Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1). At what point does line A intersect line B?
Complete the statement f(3) is
The corresponding output for an input value of 3 is -1. Hence f(3) is -1
from the mapping function given, the domain values are the input values of the function while the range is the output.
To get the value of f(3), we need to check the corresponding output when the input variable is 3.
From the given one-on-one mapping, we can see that the corresponding output for an input value of 3 is -1. Hence f(3) is -1
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2x-3y=8 solve for (y)?
To which subset of real numbers does -18 not belong?
We have that the -18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.
Rational number & Integer
Real numbersGenerally
The subsets of the actual numbers are as follows
Irrational numbersRational numbersWhole numbersNatural numbers etc-18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.
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A board is 27 inches long. How long is the board in centimeters? Use the following conversion: 1 inch is 2.54 centimeters.
1 inch = 2.54 cm
so multiply 27 by 2.54
27 x 2.54 = 68.58 cm long
To convert 27 inches to centimeters, multiply 27 by the conversion factor of 2.54 cm per inch, resulting in 68.58 centimeters.
The student has asked how long a board that is 27 inches long is in centimeters, given the conversion factor that 1 inch is equal to 2.54 centimeters. To convert inches to centimeters, you multiply the length in inches by the conversion factor. In this case, you would multiply 27 inches by 2.54 to find the length in centimeters.
Here is the calculation:
27 inches x 2.54 cm/inch = 68.58 centimeters.
Therefore, a board that is 27 inches long is 68.58 centimeters long.
Is the data set “heights of the women in the U.S. Congress” quantitative or qualitative? If it is quantitative, is it discrete or continuous?
Answer with explanation:
The “heights of the women in the U.S. Congress” is Quantitative,because height of person does not represent Quality, it shows "Quantity".It means it has Magnitude.
We can find mean , median and mode of women in Congress.
So, Height of women in US congress is Quantitative.
As, different Women have different Heights, that is any rational number , so The Height of different women will be a discrete data set.For, example, height of different women can be={167 cm, 187.6, 176.6,165.5,.....}
The function H(t) = −16t2 + 80t + 112 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 20 + 5.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 3 through 6 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
I'm having a bit of trouble, could you help?
A ladder is leaning up against a 17 foot Wall at an angle of elevation of 37°. How far is the foot of the latter from the wall? Round your answer to the nearest 10th of a foot
what is the last line of proof
1) 8k-(6k-4)=10 show work please
2) -12x+8+5x=36 show work please
3) -2y+4=8y-6
1) 8k - (6k - 4) = 10
[tex]\mathsf{8k-6k+4=10}\\\\ \mathsf{2k=10-4}\\\\ \mathsf{2k=6}\\\\ \underline\mathsf{k=\dfrac{6}{2}=3}}[/tex]
2) -12x + 8 + 5x = 36
[tex]\mathsf{-12x+8+5x=36}\\\\ \mathsf{-12x+5x=36-8}\\\\ \mathsf{-7x=28}\\\\ \mathsf{x={28}{-7}}\\\\ \underline{\mathsf{x=-4}}[/tex]
3) -2y + 4 = 8y - 6
[tex]\mathsf{-2y+4=8y-6}\\\\ \mathsf{-2y-8y=-6-4}\\\\ \mathsf{-10y=-10}\\\\ \mathsf{y=\dfrac{-10}{-10}}\\\\ \underline{\mathsf{y=1}}[/tex]
At the Atkins County Fair, the crowd for a concert by The Cooper Band cannot exceed a certain number. The limit for the number of people who can attend the concert is 0.04 people per square foot of space in the arena. If the arena is shaped as a rectangle with sides 220 feet by 200 feet, how many people can attend the concert?
What part of a aday is 4 hours and 20 mintes?
Gitta is asked to find the probability of getting all heads on 3 coin tosses. This is a compound event. True or False?
Answer with explanation:
Event Joining by two or more Simple events is called Compound Event.
When you throw a coin once, getting either Head or Tail is a Simple event.
And , when you throw a coin and dice together, getting , Head and 1 , is a Compound event.Because here we joined two simple events, one is Throwing of a coin and another one is throwing a dice.
When you toss a coin thrice, it is combination of three simple events, that is tossing of coin three times .So total possible outcome
[tex]=2^3\\\\=8[/tex]
Which can be written as: {(HHH),(HHT),(HTH),(THH),(HTT),(THT),(TTH),(TTT)}
Probability of getting all heads on 3 coin tosses
= Sum of three simple events
[tex]=\frac{HHH}{\text{Total 8 Outcome}}\\\\=\frac{1}{8}[/tex]
or
Probability of Getting head in all three throws
[tex]=\frac{1}{2}\times \frac{1}{2} \times \frac{1}{2}\\\\=\frac{1}{8}[/tex]
Yes, this is a Compound event.
What is the distance, in radians, between 0 and 0=pie , sin0=0
Answer:
What is the distance, in radians, between 0 and the value you identified in part A? (PLATO QUESTION) pi (PLATO ANSWER)
Step-by-step explanation:
pi is the answer for plato users
What is the graph of the function?
f(x) = 2x 2
Answer:
For f(x)=2x² graph, the answer is A.
Step-by-step explanation:
For x = -2; y = 8For x = -1; y = 2For x = 0; y = 0For x = 1; y = 2For x = 2; y = 8If a sphere has a radius of 2 cm what is the approximate surface area of the sphere
How did Greek mathematician Pythagoras come up with the Pythagorean Theorem. Explain
what is the simplified form of (6^2+4)-15
what is 67912 to the nearest 10
The mapping diagram shows a relation.
What is the domain of the relation?
{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 11, 3}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 11, 3}.
Answer:B. {x| x = –7, –6, 2, 11, 3}.
concert venue sells adult tickets for $15 and student tickets for $10 . Monday, a total of 85 tickets were sold, and the total money collected was $1,115 . How many adult tickets and how many student tickets were sold?
In two supplemantary angles, the measure of one angles is 6 more than the twice the measure of the other.the measure of these two angles are
Please read the attached pic. I don't remember ever being taught this...
The solutions to the inequalities 0≤x≤2,0≤y≤1, and y≤−12x+32 form a polygonal region in the plane. How many sides does this polygon have?
It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own
It would take Brian 20 hours to build the model car on his own.
To determine the time it would take Brian to build the model car on his own, we can follow these steps:
1. Let's denote the time it takes John to build the model car as J hours.
2. Since it takes Brian 15 hours longer than John, we can express the time it takes Brian as J +15 hours.
3. If they work together, they can build the model car in 4 hours. This means that in 1 hour, they complete [tex]\(\frac{1}{4}\)[/tex] of the job together.
4. In 1 hour, John completes [tex]\(\frac{1}{J}\)[/tex] of the job, and Brian completes [tex]\(\frac{1}{J + 15}\)[/tex] of the job.
5. So, the equation representing the rate at which they work together is:
[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]
6. Now, we solve this equation to find J, the time it takes John to build the model car on his own.
7. Once we find J, we can find J+15 which represents the time it takes Brian to build the model car on his own.
So, the equation representing the rate at which they work together is:
[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]
To solve this equation, we can multiply both sides by the least common denominator, which is [tex]\( 4J(J + 15) \)[/tex], to clear the fractions:
[tex]\[ 4(J + 15) + 4J = J(J + 15) \][/tex]
Expanding and simplifying:
[tex]\[ 4J + 60 + 4J = J^2 + 15J \]\[ 8J + 60 = J^2 + 15J \]\[ J^2 + 15J - 8J - 60 = 0 \]\[ J^2 + 7J - 60 = 0 \][/tex]
Now, we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. Let's use factoring:
[tex]\[ (J - 5)(J + 12) = 0 \][/tex]
Setting each factor equal to zero:
[tex]\[ J - 5 = 0 \] or \( J + 12 = 0 \)[/tex]
Solving each equation:
[tex]For \( J - 5 = 0 \), we get \( J = 5 \).For \( J + 12 = 0 \), we get \( J = -12 \).[/tex]
Since time cannot be negative, we discard the negative solution.
Now that we have found J=5 hours, which represents the time it takes John to build the model car on his own, we can find [tex]\( J + 15 = 5 + 15 = 20 \)[/tex] hours.
Please help with this question on simple interest!!! Attachment below.
A building manager installs sensors to see how often people turn off the lights when they leave a room. After a month, the manager has a sample size of 400, a sample mean of 47%, and a sample standard deviation of 4%. What is the confidence level for a confidence interval of 46.6% to 47.4%?
A. 68%
B. 85%
C. 99.7%
D. 95%
The answer is C.
The figures in your problem are inconsistent with
the data.
The sample std deviation is not and cannot be .04 (4%).
the sample std dev is sqrt[(.47)(1-.47)/400]=.02495.
The margin of error from your CI is .474 -.47= .004 (very
small).
This would represent .02495/.004= 6.24 std dev. from
expected, which would have a very
high level of confidence (99.97.. %). Something is likely
wrong with the figures in your problem.
Answer: 95%
Step-by-step explanation:
Identify the terms and coefficients for4p+5-3g
A ramp 24 ft long rises to a platform that is 20 ft off the ground. find x , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.
Final answer:
To determine the angle of elevation x, we use the sine function with the opposite side (20 ft) and the hypotenuse (24 ft) to get sin(x) = 20/24, and by taking the arcsin of the result, we find that x ≈ 56.4° when rounded to the nearest tenth of a degree.
Explanation:
To find x, the angle of elevation of the ramp, we can use trigonometric functions. Since we have the length of the ramp (hypotenuse) and the height of the platform (opposite side) in a right-angled triangle, we can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse.
Using the sine function: sin(x) = opposite/hypotenuse = 20/24.
We first calculate the ratio: sin(x) = 20/24 = 0.8333.
To find the angle x, we take the inverse sine (also known as arcsine) of the ratio: x = arcsin(0.8333).
Using a calculator set to degree mode, we find that x ≈ 56.4° when we round to the nearest tenth of a degree.