t) = -16t^2 + 38t + 5\\h(0) = -16(0)^2 + 38(0) + 5 = 5[/tex]
As a result, the discus's starting height is 5 feet.
[tex]-16t^2 + 38t + 5 = 0\\[/tex]
To find t, we can apply the quadratic formula:
t = (-b \sqrt(b2 - 4ac)) (2a)
where a=-16, b=38, and c=5.
[tex]t = (-38 + \sqrt(38^2 - 4(-16)(5))) / (2(-16))\\t = (-38 + \sqrt(1524)) / (-32) (-32)\\t = (-38 + 39) / (-32) (-32)\\[/tex]
As a result, [tex]t = (-38 + 39) / (32) or t = (-38 - 39) / (32) (-32)[/tex]
t = 1/32 or t = 77/32
As the negative value doesn't make sense in this situation, we chose the positive value:
t = 1/32
As a result, the discus takes approximately 0.03125 seconds to strike the ground.
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In Princeton, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 7 miles and the distance between the courthouse and the city pool is 8 miles, how far is the library from the community pool? If necessary, round to the nearest tenth.
Please respond.
Thank you!
Answer:
3.9 miles
Step-by-step explanation:
To find:-
Distance between library and community pool .Answer:-
The given situation is represented in the attachment.
We can see that there is a formation of right angled triangle , hence we can use Pythagoras theorem here , according to which,
[tex]\rm\implies a^2+b^2=h^2 \\[/tex]
where h is the longest side (hypotenuse) of the triangle of the triangle . From the attached figure we can see that 8miles is hypotenuse and one of the other side is 7miles .
On substituting the respective values, we have;
[tex]\rm\implies 7^2+b^2=8^2 \\[/tex]
[tex]\rm\implies 49+b^2=64 \\[/tex]
[tex]\rm\implies b^2 = 64-49\\[/tex]
[tex]\rm\implies b =\sqrt{15}\\[/tex]
[tex]\rm\implies \red{b = 3.9 } \\[/tex]
Hence the distance between the swimming pool and the Library is 3.9 miles .
He amount of soda in a 12 ounce bottle is supposed to be 12 ounces, right? There is some variability in the amount that the machines dispense into the bottles. Let the real amount of soda in each bottle follow a Normal distribution with mean 12. 2 and standard deviation 0. 3.
If the bottle can only hold 13 ounces, what is the probability the bottle will overflow?
(In other words, what is the probability that the machine dispenses more than 13 ounces?)
If the bottle can only hold 13 ounces, then the probability the bottle will overflow is approximately 0.0032 or 0.32%.
First, we need to calculate the z-score, which is the number of standard deviations that the mean value of 12.2 ounces is away from the bottle's capacity of 13 ounces. We can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the bottle capacity (13 ounces), μ is the mean value of soda dispensed by the machine (12.2 ounces), and σ is the standard deviation (0.3 ounces).
Substituting the values, we get:
z = (13 - 12.2) / 0.3 = 2.67
The z-score of 2.67 means that the bottle capacity of 13 ounces is 2.67 standard deviations away from the mean value of soda dispensed by the machine.
Substituting the values, we get:
P(Z > 2.67) = 1 - P(Z ≤ 2.67) = 1 - 0.9968 = 0.0032
Therefore, the probability of the soda bottle overflowing is approximately 0.0032 or 0.32%.
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kira will rent a car for the weekend. she can choose one of two plans. the first plan has an initial fee of $45 and costs an additional $0.30 per mile driven. the second plan has no initial fee but costs $0.80 per mile driven. for what amount of driving do the two plans cost the same? miles what is the cost when the two plans cost the same? $
The two plans will cost the same if Kira drives 90 miles over the weekend.
The two plans cost the same when Kira drives 90 miles, and the cost of each plan is $72.
To find the mileage for which the two plans cost the same and the cost at that mileage, you should set the cost expressions for both plans equal to each other. After that, you will solve for the mileage (x).
The steps to do this are as follows:Let the mileage be x
The cost of plan 1 (C1) is given by:
C1 = 45 + 0.30x
The cost of plan 2 (C2) is given by:
C2 = 0.80 x
To find the mileage at which both plans cost the same, set C1 equal to C2 and solve for x:
45 + 0.30 x = 0.80 x x (0.30 - 0.80) = - 45- 0.50 x = -45 x = -45/-0.50 x = 90
To find the cost when the two plans cost the same,
substitute x = 90 into one of the expressions for cost.
C1 = 45 + 0.30x = 45 + 0.30(90) = 45 + 27 = $72C2 = 0.80x = 0.80(90) = $72
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