For two statements p and q, and the compounded statement "If p, then q", we have the following definitions for the inverse, converse, and contrapositive of this compounded statement:
inverse: If not p, then not q.
converse: If q, then p.
contrapositive: If not q, then not p.
So, for the presented statement, i. e., "If you will be driving, then you should not take this medicine" we have:
p: you will be driving
q: you should not take this medicine
Notice that:
not p: you will not be driving
not q: you may take this medicine
Then, using the above definitions, we write:
inverse: If you will not be driving, then you may take this medicine.
converse: If you should not take this medicine, then you will drive.
contrapositive: If you may take this medicine, then you will not be driving.
Find the slope and the x- & y-intercepts of x + 2y = 6(5 pts) (Show work for finding X- & y-intercepts)
First, we need to write our equation in standard form — the y should be on the left- hand - side and the x should be on the right- hand side.
The first step is to subtract x from both sides, doing this we get:
[tex]2y=6-x[/tex]Now we divide both sides of the equation by 2 (this isolates the y on LHS), doing this gives us:
[tex]y\text{ = }\frac{6-x}{2}[/tex]which can also be written as
[tex]y=\frac{-x}{2}+3[/tex]The y-intercept is the point at which the line described by our equation intersects the y-axis. This intersection happens when x = 0; therefore, the y-intercept is
[tex]y=\frac{-0}{2}+\text{ 3}[/tex][tex]y=0\text{.}[/tex]The x-intercept is the point at which the line intersects the x-axis. This happens when y =0; therefore, the x-intercept is
[tex]0=\frac{-x}{2}+3[/tex][tex]-3\text{ = }\frac{-x}{2}[/tex][tex]x\text{ = 6.}[/tex]Now we see that the slope of the equation is -1/2 (the coefficient of x ). The y-intercept is y = 3 and the x-intercept is 6.
Seventeen percent of people say they've seen a ghost or felt its presence. If 10 people are asked, what is the probability that at least two have seen a ghost or felt its presence?Round your answer to at least three decimals.
Answer: the probability that at least two have seen a ghost or felt its presence is 0.527
Explanation:
In this scenario, it is either a person asked has seen seen a ghost or felt its presence or they have not. These outcomes are independent of each other. Thus, it's a binomial distribution. We would apply the formula for calculating binomial probability which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
p = probability of success
q = 1 - p = probability of failure
n = sample size
x = number of successes
From the information given, we are concerned with the people that say they've seen a ghost or felt its presence. Thus,
p = 17% = 17/100 = 0.17
q = 1 - 0.17 = 0.83
n = 10
x = 2
We want to find P(x ≥ 2)
P(x ≥ 2) = 1 - [P(x = 0) + P(x = 1)
P(x = 0) = 10C0 * 0,17^0 * 0.83^(10 - 0) = 0.1552
P(x = 1) = 10C1 * 0,17^1 * 0.83^(10 - 1) = 0.3178
P(x ≥ 2) = 1 - (0.1552 + 0.3178) = 1 - 0.473
P(x ≥ 2) = 0.527
the probability that at least two have seen a ghost or felt its presence is 0.527
If A and B are supplementary angles and A is nine times as large as B, find the measures of A and B.
Supplementary angles add up to 180°
A+ B = 180
A is 9 times as large as B.
A = 9B
We have the system of equations:
A+ B = 180
A = 9B
Put the second equation into the first one, and solve for B
(9B)+ B = 180
10B = 180
B= 180/10
B = 18
Replace the value of B on any equation and solve for A:
A = 9B
A= 9(18)
A= 162
A= 162°
B=18°
f(x+h)-f(x)
h
lim:
h→0
i) The average rate of change of f(x) over the interval [x, x + h]
ii) The slope of the line tangent to f(x) at the point (x, f(x))
iii) The slope of the line secant to f(x) over the interval [x, x + h]
iv) The derivative of f(x)
O A. ii and iii
O B. i and iii
O c. ii
OD. i
...
O E.
i and iv
O F. ii and iv
Answer: F
Step-by-step explanation:
(i) The interval is meant to have infinitesimal width because the limit is approaching 0.
(ii) This gives the derivative at [tex](x, f(x))[/tex], which is the same as the slope of the tangent line.
(iii) False, this deals with the tangent line, not the secant.
(iv) True by definition.
In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T(a,0). What are the coordinates of S?A. (a, b)B. (a+b, d)C. (a+b, b)D. (a, d)
In a parallelogram, the opposite sides are parallel.
This means that RS is parallel to OT. So, the y value of S is the same as the y value of R, which is d, so y = d. Thus:
[tex]S=(x,y)=(x,d)[/tex]Now, we need to find x.
Since the sides RO and ST are also parallel, the x distance from O to R is the same as the x distance from T to S.
The x distance from O to R is
[tex]b-0=b[/tex]The x distance from T to S is
[tex]x-a[/tex]Since these x distances are equal, then:
[tex]\begin{gathered} b=x-a \\ x=a+b \end{gathered}[/tex]Then, the coordinates of S are:
[tex](a+b,d)[/tex]Which corresponds to option B.
About how much more is the total weight of the pacific halibut and conger than the weight of the yellowfin tuna ? Explain
The weight of pacific halibut is 459 pounds and weight of yellowfin tuna is 387 pounds.
There is 72 pounds more is the total weight of pacific halibut than the yellowfin tuna.
How many 7 digit phone numbers can be created if the first digit cannot be a zero, and the lastnumber must be an odd number?
Given:
Number of digits = 7
The first digit cannot be zero
Last number = odd number
The possible numbers between other than zero is 9
and there are 5 odd numbers.
Hence, the number of possible combinations is:
[tex]\begin{gathered} =\text{ 9 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 5} \\ =\text{ 4500000} \end{gathered}[/tex]Answer: Option A
determine the interview on which the function is concave upward and concave downward
We have to identify the intervals where the function is concave upwards and where is concave downward.
We can differentiate them in a graph as:
We then have only one interval where the function is concave upwards: between x = -1 and x = 4. We can identify other intervals where the function is concave downwards and interrupted by discontinuities.
Then, we can write all the intervals as:
[tex]\begin{gathered} (-\infty,-5)\longrightarrow\text{Concave downward.} \\ (-5,-1)\longrightarrow\text{Concave downward.} \\ (-1,4)\longrightarrow\text{Concave upward}. \\ (4,\infty)\longrightarrow\text{Concave downward.} \end{gathered}[/tex]Graph the image of rectangular TUVW after a translation 5 units right and 4 units up.
From the rectangle TUVW, the coordinates of the points are shown below:
T(-5, -5), U(-1, -5), V(-1, 4), and W(-5, 4)
If TUVW is translated 5 units right and 4 units up, the coordinates of the new rectangle are in the form (x+5, y+4):
T'(0, -1), U'(4, -1), V'(4, 8), and W'(0, 8)
A credit card bill for $562 was due on September 14. Purchases of $283 were made on September 19, and $12 was charged on September 28. A payment of $350 was made on September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year. Round your answer to the nearest cent.)
The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).
So, the finance charge will be;
(+) $ 562 due on sep 14, $ 562 x (19.5 x31) / (100 x 365) = $ 9.20
(+) purchase $ 283 on Sep 19, $ 283 x (19.5x26 ) / (100 x365) = $ 2.42
(+) finance charge on sep 28, $ 18 x(19.5 x17 ) / (100 x 365) = $ 0.17
(-) Repayment on 25 sep , $ 250 x (19.5 x20 ) / (100 x 365) = (2.745)
Finance charges from 14 sep to 14 oct will be $ 9.7= appr. 10
The Amount due on 14 October = $562 +$283 +$15+$11.855- $250
= $ 623
Therefore, The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623
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If r is the nominal rate and n is the number of times interest is compounded annually, then R=(1+r/n)^(n)-1 is the effective rate. Here, R represents the annual rate that the investment would earn if simple interest were paid. Use this formula to determine the effective rate for $1 invested for 1 year at 4.8% compounded semiannually.
Effective Rate in Compound Interest
Given r as the nominal rate of investment and n the number of times the interest is compounded annually, the formula for the effective rate is:
[tex]R=\mleft(1+\frac{r}{n}\mright)^n-1[/tex]We are required to find the effective rate for a rate of r=4.8% compounded semiannually. This means the value of n is 2 since there are two periods where interest is added to the principal per year.
Substituting the given values in the formula (recall r must be used as a decimal value, i.e. r=4.8/100=0.048):
[tex]R=(1+\frac{0.048}{2})^2-1[/tex]Calculating:
[tex]R=(1.024)^2-1=0.048576[/tex]The effective rate is 4.86%
Kyree needs to fill up his truck with gasoline to drive to and from school. Gas costs $2.79 per gallon, and his truck holds a maximum of 28 gallons.Domain:Range:
Let x represent the cost per gallon of gasoline.
Let y or f(x) represent the cost of x gallons of gasoline.
Given that the cost per gallon is $2.79,
The function would be
f(x) = 2.79x
The domain refers to all possible values of x that can fit into the function. Given that the truck holds a maximum of 28 gallons, the maximum value of x is 28. When the truck is empty, the minimum value of x is 0. Therefore, the domain is 0 to 28
The range refers to all possibel values of y or f(x) that can satisfy the function.
When x = 0, f(x) = 2.79 * 0 = 0
When x = 28, f(x) = 2.79 * 28 = 78.12
The range would be 0 to 78.12
Domain: 0 to 28
Range: 0 t0 78.12
What is the probability of rolling a 2 or a 3 when rolling a fair six-sided die?
Answer:
It would be a 2/6 chance, or a 1/3 chance.
Step-by-step explanation:
Angles A and B are supplementary angles. The measure of angle A is
73∘
What is the measure of angle B?
Answer:
17
Step-by-step explanation:
73+b=90
b=90-73
b=17
22 8(11 + 2r) = 126r + 3
8(11 + 2r) = 126r + 3
first open the parenthesis
88 + 16r = 126r + 3
88 - 3 = 126r - 16 r
85 = 110r
divide both-side of the equation by 110
85/110 = r
r= 17/22
which of the following properly describes "slope"? select all that apply. A. y2 - y1/ x2 - x1 B. x2-x1/y2-y1 C. run/rise D. rise/run E. ratio of change in y values (rise) for a segment of the graph to the corresponding change in x values (run)
The formula to calculate the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A is right
also, the slope can be calculated with rise and run
[tex]m=\frac{rise}{run}[/tex]the correct formula is D.
and also apply E
the answer will be A,D and E
Forty percent of 90 is what number
90 represents the 100%
Let's call x to the number that represents the 40%
To find the 40%, we can use the next proportion:
[tex]\frac{90}{x}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 90\cdot40=100\cdot x \\ \frac{3600}{100}=x \\ 36=x \end{gathered}[/tex]36 is 40% of 90
What is the mean of 3x, 4x - 5 and 2x - 1?
The American Water Works Association reports that the per capita water use in a single-family home is 69 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day.
At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?
What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0: µ ≥ 69 when the test statistic is less than ____.
a. The decision rule for this question would be to reject the null hypothesis if test statistic is less than the critical value.
b. The test statistic is given as: -3.4091
What is the hypothesis?We have the null hypothesis as
h0 : μ ≥ 69
The alternate hypothesis is
H1 : μ < 69
a. The decision rule would be to reject the null if the test statistic is greater than the critical value
at α = 0.10 the degree of freedom = 36 - 1 = 35
the critical value is -1.306
The test statistic calculation
[tex]t =\frac{ x - u}{s/\sqrt{n} }[/tex]
[tex]t = \frac{64-69}{8.8/\sqrt{36} }[/tex]
t = -3.4091
The decision rule would be to Reject H0: µ ≥ 69 when the test statistic is less than -1.306.
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Which of the following are mathematical sentences? Check all that apply. A. 34 B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1
The mathematical sentences that can be found in the sentence are:
B. r + 7 = 4 C. 5g = 9 D. 4x E. 8r = 12 F. x = 1What are mathematical sentences?A mathematical sentence can be described as the statement that comprises the two expressions nor more than two expression.
It should be noted that these two expressions can make use of the numbers as well as the variables and in some of the cases combination of them however the mathematical sentence do encompass the symbols which could be inform of equals, greater than, as well as less than.
Therefore, the options that are examples of mathematical sentences are option B C D E F.
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The mathematical sentences which can be found in the sentence are;
B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1
What are mathematical sentences?A mathematical sentence can be described as a statement that comprises two expressions or more than two expressions.
Expression can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Remember that these two expressions can make use of the numbers as well as the variables and in some cases a combination of them however the mathematical sentence does encompass the symbols which could be in form of equals, greater than, as well as less than.
Hence, the options that are examples of mathematical sentences are ; B. r + 7 = 4, C. 5g = 9, D. 4x, E. 8r = 12 and F. x = 1
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What are three ratios equivalent to 9/5?
The given ratio is 9/5
This ratio is already in the simplified form. To find equivalent ratios, we would multiply the numerator and denominator by constant numbers. We have
If we multiply by 2, it becomes
9 * 2/5 * 2 = 18/10
If we multiply by 3, it becomes
9 * 3/5 * 3 = 27/15
If we multiply by 4, it becomes
9 * 4/5 * 4 = 36/20
Thus, three equivalent ratios are
18/10, 27/15 and 36/20
The electronics company makes two types of switches. Type a takes 4 minutes to make and requires $3 worth of materials.Type b takes 5 minutes to make and requires $5 of materials. In the latest production bath, it took 32 hours to make these switches and the materials cost 1740. How many of each type of switch was made?
Let
x ------> number of switch type A
y -----> number of switch type B
so
Remember that
1 hour=60 min
32 hours=32*60=1,920 minutes
4x+5y=1,920 -------> equation 1
3x+5y=1,740 ------> equation 2
Solve the system of equations
Solve by graphing
using a graphing tool
see the attached figure
Solution is
x=180
y=240
therefore
the number of switch type A was 180the number of switch type B was 240I'm not sure what to do for this question I have already tried could you help me with this?
1) Take into account that a linear relation can be written as follow:
y = mx + b
where m is the slope of the line and the constant b the y-coordinate of the y-intercept.
Due to Rocco started to count from a distance of 4 miles, this is a constant number, which is equivalent to b, that is, b = 4.
If the constant rate of the walk is 3 miles per 2 hours, then, m = 3/2 (because the slope is also a constant rate of change).
Then, you have the following linear equation for the relation between the distance traveled by Rocco and the time.
y = 3/2*x + 4
y is the number of miles of the Rocco walking
x is the time (in hours) he takes for the walking
2) Now, based on the previous equation, you have for the table:
3) The relation between the given variables is proportional because a change in x makes that y changes too.
The distance traveled by Rocco is given by the value of y when x = 4. As you can notice on the table, such a distance is 10 miles.
You have been tracking an adult female Australian flatback sea turtle who weighs 25 kg. How many kilocalories must she consume each day to maintain her body weight?
The kilocalories that she must consume each day to maintain her body weight is 6250 kilocalories.
How to calculate the value?From the information, the person has been been tracking an adult female Australian flatback sea turtle who weighs 25 kg.
It should be noted that the requirements is 250kcal per kilograms.
Therefore, the calories will be:
= Weight × Required calories
= 250 × 25
= 6250 kcaloriies
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Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY = NW No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent. Yes; two opposite sides are both parallel and congruent. Yes; diagonals of a parallelogram bisect each other.
A parallelogram is a quadrilateral that has the following characteristics:
The opposite sides are parallel and congruent.
The opposite angles are congruent.
The consecutive angles are supplementary.
If any one of the angles is a right angle, then all the other angles will be at right angle.
The two diagonals bisect each other.
Since:
[tex]XN\cong NZ;NY\cong NW[/tex]We can conclude that the answer is:
Yes; diagonals of a parallelogram bisect each other.
Hello! I need some assistance with this homework question, pleaseQ12
Answer:
A(-1,4) and B(2,0)
Step-by-step explanation:
The quadratic parabola equation is represented as;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':
[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]Hence, the equation for the parabola:
[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]Now, for the line since it is a horizontal line, the equation would be:
[tex]g(x)=5[/tex]Then, for (f+g)(x):
[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]Then, the graph for the composite function and the points that lie on the graph:
A(-1,4) and B(2,0)
Graph the reflection of the polygon in the given line #5 Y=2
We have the next image
the line of reflection is the line in red
the original polygon ABCD is the one in blue
the reflected polygon A'B'C'D' is the one in green
justify proposes each step
the answer is associative property of multiplicaction
because
A*(B*C)=(A*B)*C
A random survey of 10 students recorded their number of hours of activity each week and their Body Mass Index (BMI). The results are shown in the table below. Student Body Mass Number of Hours of Activity Each Week Index Which of the following best describes the data? O linear positive association linear negative association no association O non-linear association
According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.
Hence, the answer is D.question 18:Evaluate: summation from n equals 2 to 8 of 12 times 4 tenths to the n plus 1 power period Round to the nearest hundredth. (1 point)
Given:
[tex]\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]Required:
Sum of the numbers
Explanation:
Let
[tex]A_n=\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]when n = 2, Aₙ becomes
[tex]A_2=12(0.4)^{2+1}=12\times(0.4)^3=0.768[/tex]when n = 3, Aₙ becomes
[tex]A_3=12(0.4)^{3+1}=12\times(0.4)^4=0.3072[/tex]when n = 4, Aₙ becomes
[tex]A_4=12(0.4)^{4+1}=12\times0.4^5=0.12288[/tex]
when n = 5, Aₙ becomes
[tex]A_5=12(0.4)^{5+1}=12\times0.4^6=0.049152[/tex]when n = 6, Aₙ becomes
[tex]A_6=12(0.4)^{6+1}=12\times0.4^7=0.0196608[/tex]when n = 7, Aₙ becomes
[tex]A_7=12(0.4)^{7+1}=12\times0.4^8=0.007866432[/tex]when n = 8, Aₙ becomes
[tex]A_8=12(0.4)^{8+1}=12\times0.4^9=0.003145728[/tex]So now,
[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8 \\ \\ A=0.768+0.3072+0.12288+0.049152+0.0196608+0.00786432+0.003145728 \\ \\ A=1.277902848\approx1.28 \end{gathered}[/tex]Final answer:
The