Answer:
(1) Insufficient data
(2) Sufficient data
Step-by-step explanation:
We need to check whether the given data is sufficient or not to prove that a rectangular region has perimeter P inches and area A square inches, is the region square.
Assume that the given conditions are
1. [tex]P=\frac{4}{3}A[/tex]
2. [tex]P=4\sqrt{A}[/tex]
Area of square is
[tex]A=a^2[/tex]
Taking square root on both sides.
[tex]\sqrt{A}=a[/tex] .... (1)
where a is side length.
Perimeter of square is
[tex]P=4a[/tex] ... (2)
From (1) and (2) we get
[tex]P=4\sqrt{A}[/tex]
It means second condition is sufficient to prove that the rectangle reason is square, because it is true for all.
For a=3,
A=9 and P=12
[tex]12=\frac{4}{3}(9)[/tex]
[tex]12=12[/tex]
LHS=RHS
For a=6,
A=36 and P=24
[tex]24=48[/tex] (False statement)
The first condition is insufficient because it may or may not be true.
Consider the functions.
f(x)=4x^2
g(x)=15/4x^2
h(x)=4/15x^2
Answer:
see the explanation
Step-by-step explanation:
we know that
As the leading coefficient of the quadratic equation gets larger the parabola gets steeper and "narrower"
we have
[tex]f(x)=4x^{2}[/tex]
[tex]g(x)=\frac{15}{4}x^{2}[/tex]
[tex]h(x)=\frac{4}{15}x^{2}[/tex]
Compare the leading coefficients
The leading coefficient of f(x) is 4
The leading coefficient of g(x) is 15/4=3.75
The leading coefficient of h(x) is 4/15=0.27
so
4> 3.75> 0.27
therefore
f(x) is steeper than g(x) and h(x)
g(x) is steeper than h(x)
Verify each statement
1) f(x) is steeper than h(x)
The statement is true
2) h(x) is steeper than g(x)
The statement is false
3) g(x) is steeper than f(x)
The statement is false
A civics teacher asked her students to indicate whether they believed each of two headlines. One headline was false and the other was true, but the students did not know this. The probability that a student selected at random believed the true headline was 90% and the probability that the student believed the false headline was 82%. She found that 75% of the students believed both headlines. In this sample, are the events "believed the false headline" and "believed the true headline" mutually exclusive?
Answer:
Not mutually exclusive
Step-by-step explanation:
In the rule of probability, for two events to be mutually exclusive, the probability of them occuring at the same time must be 0.
In this case P(true and false) = 0 to be mutually exclusive.
In the term of Vann diagram 'true and false' in this case represent the intersection of two events 'true' and 'false'. And if it is shown in Vann diagram, both group will be apart from each other or the value inside the Vann diagram is 0.
Therefore,
We know from statistics that
P(A and B) = P(A) + P(B) - P(A or B)
Translating into this case
P(true or false) = P(true) + P(false) - P(true and false)
= 0.9 + 0.82 - 0.75 = 0.97
Therefore, this event is not mutually exclusive.
Answer:
no and 0.97
Step-by-step explanation:
At a popular theme park, there were 2,000,000 visitors last year. This year, there were 2,100,000 visitors. What is the percent increase in visitors from last year to this year? (Enter an exact number.)
Answer:
There was 5% increase in visitors from last year to this year.
Step-by-step explanation:
Given:
Number of Visitors at theme park last year = 2000000
Number of Visitors at theme park this year = 2100000
We need to find the percent increase in visitors from last year to this year.
First we will find Number of increase in visitors from last year to this year.
Number of increase in visitors is equal to Number of Visitors at theme park this year minus Number of Visitors at theme park last year.
Framing in equation form we get;
Number of increase in visitors = 2100000 - 2000000 = 100000
Now Percent of increase in visitors is can be calculated by dividing Number of increase in visitors with Number of Visitors at theme park last year and then multiplied with 100.
Framing in equation form we get;
Percent of increase in visitors = [tex]\frac{100000}{2000000}\times 100 = 5\%[/tex]
Hence There was 5% increase in visitors from last year to this year.
There was a 5% increase in visitors to the theme park from last year to this year, calculated using the formula for percent increase.
Explanation:The question is asking for the percent increase in visitors from one year to the next at a popular theme park. To find this, we'll use the formula for percent increase: ((new value - old value) / old value) * 100%.
In this case, the 'old value' is the number of visitors last year, which is 2,000,000. The 'new value' is the number of visitors this year, which is 2,100,000. Substituting these numbers into our formula gives us: ((2,100,000 - 2,000,000) / 2,000,000) * 100%.
This simplifies to: (100,000 / 2,000,000) * 100%. Then, converting 100,000 / 2,000,000 to a decimal gives us 0.05. Multiplying 0.05 by 100% gives us a 5% increase in visitors from last year to this year.
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If 10 50-74 is written as an integer in base decimal notation, what is the sum of the digits in that integer?
Answer:
The required sum of the digits in that integer is 440.
Step-by-step explanation:
Consider the provided expression.
[tex]10^{50}-74[/tex]
We need to find the sum of the digits in that integer.
For [tex]10^2[/tex] = 100 (3 digits)
Now subtract 74 from it.
100-74=26
For [tex]10^3[/tex] = 1000 (4 digits)
Now subtract 74 from it.
1000-74=926
For [tex]10^4[/tex] = 100000 (5 digits)
Now subtract 74 from it.
10000-74=9926
Similarly,
[tex]10^50[/tex] = 1000....[51 digits]
Now subtract 74 from it.
[tex]10^50-74=99999....26[/tex]
The number of 9 after subtracting 74 is 3 less than the number of digits.
Therefore, the number of 9 after subtracting 74 from [tex]10^50[/tex] must be: 51-3=48
The sum of the digits is = 9×48 + 2 + 6 = 432 + 2 + 6 = 440.
Hence, the required sum of the digits in that integer is 440.
Final answer:
The sum of the digits in the integer 10⁵⁴ - 74 is 476, which is calculated by adding the contribution of the 52 nines and the digits in '26'.
Explanation:
To determine the sum of the digits of the integer written in base decimal notation for 10⁵⁴ - 74, we first need to understand what 10⁵⁴ represents. This value is a 1 followed by 54 zeros in decimal form. When we subtract 74 from this value, we alter only the last two non-zero digits. This results in a number that looks like 999...9926, where the '9's continue until the last two digits, which are '26'.
To find the sum of the digits, we simply add up the '9's and '26'. Since there are 52 nines (54 digits minus the last two which are '26'), and each nine contributes nine to the sum, we can calculate this part of the sum as 52 multiplied by 9. Then we also add the sum of the digits in '26'.
Therefore, the sum of digits in 10⁵⁴ - 74 is (52 × 9) + 2 + 6 = 468 + 8 = 476.
4n-12=12-4n(If there is no solution, type in "no solution") n= Answer
Answer:
n = 3
Step-by-step explanation:
Choose the correct graph of the given system of equations.
y + 2x = −1
3y − x = 4
A.) graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1
B.) graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1
C.) graph of two parallel lines with positive slopes with text on the graph that reads No Solution
D.) graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions
A.) graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1
Step-by-step explanation:
The two simultaneous equation given are;
y+2x= -1
3y-x=4
multiply the first equation by 1 and the second equation by 2 to make the terms with x equal
y+2x = -1
6y-2x=8
-------------- ---add the terms with x to eliminate x
7y=7 -------divide both sides by 7 to remain with y
7y/7 =7/7
y= 1 -----use the value of y in the first equation
y+2x= -1
1+2x= -1
2x= -2
2x/2= -2/2
x= -1
The solution is (-1,1)
You can plot the equations on a graph tool as shown below to visualize the solution where the two linear equations intersect
See attached graph
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graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1
The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?
Answer:
[tex]2\sqrt{2}\ ft\ longer[/tex]
Step-by-step explanation:
Area Of A Cube
Suppose a cube with side length s, the area of one side is
[tex]A_s=s^2[/tex]
Since the cube has 6 sides, the total area is
[tex]A=6A_s=6s^2[/tex]
But if we have the area, we can solve the above formula for s to get
[tex]A=6s^2[/tex]
[tex]\displaystyle s=\sqrt{\frac{A}{6}}[/tex]
We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths
[tex]\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}[/tex]
[tex]\displaystyle s_1=10\sqrt{2}\ ft[/tex]
[tex]\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}[/tex]
[tex]\displaystyle s_2=8\sqrt{2} ft[/tex]
The difference between them is
[tex]10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft[/tex]
The side of the cube with area 1,200 square inches is [tex]2\sqrt{2}\ ft[/tex] longer then the side of the cube with area 768 square inches
Answer:
Its B
Step-by-step explanation:
Edge 2021
A group of 40 children attend a baseball game. Each child received either a hotdog or a bag of popcorn. Hotdogs were $2.25 and popcorn was $1.75. If the total bill was $83.50, how many hotdogs and bags of popcorn were purchased
Answer:
27 hot dogs13 bags of popcornStep-by-step explanation:
Had all received popcorn, the bill would have been 40×$1.75 = $70. The bill was $13.50 more than that. Each hot dog purchased in place of popcorn adds $0.50 to the bill, so the number of hot dogs must be ...
$13.50/$0.50 = 27
Of course, the remainder of the 40 items were popcorn, so 13 bags of popcorn.
27 hot dogs and 13 bags of popcorn were purchased.
You have to decide between two different companies that sell dirt. Company A sells dirt for $137.5 for 50 square feet and has a delivery fee of $100 dollars. Company B sells dirt for $15 for 5 square feet and offers free delivery. How much dirt do you need to buy for both companies to charge the same.
You need to buy 400 square feet of dirt for both companies to charge the same
Solution:
Given that,
Company A sells dirt for $137.5 for 50 square feet and has a delivery fee of $100 dollars
Dirt sold for $137.5 for 50 square feet
Let us find dirt sold for 1 square feet:
50 square feet = $ 137.5
1 square feet = [tex]\frac{137.5}{50} = 2.75[/tex]
Thus dirt sold for $2.75 for 1 square feet
Company A has a delivery fee of $ 100 dollars
Amount Charged by company A:
Let "x" be the amount of dirt bought for 1 square feet
A = 2.75(x) + 100
A = 2.75x + 100 --- eqn 1
Company B sells dirt for $15 for 5 square feet and offers free delivery
Dirt sold for $ 15 for 5 square feet
5 square feet = $ 15
1 square feet = [tex]\frac{15}{5} = 3[/tex]
Thus dirt sold for $ 3 for 1 square feet
Company B offers free delivery
Amount Charged by company B:
A = 3x ---- eqn 2
Let us equate eqn 1 and eqn 2 to find the dirt you need to buy for both companies to charge the same
2.75x + 100 = 3x
3x - 2.75x = 100
0.25x = 100
x = 400
Thus you need to buy 400 square feet of dirt for both companies to charge the same
If f is a continuous function such that the integral from 1 to 4 of f of x, dx equals 10, evaluate the integral from 2 to 8 of 2 times f of 2 times x, dx.
Answer: 10
Step-by-step explanation:
Since integral from 1 to 4 of f(x) =10
To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method
Let U = 2x, dU = 2dx, dx = dU/2
Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.
Since this limit are the same as the limit for the question,
Therefore, F(4) - F(1) = F(8) - F(2) = 10
Substituting dx=dU/2
Gives,
Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10
Answer
Step-by-step explanation:
answer c
Arianna claims that the rectangles shown below are similar, while Miguel claims that they are not similar.
Whose claim is correct and why?
A
Miguel is correct because the two rectangles are not oriented in the same direction.
B
Arianna is correct because the four angles of the smaller rectangle are the same as the four angles of the larger rectangle.
C
Arianna is correct because the smaller rectangle has side lengths that are half the size of the side lengths of the larger rectangle.
D
Miguel is correct because the measures of the sides of the smaller rectangle are not proportional to the measures of the sides of the larger rectangle.
Answer:
D
Step-by-step explanation:
two jets leave an air base at the same time and travel in opposite directions. one jet travels 71 mih slower than the other. if the two jets are 5764 miles apart after 4 hours, what is the rate of each jet?
Answer:
Speed of Faster jet is 756 miles/hr and speed of slower jet is 685 miles/hr.
Step-by-step explanation:
Let the speed of faster jet be represent as 's'
Now Given:
one jet travels 71 mih slower than the other.
Hence Speed of slower jet will be = [tex]s-71[/tex]
Distance = 5764 miles
Time = 4 hrs
Now we know that;
Distance is equal to product of speed and time.
Framing in equation for we get;
Distance = (Speed of Faster Jet + Speed of Slower jet) × Time.
Substituting the given values we get;
[tex]5764=(s+s-71)\times 4\\\\5764= (2s-71)\times 4\\\\\frac{5764}{4} = 2s-71\\\\1441=2s-71\\\\2s=1441+71\\\\2s =1512\\\\s =\frac{1512}{2} = 756\ mi/h[/tex]
Speed of faster jet = 756 miles/hr
Speed of slower jet = [tex]s-71 =756-71 = 685\ mi/hr[/tex]
Hence Speed of Faster jet is 756 miles/hr and speed of slower jet is 685 miles/hr.
Now we will check the answer;
Distance traveled by faster jet = speed × time = 756 × 4 = 3024 miles.
Distance traveled by Slower jet = speed × time = 685 × 4 = 2740 miles
Hence Total Distance = 3024 + 2740 = 5764 miles.
The area of the bottom of a shoebox can be written as a(x) = 2x2 - 4 and the height of the shoebox can be written as h(x) = 3x + 2. write an expression to represent the volume v(x) of the shoebox.
a.v(x) = 6x3 - 8
Answer:V(x) = 6x³ + 4x² - 12x - 8
Step-by-step explanation:
The shoe box can either be cube shaped or cubiod shaped. The volume of the box is length × breadth × height
Since Area = Length × Breadth
Volume = Area × Height
V(x) = A(x) × H(x)
A(x) = 2x² - 4
H(x) = 3x + 2
V(x) = (2x² - 4)(3x + 2)
V(x) = 6x³ + 4x² - 12x - 8
.
Which of the following is NOT an arithmetic sequence?
A) 4, 7, 10, 13, 16
B) 1, 2, 3, 4, 5
C) 15, 9, 3, -3, -9
D) 2, 4, 8, 16, 32
Answer:
D) 2, 4, 8, 16, 32
Step-by-step explanation:
We have given four sets of sequence.
And we have to find out which sequence is not an arithmetic sequence.
For this the given sequences should satisfy the value of common difference(d) and Arithmetic Progression formula.
A.P. Formula,
[tex]T_n=a+(n-1)d[/tex]
Where [tex]T_n[/tex] = nth term of an A.P.
a = first term of an A.P.
n = number of terms.
d = common difference.
'd' is calculated by subtracting fist term from second term.
[tex]d = second\ term-first\ term[/tex]
A) 4, 7, 10, 13, 16
[tex]d = 7-4=3[/tex]
[tex]d = 10-7=3[/tex]
Here d=3 and 5th term is 16.
So we find out the 5th term by using the formula of A.P. To check whether the sequence is in A.P. or not.
[tex]T_5=4+(5-1)3=4+4\times\ 3=4+12=16[/tex]
Here the given sequence fulfills the condition of being in A.P.
Hence the given sequence is an arithmetic sequence.
B) 1, 2, 3, 4, 5
[tex]d =2-1=1[/tex]
[tex]d =3-2=1[/tex]
Here d=1 and 5th term is 5.
[tex]T_5=1+(5-1)1=1+4=5[/tex]
Here the given sequence fulfills the condition of being in A.P.
Hence the given sequence is an arithmetic sequence.
C) 15, 9, 3, -3, -9
[tex]d =9-15=-6[/tex]
[tex]d =3-9=-6[/tex]
Here d=-6 and 5th term is -9.
[tex]T_5=15+(5-1)-6=15+4\times -6=15+(-24)=-9[/tex]
Here the given sequence fulfills the condition of being in A.P.
Hence the given sequence is an arithmetic sequence.
D) 2, 4, 8, 16, 32
[tex]d_1=4-2=2[/tex]
[tex]d_2=8-4=4[/tex]
Here [tex]d_1=2\ But\ d_2=4[/tex]
The common difference between the terms is not same.
In case of [tex]d_1[/tex].
[tex]T_5=2+(5-1)2=2+4\times 2=2+8=10[/tex]
In case of [tex]d_2[/tex].
[tex]T_5=2+(5-1)4=2+4\times 4=2+16=18[/tex]
Here the given sequence does not fulfills the condition of being in A.P.
Hence the given sequence is not an arithmetic sequence.
Hence the correct option is D) 2, 4, 8, 16, 32.
Diane is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of English is Fun she sells. Suppose that x and y are related by the equation =+160090xy. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
1.What is the change in Mary's total pay for each copy of English is Fun she sells?
2.What is Mary's total pay if she doesn't sell any copies of English is Fun? ?
There is an error in the equation provided. Looking at other similar question such as this, I think the equation related to x and y should be 90x + 1600 = y
Answer:
a) 90
b) 1600
Step-by-step explanation:
The equation 90x + 1600 = y is an equation of a straight line in the form y = mc + c
Adjusting the equation to the general form we get
y = 90x + 1600
m = 90
c = 1600
a) the change in Mary's total pay for each copy she sells in this case is referring to the change of y to the change of x.
In other word, it is the slope of the function.
m = 90
b) if Mary didn't sell any copies, the value of x will be 0.
In graph of a straight line, the value when x= 0 is at the value of y-intercept,
c = 1600
After she creates the budget above, Zoe moves in with a roommate so she can save money for a car. Her rent is now 25 percent of her salary. Which of these should she do to buy a car quickly? Increase savings to 15 percent and increase entertainment to 20 percent Increase savings to 15 percent and increase gas to 15 percent Increase savings to 25 percent and decrease clothing to 10 percent Increase savings to 30 percent?
Answer:
Increase savings to 25 percent and decrease clothing to 10 percent
Step-by-step explanation:
i got it right
Zoe should increase her savings to 25% of her income and reduce non-essential expenses like clothing to save for a car more quickly.
Explanation:To assist Zoe in saving money for a car quickly after moving in with a roommate and having her rent reduced to 25% of her salary, she should adjust her budget to allocate more towards savings.
The most effective strategy for this goal would be to:
Increase savings to a higher percentage of her income.Reduce or maintain other expense categories at a lower percentage to compensate for the increased savings.Specifically, increasing savings to 25% of her income and decreasing clothing expenses to 10% is an advisable option.
She should avoid increasing expenses in non-essential categories like entertainment or gasoline if her goal is to save for a car as quickly as possible.
Let R and S be partial orders on a nonempty set A prove that T = R intersection S is also a partial order on A.
Answer:
See proof below
Step-by-step explanation:
We denote (x,y)∈R as xRy, and we also use the similar notation xSy for (x,y)∈S. Remember that R and S are reflexive, antisymmetric and transitive relations (the definition of partial order).
To prove that R∩S⊆A is a partial order, we will prove that R∩S is reflexive, antisymmetric and transitive.
Reflexive: Let a∈A. R is reflexive thus aRa. S is also reflexive, then aSa. Then (a,a)∈R and (a,a)∈S which implies that (a,a)∈R∩S, that is, a(R∩S)a for all a∈A.Antisymmetric: Let a,b∈A and suppose that a(R∩S)b and b(R∩S)a hold. In particular, aRb and bRa. Since R is antisymmetric, a=b.Transitive: Let a,b,c∈A and suppose that a(R∩S)b and b(R∩S)c hold. Then aRb, bRc, aSb and bSc are true. The first two statements imply by the transitivity of R that aRc. Similarly, from the last two we have that aSc. Thus a(R∩S)c as we wanted to prove.Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest. If that interest was approximately 6.5 percent of the bond's selling price, approximately what was the bond's selling price?A. $4,063
B. $5,325
C. $5,351
D. $6,000
E. $6,154
Answer:
E. $6,154
Step-by-step explanation:
Let x represent selling price of the bond.
We have been given that last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest.
Let us calculate 8% of $5,000 to find amount of interest as:
[tex]\text{Amount of interest }=\$5,000\times \frac{8}{100}[/tex]
[tex]\text{Amount of interest }=\$50\times 8[/tex]
[tex]\text{Amount of interest }=\$400[/tex]
We are also told that the amount of interest was approximately 6.5 percent of the bond's selling price. 6.5 percent of the bond's selling price would be [tex]\frac{6.5}{100}x[/tex].
We can represent our given information in an equation as:
[tex]\frac{6.5}{100}x=\$400[/tex]
[tex]100*\frac{6.5}{100}x=\$400*100[/tex]
[tex]6.5x=\$40,000[/tex]
[tex]\frac{6.5x}{6.5}=\frac{\$40,000}{6.5}[/tex]
[tex]x=\$6,153.846153846[/tex]
[tex]x\approx \$6,154[/tex]
Therefore, the selling price of the bond was approximately $6,154 and option E is the correct choice.
A group of 444 friends is playing cards. The deck has 707070 cards. To start the game, the dealer makes a pile of 151515 cards in the center. Then she deals the remaining cards one at a time to each player until all the cards are gone. What is the greatest number of cards any player will have after all the cards are dealt?
Answer:
The correct answer is 14 not 17 or 7
Step-by-step explanation:
Howdy! Id love to have these questions answered asap! Thank you for the help!
1) Which angle is not coterminal to 120 degrees?
A. 840
B. -180
C. 480
2) Use the unit circle and the reference angle to determine which of the following trigonometric values is correct when theta = -90
A. Cos theta = undefined
B. Sin theta = -1
C. Tan = 0
1) Which angle is not coterminal to 120 degrees?
A. 840
B. -180
C. 480
Answer:From given options, -180 is not a coterminal angle of 120 degrees
Solution:Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians
Coterminal angles of 120 degrees are:
120 degrees + 360 degrees = 480 degrees
120 degrees - 360 degrees = 240 degrees
720 degrees + 120 degrees = 840 degrees
120 degrees - 720 degrees = -600 degrees
Therefore:
Positive Angle 1 (Degrees) 480
Positive Angle 2 (Degrees) 840
Negative Angle 1 (Degrees) -240
Negative Angle 2 (Degrees) -600
Therefore from given options, -180 is not a coterminal angle of 120 degrees
2) Use the unit circle and the reference angle to determine which of the following trigonometric values is correct when theta = -90A. Cos theta = undefined
B. Sin theta = -1
C. Tan theta = 0
Answer:Sin theta = -1 is correct
Solution:given angle is -90
Find the reference angle for -90
Reference angle = 360 - 90 = 270 degrees
Unit circle diagram is attached below
And from the unit circle, we know the coordinates for 270 degrees are (0, -1)
Our angle - 90 degrees lies in (0, -1)
Unit circle coordinates are given by [tex](cos \theta , sin \theta )[/tex]
This means,
cos (-90 ) = 0 and sin(-90) = -1
We know that,
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
[tex]tan \theta = \frac{-1}{0}[/tex] = undefined
Therefore from options, sin theta = -1 is correct
Martina will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $54 and costs an additional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?
Answer:
100 miles
Step-by-step explanation:
Let
x ----> the number of miles driven
y ---> the total cost
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value
In this problem we have
First Plan
The slope is equal to [tex]m=\$0.15\ per\ mile[/tex]
The y-intercept is [tex]b=\$54[/tex]
so
The linear equation is
[tex]y=0.15x+54[/tex] -----> equation A
Second Plan
The slope is equal to [tex]m=\$0.10\ per\ mile[/tex]
The y-intercept is [tex]b=\$59[/tex]
so
The linear equation is
[tex]y=0.10x+59[/tex] -----> equation B
To find out for what amount of driving do the two plans cost the same, equate equation A and equation B
[tex]0.15x+54=0.10x+59[/tex]
solve for x
[tex]0.15x-0.10x=59-54[/tex]
[tex]0.05x=5[/tex]
[tex]x=100\ miles[/tex]
Find the cost
for x=100 miles
substitute in equation A or equation B (the cost is the same)
[tex]y=0.15(100)+54=\$69[/tex]
Final answer:
The two car rental plans cost the same for 100 miles driven. To find this, the total cost equations for both plans are set equal to each other, and the resulting equation is solved for the number of miles.
Explanation:
To determine when the two car rental plans cost the same, we need to set up and solve an equation where the total costs of both plans are equal. We will let x represent the number of miles driven.
Cost Equations for Two Plans:
Plan 1: $54 + $0.15x
Plan 2: $59 + $0.10x
To find where they cost the same, we set the cost equations equal to each other:
54 + 0.15x = 59 + 0.10x
We then solve for x by first subtracting $0.10x from both sides:
54 + 0.05x = 59
Next, we subtract $54 from both sides:
0.05x = 5
Finally, we divide both sides by 0.05:
x = 100
Therefore, the two plans cost the same when Martina drives 100 miles.
I really need help ASAP
Answer choices: 101,19,50,60,79
A=
B=
C=
D=
E=
Answer:
Step-by-step explanation:
1) The sum of the angles on a straight line is 180 degrees. This means that
51 + b + 110 = 180
161 + b = 180
b = 180 - 161 = 19 degrees
2) Angle a = 60 degrees. This is so because they are vertically opposite angles.
3)The sum of angles in a triangle is 180 degrees. Therefore
angle a + angle b + angle c
60 + 19 + c = 180
79 + c = 180
c = 180 - 79 = 101 degrees
4) d + c = 180(sum of the angles on a straight line is 180 degrees). Therefore
d + 101 = 180
d = 180 - 101 = 79 degrees.
5) e + 51 + b + a = 180( sum of the angles in a triangle is 180 degrees). Therefore
e + 51 + 60 + 19 = 180
e + 130 = 180
e = 180 - 130 = 50 degrees
Statistics show that ________ of homeless adults living in shelters experience mental illness.
Answer:
26%
Step-by-step explanation:
For similar questions check the following link for flash cards:
https://quizlet.com/207660833/chapter-16l23-25-flash-cards/
The question is about the incidence of mental illness among homeless adults in shelters. The specific percentage is not provided, but the rate is recognized as high, indicating the need for mental health resources to effectively address homelessness.
Explanation:The question you've asked is related to the prevalence of mental illness among homeless adults residing in shelters. A specific percentage is not given, but it is commonly understood that a significant percentage of the homeless population does struggle with mental illness. However, it is essential to note that the exact percentage can vary due to different factors, such as location, available resources, and demographics. Hence, this information accentuates the need for mental health resources in addressing and alleviating homelessness.
Learn more about Mental Illness here:https://brainly.com/question/33861241
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Jane had 27 stickers two weeks ago. She was buying stickers each day for those two weeks. She bought 3 stickers two weeks ago, and on each day she bought two more stickers than she bought on the previous day. How many stickers does she have now?
Answer:
At Present Jane has Total Stickers = 251
Step-by-step explanation:
Stickers Initially = 27
Jane bought stickers on 1st day = 3
Remaining days = 13
Each next day she bought 2 more stickers than the previous day, so:
Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))
here n =3
So:
Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29
Stickers bought in the last 2 weeks (14 days) = 224
At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)
At Present Jane has Total Stickers = 27+224
At Present Jane has Total Stickers = 251
The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min. t (min) 0 0.5 1 1.5 2 2.5 3 r (l/min) 44 40 37 34 30 27 23
Answer:
100.75 liters
Step-by-step explanation:
Data provided in the question:
t (min) 0 0.5 1 1.5 2 2.5 3
r (l/min) 44 40 37 34 30 27 23
Now,
left endpoint approximation
= 0.5 × ( 44 + 40 + 37 + 34 + 30 + 27 )
= 0.5 × 212
= 106
Right endpoint approximation
= 0.5 × ( 40 + 37 + 34 + 30 + 27 + 23 )
= 0.5 × 191
= 95.5
Therefore,
the average of the left- and right-endpoint approximations
= [ 106 + 95.5 ] ÷ 2
= 100.75 liters
The total amount of water drained during the first 3 min is: 100.75 liters/min.
Total amount of waterLeft endpoint approximation
r = 1/2 ( 44 + 40 + 37 + 34 + 30 + 27 )
r= 1/2 × 212
r= 106 L/m
Right endpoint approximation
r= 1/2 × ( 40 + 37 + 34 + 30 + 27 + 23 )
r= 1/2 × 191
r= 95.5 L/min
Average of the left- and right-endpoint approximations
Average= [ 106 + 95.5 ] ÷ 2
Average=201.5÷2
Average= 100.75 liters/min
Inconclusion the total amount of water drained during the first 3 min is: 100.75 liters/min.
Learn more about total amount of water here:https://brainly.com/question/26007201
Cans of regular Coke are labeled as containing 12 oz12 oz. Statistics students weighed the contents of 88 randomly chosen cans, and found the mean weight to be 12.0912.09 ounces. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz12.00 oz and a standard deviation of 0.1 oz0.1 oz. Find the probability that a sample of 88 cans will have a mean amount of at least 12.09 oz12.09 oz.
Answer: 0.0055
Step-by-step explanation:
Let [tex]\overline{x}[/tex] denotes the sample mean amount that can has.
We assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.1 oz.
i.e. [tex]\mu=12[/tex] and [tex]\sigma=0.1[/tex]
sample size : n= 8
Then, the probability that a sample of 88 cans will have a mean amount of at least 12.09:
[tex]P(\overline{x}\geq12.09)=1-P(\overline{x}<12.09)\\\\=1-P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{12.09-12}{\dfrac{0.1}{\sqrt{8}}})\\\\=1-P(z<2.5456)\ \ [\because z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9945\ \ [\text{By z-table}]\\\\=0.0055[/tex]
Hence, the required sample size = 0.0055
Which choice could be the equation of a line parallel to the line represented by this equation?
3x− 2y = 6
a. 2x− 3y = 6
b. y=3/2x+4
c. 5x− y = −2
d. y=2/3x-8
A cylinder has radius r and height h how many times greater is the surface area of a cylinder when both dimensions are multiplied by a factor of 2?3?5?10?
Answer:
Correct answer: 4, 9, 25, 100
Step-by-step explanation:
Surface area of cylinder A = 2r²π + 2rπ h = 2rπ (r+h)
r₁ = 2r and h₁ = 2h => A₁ = 2 (2r) π (2r+2h) = 2 2rπ 2(r+h) = 4 2rπ (r+h)
A₁ = 4 A
r₁ = 3r and h₁ = 3h => A₁ = 2 (3r) π (3r+3h) = 3 2rπ 3(r+h) = 9 2rπ (r+h)
A₁ = 9 A and so on......
God is with you!!!
A necklace at Jared is originally $99. It is on sale for 10% off. If there is a 3% tax on the DISCOUNTED PRICE, what is the total price of the necklace? Round to the nearest cent!
Answer: the total price of the necklace is $91.8
Step-by-step explanation:
The original Price of the necklace at Jared is is $99. It is on sale for 10% off. This means that there is a discount on the original price. The discount is 10/100 × 99 = $9.9
The new price of the necklace at Jared is the original price - the discount. It becomes
99 - 9.9 = $89.1
If there is a 3% tax on the discounted price, the amount of tax would be 3/100×89.1 = $2.673
The total cost of the necklace will be new cost + the amount of tax. It becomes
89.1 + 2.673 = $91.8
Find the regression equation, letting the first variable be the
predictor (x) variable.
Using the listed duration and interval after times, find the best predicted "interval after" time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption with a duration of 253 seconds and an interval after time of 83 minutes?
Duration - 242 - 255 - 227 - 251 - 262 - 207 - 140
Interval After - 81 - 81 - 92 - 102 - 94 - 91
Answer:
[tex]y=0.00673(253) +90.190=91.894[/tex]
And the difference is given by:
[tex]r_i =91.894-83=8.894[/tex]
Step-by-step explanation
We assume that th data is this one:
x: 242-255 -227-251-262-207-140
y: 91- 81 -91 - 92 - 102 - 94 - 91
Find the least-squares line appropriate for this data.
For this case we need to calculate the slope with the following formula:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i =242+255+227+251+262+207+140=1584[/tex]
[tex]\sum_{i=1}^n y_i =91+ 81 +91 + 92 + 102 + 94 + 91=642[/tex]
[tex]\sum_{i=1}^n x^2_i =242^2 +255 ^2 +227^2 +251^2 +262^2 +207^2 +140^2=369212[/tex]
[tex]\sum_{i=1}^n y^2_i =91^2 + 81 ^2 +91 ^2 + 92 ^2 + 102 ^2 + 94 ^2 + 91^2=59108[/tex]
[tex]\sum_{i=1}^n x_i y_i =242*91 +255*81 +227*91 +251*92 +262*102 +207*94 +140*91=145348[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=369212-\frac{1584^2}{7}=10775.429[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=145348-\frac{1584*642}{7}=72.571[/tex]
And the slope would be:
[tex]m=\frac{72.571}{10775.429}=0.00673[/tex]
Now we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{1584}{7}=226.286[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{642}{7}=91.714[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=91.714-(0.00673*226.286)=90.190[/tex]
So the line would be given by:
[tex]y=0.00673 x +90.190[/tex]
The prediction for 253 seconds is:
[tex]y=0.00673(253) +90.190=91.894[/tex]
And the difference is given by:
[tex]r_i =91.894-83=8.894[/tex]