`Both Meg and Cassandra are incorrect in their assessments (option a).
Meg and Cassandra have both misunderstood the logical relationships between the statements. Let's analyze each statement and compare their claims:
Statement 1: "If she is stuck in traffic, then she is late."
Statement 2: "If she is late, then she is stuck in traffic."
Statement 3: "If she is not late, then she is not stuck in traffic."
Meg's claims: Meg states that Statement 3 is the inverse of Statement 2 and the contrapositive of Statement 1. However, this is incorrect. The inverse of Statement 2 would be "If she is not stuck in traffic, then she is not late," and the contrapositive of Statement 1 would be "If she is not late, then she is not stuck in traffic." So Meg's analysis is incorrect.
Cassandra's claims: Cassandra states that Statement 2 is the converse of Statement 1 and the inverse of Statement 3. However, this is also incorrect. The converse of Statement 1 would be "If she is late, then she is stuck in traffic," and the inverse of Statement 3 would be "If she is late, then she is stuck in traffic." So Cassandra's analysis is incorrect as well.
Therefore, both Meg and Cassandra are wrong in their assessments. The correct logical relationships are as follows:
- The contrapositive of Statement 1 is Statement 3.
- The converse of Statement 1 is Statement 2.
Hence, the correct answer is that both Meg and Cassandra are incorrect.
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Ralph chase plans to sell a piece of property for $145000. He wants the money to be paid off in two ways-short term note at 10% interest and a long term note at 8% interest. Find the amount of each note if the total annual interest paid is $13100.
10%:
8%:
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the amount of money Ralph Chase will receive through the short-term note is represented by "x" and the amount through the long-term note is represented by "y".
According to the problem, the total amount Ralph plans to sell the property for is $145,000. Therefore, we have the equation:
[tex]\displaystyle x+y=145000[/tex] ...(1)
Now let's consider the interest paid annually. The interest paid on the short-term note at 10% is calculated as [tex]\displaystyle 0.10x[/tex], and the interest paid on the long-term note at 8% is [tex]\displaystyle 0.08y[/tex]. The total annual interest paid is given as $13,100. Therefore, we have the equation:
[tex]\displaystyle 0.10x+0.08y=13100[/tex] ...(2)
We now have a system of two equations (1) and (2). We can solve this system to find the values of "x" and "y".
Multiplying equation (2) by 100 to eliminate decimals, we get:
[tex]\displaystyle 10x+8y=1310000[/tex] ...(3)
Now we can solve equations (1) and (3) simultaneously using any method such as substitution or elimination.
Multiplying equation (1) by 10, we get:
[tex]\displaystyle 10x+10y=1450000[/tex] ...(4)
Subtracting equation (3) from equation (4), we can eliminate "x" and solve for "y":
[tex]\displaystyle 2y=140000[/tex]
Dividing both sides by 2, we find:
[tex]\displaystyle y=70000[/tex]
Now substituting the value of "y" back into equation (1), we can solve for "x":
[tex]\displaystyle x+70000=145000[/tex]
Subtracting 70000 from both sides, we have:
[tex]\displaystyle x=75000[/tex]
Therefore, the amount of money Ralph Chase will receive through the short-term note is 75,000 and through the long-term note is $70,000.
A circles radius is 1 1/3 yard whats the perimeter
Step-by-step explanation:
Perimeter = pi * diameter
radius = 1 1/3 yard then diameter = 2 2/3 yd
perimter = pi * 2 2/3 yds = 8.38 yds
4. Brooke earns a salary of $38 000 per year as a cook and works part-time in a department
store.
Her part-time job pays $10.25 per hour and she usually works 12 hours per week.
a) Determine her monthly income.
b) She is looking at renting a new apartment. The rent is $975 per month and includes
utilities. If she takes this apartment, will it fall within the guidelines for housing?
a) Brooke's monthly income is $3,166.67 from her full-time job as a cook, and an additional $532.59 from her part-time job, resulting in a total monthly income of $3,699.26.
b) Yes, the rent of $975 per month for the new apartment falls within the housing guideline of spending 30% or less of her monthly income on housing.
a) To determine Brooke's monthly income, we need to calculate her earnings from both her full-time and part-time jobs.
Full-time job income: Brooke earns $38,000 per year as a cook.
To find her monthly income from this job, we divide her annual salary by 12:
Monthly income from full-time job = $38,000 / 12 = $3,166.67
Part-time job income: Brooke earns $10.25 per hour and works 12 hours per week.
To find her weekly income from this job, we multiply her hourly rate by the number of hours she works:
Weekly income from part-time job = $10.25/hour x 12 hours/week = $123
To find her monthly income, we multiply her weekly income by the average number of weeks in a month (approximately 4.33):
Monthly income from part-time job = $123/week x 4.33 weeks/month = $532.59 (rounded to the nearest cent)
To calculate Brooke's total monthly income, we add her full-time and part-time job incomes:
Total monthly income = $3,166.67 + $532.59 = $3,699.26 (rounded to the nearest cent)
b) The rent for the new apartment is $975 per month, including utilities. To determine if it falls within the housing guidelines, we need to compare it to a percentage of Brooke's monthly income.
Typically, a common guideline is to spend no more than 30% of your monthly income on housing.
Percentage of monthly income for housing = 30% of total monthly income
= 30/100 x $3,699.26
= $1,109.78 (rounded to the nearest cent)
Since the rent of $975 is lower than the guideline of $1,109.78, if Brooke takes this apartment, it will fall within the housing guidelines.
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please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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PLEASE HELP 100 POINTS
Select the correct answer.
The length, l, of a rectangle is modeled by the equation l = w + 4, where w is the width of the rectangle in centimeters.
Two equations have been determined that represent the area of the rectangle, A, in square centimeters:
The first equation was created using the formula for the area of a rectangle: A = w2 + 4w.
The second equation models the relationship between the rectangle's area and width: A = 4w + 45.
Which statement describes the solution(s) of the system?
A.
There are two solutions, and neither are viable.
B.
There are two solutions, but only one is viable.
C.
There are two solutions, and both are viable.
D.
There is only one solution, and it is viable.
Answer:
B) There are two solutions, but only one is viable.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]
To solve the system of equations, substitute the first equation into the second equation:
[tex]w^2+4w=4w+45[/tex]
Solve for w using algebraic operations:
[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]
Therefore, there are two solutions to the given system of equations.
However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.
At what points is the function y=sinx/3x continuous?
Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]
Step-by-step explanation:
The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.
please answer ASAP I will brainlist
The correct answer choice is: A. The system has exactly one solution. The solution is (11, 7).
The correct answer choice is: A. all three countries had the same population of 7 thousand in the year 2011.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the countries listed are approximated by the following system of equations:
-x + 20y = 129
-x + 10y = 59
y = 7
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(7) = 129
x = 140 - 129
x = 11
-x + 10(7) = 59
x = 70 - 59
x = 11
Therefore, the system of equations has only one solution (11, 7).
For the year when the population are all the same for three countries, we have:
x = 2010 + (11 - 10)
x = 2011
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Express 250% as fraction
Answer:
[tex]\frac{2.5}{1}[/tex]
Step-by-step explanation:
To express it as a fraction, divide 250 by 100 first to get 2.5. Then put that over 1.
Hope this helps!
what is (0.3)0 in binominal distribution
Answer:
When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).
So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.
Jana entered the following group of values into the TVM Solver of her
graphing calculator. N=48; 1% = 0.6; PV = ; PMT=-290; FV = 0; P/Y = 12; C/Y
= 12; PMT:END. Which of these problems could she be trying to solve?
OA. A person can afford a $290-per-month loan payment. If he is being
offered a 48-year loan with an APR of 7.2%, compounded monthly,
what is the mosioney that he can borrow?
B. A person can afford a $290-per-month loan payment. If he is being
offered a 4-year loan with an APR of 0.6%, compounded monthly,
what is the most money that he can borrow?
C. A person can afford a $290-per-month loan payment. If he is being
offered a 48-year loan with an APR of 0.6%, compounded monthly,
what is the most money that he can borrow?
D. A person can afford a $290-per-month loan payment. If he is being
offered a 4-year loan with an APR of 7.2%, compounded monthly,
what is the most money that he can borrow?
Answer:
Jana is likely trying to solve option B:
"A person can afford a $290-per-month loan payment. If he is being offered a 4-year loan with an APR of 0.6%, compounded monthly, what is the most money that he can borrow?"
Step-by-step explanation:
Option B is the correct choice because it aligns with the values entered by Jana into the TVM Solver. Jana set the loan term (N) to 48, which represents 48 months (4 years). The APR value of 0.6% also matches what Jana inputted.
By selecting option B, Jana is attempting to find out the maximum amount of money she can borrow given that she can afford a $290-per-month loan payment and is offered a 4-year loan with an APR of 0.6%, compounded monthly.
This calculation will help Jana determine the loan amount that corresponds to her desired monthly payment and the given loan terms.
A company Charting its profits notices that the relationship between the number of units sold,x, and the profit,P, is a linear. If 170 units sold results in $20 profit and 220 units sold results in $2820 profit, write the profit function for this company.
P=
Find the marginal profit
$
Step-by-step explanation:
a linear relationship or function is described in general as
y = f(x) = ax + b
Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".
here f(x) is P(x) :
P(x) = ax + b
now we are using both given points (ordered pairs) to calculate a and b :
20 = a×170 + b
2820 = a×220 + b
to eliminate first one variable we subtract equation 1 from equation 2 :
2800 = a×50
a = 2800/50 = 280/5 = 56
now, we use that in any of the 2 original equations to get b :
20 = 56×170 + b
b = 20 - 56×170 = 20 - 9520 = -9500
so,
P(x) = 56x - 9500
There are 12 containers containing various amounts of water, as shown below. ←+ 0 H ½ X X X X X X 1 X 1½ X X X 2 Cups If all of the water were dumped into one container, how many cups would be in the container?
Answer: it contains 12 containers
Step-by-step explanation: i dont know what the answer is but i know what i can help you with all you have to do is round the answer.
On a coordinate plane, a curved line, labeled D, with a minimum value of (3, negative 8), labeled C, with x-intercept (1, 0), labeled B, and y-intercept (0, 10), labeled A. Match the letter of the key feature on the graph with its name. x-intercept: y-intercept: Relative minimum: Increasing interval:
The interval for the graphed function that has a local minimum of 0 is [-2, 0].
To determine the interval for the graphed function that has a local minimum of 0, we need to examine the behavior of the graph around the x-values where it crosses the x-axis.
We know that the graph crosses the x-axis at -2.5, 0, and 3. Since the local minimum occurs at 0, we need to find the interval where the graph is decreasing to the left of 0 and increasing to the right of 0.
From the given information, we can determine the following:
The graph is decreasing between -2.5 and 0 because it crosses the x-axis at -2.5 and 0, and the minimum value is at (-1.56, -6).
The graph is increasing between 0 and 3 because it crosses the x-axis at 3, and the maximum value is at (1.2, 2.9).
The correct option is [–2, 0].
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Question
On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [2, 4]
f(x)=x^2. What is g(x)?
Answer:
D, g(x) = 1/4 x^2
Step-by-step explanation:
You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.
Find the value of each variable. Round your answers
to the nearest tenth.
12
X
25°
The value of 12 remains 12.
The value of X cannot be determined without additional information.
The value of 25° remains 25°.
To find the values of the variables in the given information, we have:
12: This is a given value and does not require calculation. Therefore, the value of 12 remains as it is.
X: Without additional information or an equation to solve, we cannot determine the value of X. It could represent any unknown quantity or variable, and its specific value would depend on the context or problem being solved.
25°: This is an angle measure in degrees. The value of 25° remains as it is.
To summarize:
The value of 12 remains 12.
The value of X cannot be determined without additional information.
The value of 25° remains 25°.
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What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
HELP THIS QUESTION IS HARD
Answer:
a)
[tex] \frac{1}{( - 7)^{4} } [/tex]
Answer:
[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]
Step-by-step explanation:
The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.
According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.
Thus, the negative exponent rule is given as:
[tex]b^-^n=\frac{1}{b^n}[/tex]
Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]
Identify an equation in point-slope form for the line parallel to y = 3/4x - 4 that passes through (-1, 7).
Answer:
A) [tex]y-7=\frac{3}{4}(x+1)[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)\\y-7=\frac{3}{4}(x-(-1))\\y-7=\frac{3}{4}(x+1)[/tex]
Parallel lines must have the same slope, and then plugging in [tex](x_1,y_1)=(-1,7)[/tex], we easily get our equation.
Answer:
the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 3/4.
Using the point-slope form of a line, which is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line, we can substitute the values (-1, 7) for (x₁, y₁) and 3/4 for m:
y - 7 = (3/4)(x - (-1))
Simplifying further:
y - 7 = (3/4)(x + 1)
Multiplying through by 4 to eliminate the fraction:
4(y - 7) = 3(x + 1)
Expanding:
4y - 28 = 3x + 3
Rearranging the equation to put it in standard form:
3x - 4y = -31
So, the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.
Please help I am so lost thank you so much
The speed of the plane is equal to 120 mph.
What is speed?In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).
Mathematically, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Time = distance/speed
Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;
240/s = 80/s - 80
80s = 240s - 19200
19200 = 160s
s = 19200/160
s = 120 mph.
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Angela lives in New York, which has a sales tax of 8.125%. She bought some word-processing software whose full price was $110, but she presented the retailer with a coupon for $30. What was the total amount that Angela paid?
Answer: 88.94
Step-by-step explanation:
First, l found what was 8.125 out of 110 which is 8.94
then added 8.125 and 8.94 which got 118.94
But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94
Copy the axes below.
a) By completing the tables of values to help
you, plot the lines y = 2x + 1 and
y = 10 x on your axes.
b) Use your diagram to find the solution to the
simultaneous equations y = 2x + 1 and
y=2x+1
x012
Y
y = 10-x
x012
Y
= 10 - x.
y =
Y
10
-3 -2 -1
098
7
6
659
-5
-4
3
2
-1-
-2
w
1 2 3 4 5 6 7 8 9 10 x
By completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.
(a) To plot the lines y = 2x + 1 and y = 10 - x, we need to complete the tables of values and then plot the points on the axes.
For the line y = 2x + 1, we can choose some values of x and calculate the corresponding y values:
x | y
0 | 1
1 | 3
2 | 5
For the line y = 10 - x, we can also choose some values of x and calculate the corresponding y values:
x | y
0 | 10
1 | 9
2 | 8
Plot the points (0, 1), (1, 3), and (2, 5) for the line y = 2x + 1, and the points (0, 10), (1, 9), and (2, 8) for the line y = 10 - x on the provided axes.
(b) To find the solution to the simultaneous equations y = 2x + 1 and y = 10 - x,
we need to identify the point(s) where the two lines intersect on the graph.
From the plotted lines, we can see that they intersect at the point (3, 7). Therefore, the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7.
In conclusion, by completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.
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so in the same Equation i have to do use the values x=-4,0,5 to verify my solution to the equation 5+x-12=x-7 in my final answer.
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Answer:
Step-by-step explanation:
Let's revisit the equation and the solution using the values x = -4, 0, and 5.
The given equation is: 5 + x - 12 = x - 7
Let's go through the steps again to solve it:
5 + x - 12 = x - 7
Combine like terms:
x - 7 = x - 7
Now, subtract x from both sides:
x - x - 7 = x - x - 7
Simplify:
-7 = -7
The equation simplifies to -7 = -7, which is true.
Now, let's use the values x = -4, 0, and 5 to verify the solution.
For x = -4:
5 + (-4) - 12 = (-4) - 7
-11 = -11
The equation is satisfied for x = -4.
For x = 0:
5 + 0 - 12 = 0 - 7
-7 = -7
The equation is satisfied for x = 0.
For x = 5:
5 + 5 - 12 = 5 - 7
-2 = -2
The equation is satisfied for x = 5.
Therefore, the solution x = 0 is correct, and it satisfies the equation for the given values. My earlier statement that x = -4 and x = 5 do not satisfy the equation was incorrect. I apologize for the confusion caused.
The length of a rectangle is six times its width. If the area of the rectangle is 600 in2, find its perimeter.
The perimeter of the rectangle is 140 inches.
Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.
The area of a rectangle is given by the formula A = length × width. Substituting the values we have:
A = (6w) × w
600 = 6w^2
To solve for w, we divide both sides of the equation by 6:
w^2 = 100
Taking the square root of both sides:
w = ±10
Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.
Now that we have the width, we can find the length of the rectangle:
Length = 6w = 6 × 10 = 60
The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:
P = 2(60 + 10)
P = 2(70)
P = 140
Therefore, the perimeter of the rectangle is 140 inches.
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GEOMETRY 30POINTS
find x to the nearest degree!
The calculated value of x to the nearest degree is 56
How to calculate x to the nearest degreeFrom the question, we have the following parameters that can be used in our computation:
The triangle
The value of x can be caluclated using the following cosine rule
So, we have
cos(x) = 5/9
Evaluate the quotient
cos(x) = 0.5556
Take the arc cos of both sides
x = 56
Hence, the value of x to the nearest degree is 56
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Find all values of x are not in the domain of h
Answer:
x = -1, 1
Step-by-step explanation:
The function h(x) is given below:
[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]
The denominator must not equal to 0. Therefore,
[tex]\displaystyle{x^2-1\neq 0}[/tex]
Solve the inequality; factor the expression:
[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]
Hence,
[tex]\displaystyle{x \neq 1,-1}[/tex]
Therefore, x = -1, 1 both are not in the domain of h.
Darla, Ellie, and Fran ate a whole container of ice cream. Darla ate half as much as Ellie ate, and Fran ate 5 times as much as Darla ate. If the container of ice cream cost $4.00, how much, in dollars, should each person pay?
 Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
Answer:
arc LKF = 208°
Step-by-step explanation:
the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so
arc LKF = 2 × 104° = 208°
Cos5pi/3 =
A. 3/2
B.1/2
C. 2/2
D.-2/2
HELPP
Answer:
B) 1/2
Step-by-step explanation:
Note that pi=180.
Then we have 180/3=60 and so 5*60=300.
Thus cos 300=1/2.
Therefore, cos 5pi/3=1/2.
Answer: B
Step-by-step explanation:
need help please see attacged
The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.
To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.
From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).
Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).
Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.
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Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
The angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°
How to calculate for angle between the intersection of a secant and a tangent.To calculate for the angle between the intersection of a secant and a tangent we need to know the measure of the intercepted arc, and then divide it by 2 to get the angle.
If the measure of the arc HM is given to be equal to 108°, then the measure of angle MHU is calculated as:
angle MHU = 108°/2
m∠MHU = 54°
Therefore, the angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°
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