Let's first go over the definition of a polygon.
A polygon a figure formed by coplanar segments. The segments are called sides.
A circle is not considered a polygon because it's formed by a curve rather than line segments.
In an experiment, a ball is drawn from an urn containing 7 orange balls and 12 red balls. If the ball is orange, three coins are tossed. Otherwise two coins are tossed. How many elements of the sample space will have a orange ball ?
Answer:
84
Step-by-step explanation:
When an orange ball is picked, you toss 3 coins and there are 2^3 = 8 permutations for tossing 3 coins. Now since we have 7 orange balls there will be 7 * 8 = 56 sample spaces with orange balls.
In the experiment, if the ball drawn is orange, three coins are tossed. Otherwise, two coins are tossed. The sample space will have 12 elements with an orange ball.
Explanation:To determine the number of elements in the sample space that have an orange ball, we need to consider two cases: when the ball drawn is orange and when the ball drawn is not orange (red).
If the ball drawn is orange, three coins are tossed. The sample space in this case will have 23 = 8 elements, representing all possible outcomes of the coin tosses.
If the ball drawn is not orange (red), two coins are tossed. The sample space in this case will have 22 = 4 elements, representing all possible outcomes of the coin tosses.
Therefore, the total number of elements in the sample space that have an orange ball is 8 (when the ball is orange) + 4 (when the ball is not orange) = 12.
A room has 3 lamps. From a collection of 12 light bulbs of which 5 are not working, Richard selects 3 at random and puts them in the sockets. What is the probability that he will have light? ...?
Translate each sentence into an equation.
1.
Three more than four times a number is equal to twelve.
2.
The sum of a number and two is twice the number.
3.
The quotient of a number and twelve is the sum of eight and the number.
4.
Five more than three times a number is equal to eight.
5.
The sum of a number and six is seven times the number.
6.
The quotient of a number and six is equal to nine.
7.
Seven less than a number is two.
8.
Twenty-seven is the product of three and a number.
9.
Twelve less than six times a number is equal to three times the number. ...?
Final answer:
Equations are derived from verbal statements by identifying mathematical operations and their relationships to quantities. The resulting equations represent these statements algebraically, where 'n' is the variable representing the unknown number.
Explanation:
Translating sentences into equations is a fundamental skill in algebra, vital for solving problems and understanding mathematical relationships.
Three more than four times a number is equal to twelve: 4n + 3 = 12.
The sum of a number and two is twice the number: n + 2 = 2n.
The quotient of a number and twelve is the sum of eight and the number: n / 12 = n + 8.
Five more than three times a number is equal to eight: 3n + 5 = 8.
The sum of a number and six is seven times the number: n + 6 = 7n.
The quotient of a number and six is equal to nine: n / 6 = 9.
Seven less than a number is two: n - 7 = 2.
Twenty-seven is the product of three and a number: 3n = 27.
Twelve less than six times a number is equal to three times the number: 6n - 12 = 3n.
Remember to define the variable 'n' as the number mentioned in the sentences and solve the equations to find the value of 'n'.
Transversal CD←→ cuts parallel lines PQ←→ and RS←→ at points X and Y, respectively. Points P and R lie on one side of CD←→, while Q and S lie on the other side. If
m∠PXY = 64.36°, what is m∠XYS?
Answer: [tex]64.36^{\circ}[/tex]
Step-by-step explanation:
According to the question,
PQ ║ RS
And, PQ and RS are cut by the same transversal CD.
Then, By the alternative interior angle theorem,
The alternative interior angles made by the transversal CD on parallel lines PQ and RS must be congruent.
Thus, [tex]\angle PXY\cong \angle XYS[/tex]
⇒ [tex]m\angle PXY = m\angle XYS[/tex] ( by the property of congruent angles )
Here [tex]m\angle PXY = 64.36^{\circ}[/tex]
⇒ [tex]m\angle XYS = 64.36^{\circ}[/tex]
Which answer describes the type of sequence? 3, 9, 15, 21, ...
geometric
arithmetic
neither arithmetic nor geometric
Answer:
The sequence is arithmetic
Step-by-step explanation:
we know that
In an arithmetic sequence, the difference between consecutive terms is always the same and is called common difference
In this problem we have
[tex]3,9,15,21,...[/tex]
Let
[tex]a1=3, a2=9,a3=15,a4=21[/tex]
[tex]a4-a3=21-15=6[/tex]
[tex]a3-a2=15-9=6[/tex]
[tex]a2-a1=9-3=6[/tex]
The sequence is arithmetic
The common difference is equal to [tex]6[/tex]
5 times a number decreased by 2
find where the slope of the curve is defined:
x^2y-xy^2=4
The slope of the curve x²y-xy²=4 is defined everywhere except for points where x = 2y. This conclusion is reached by using implicit differentiation and the product rule to find the derivative (slope), and then determining where the slope is undefined.
Explanation:To find where the slope of the curve is defined for the equation x²y-xy²=4, we first need to find the derivative of the equation. The derivative will give us the slope of the tangent line at a specific point. This process involves using the Product Rule of differentiation. The Product Rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.
For the given equation, we first need to rewrite it in the form: y = f(x). However, as y cannot be easily expressed solely as a function of x in this case, we will need to use implicit differentiation. Implicit differentiation assumes that y is a function of x, even if it's not explicitly stated. By using the product rule, we get 2xy + x² × (dy/dx) - y² - 2xy × (dy/dx) = 0; simplifying this, we get (x² - 2xy) × (dy/dx) = y² - 2xy. So dy/dx = (y² - 2xy) / (x² - 2xy).
Thus, the slope of the curve is defined wherever the denominator, x² - 2xy, does not equal zero, since division by zero is undefined. Hence, we need to solve x² - 2xy ≠ 0. Solving this inequality, we find that the slope of the curve is defined for all (x,y) except where x = 2y.
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Help please ASAP !!!!!
Which value is equivalent to 7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9? 6 over 25 36 over 25 12 over 5 252 over 5
Answer:
c
Step-by-step explanation:
What is slope between the points (-5,7) and (4,-8)?
Write 6 2\9 as an improper fraction. ...?
Final answer:
improper fraction 56/9.
Explanation:
To write the mixed number 6 2/9 as an improper fraction, you should first multiply the whole number by the denominator of the fraction, then add the numerator of the fraction.
Multiply the whole number 6 by the denominator 9: 6 × 9 = 54.Add the numerator of the fraction to that result: 54 + 2 = 56.Write the sum as the numerator and keep the original denominator to form the improper fraction: 56/9.Which value of m will create a system of parallel lines with no solution?
y = mx – 6
8x – 4y = 12
The value of [tex]m[/tex] is [tex]2[/tex].
Given:
The given equations are:
[tex]y=mx-6[/tex] ...(i)
[tex]8x-4y=12[/tex] ...(ii)
To find:
The value of [tex]m[/tex] that will create a system of parallel lines with no solution.
Explanation:
The slope-intercept form of a line is:
[tex]y=mx+b[/tex] ...(iii)
where, [tex]m[/tex] is the slope and [tex]b[/tex] is the [tex]y[/tex]-intercept.
The slope of line (i) is [tex]m[/tex].
Equation (ii) can be rewritten as:
[tex]-4y=-8x+12[/tex]
[tex]y=\dfrac{-8x+12}{-4}[/tex]
[tex]y=2x-3[/tex]
The slope of this line is [tex]2[/tex].
We know that the slopes of parallel lines are equal. So, [tex]m=2[/tex].
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How many significant figures does the number 520 have? What is the difference between a systematic error and a random error?
for a population of 800000 subway riders, the numbers of subway trips taken per rider last january are approximately normally distributed with a mean of 56 trips and a standard deviation of 13 trips. approximately how many of the riders took between 30 and 43 trips last january??? ...?
Calculating the number of subway riders who took between 30 and 43 trips involves finding z-scores for these trip numbers, looking up the corresponding probabilities in the normal distribution table, and multiplying the difference by the total population of riders.
Explanation:The question relates to normal distribution and requires calculating the number of individuals in a given population that fall within a specific range of values. The population in question is 800,000 subway riders whose number of trips are normally distributed with a mean (μ) of 56 and a standard deviation (σ) of 13. The task is to find out how many riders took between 30 and 43 trips last January.
To solve this, we first find the z-scores for the values 30 and 43. The z-score is calculated by subtracting the mean from the value and dividing the result by the standard deviation. This will give:
Z for 30 = (30 - 56) / 13 = -2Z for 43 = (43 - 56) / 13 = -1Next, we look up these z-scores in a standard normal distribution table to find the probabilities corresponding to these z-scores. The difference between these probabilities will give us the proportion of riders who took between 30 and 43 trips. Finally, we multiply this proportion by the total population of riders (800,000) to get the number of riders. Assume that the probabilities from the z-table are 0.0228 for z = -2 and 0.1587 for z = -1.
The calculation would be approximately:
Number of riders = 800,000 * (0.1587 - 0.0228) = 800,000 * 0.1359 = 108,720 riders
PLEASE HELP!!!!!!!****
Seven runners compete in a race in, in how many ways can first, second, and third place be awarded?
A) 210.
B) 840.
C) 5040.
D) 30,240.
Bianca took out a $2,600 unsubsidized Stafford loan. She will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. The loan has an interest rate of 6.2%, compounded monthly. How much will she have to pay monthly to avoid interest capitalization?
Answer:
Bianca need to pay $13.43 monthly to avoid interest capitalization.
Step-by-step explanation:
Principal value = $2600
Time = 10 years = 120 months
Interest rate = 6.2% = 0.062
Now, Find amount of payment by using the formula :
[tex]Payment = \frac{Rate\times Principal}{1-(1+rate)^{-time}}\\\\\implies Payment = \frac{0.062\times 2600}{1-(1+0.062)^{-120}}\\\\\implies Payment = \$ 161.32 [/tex]
Total payment is to be paid in 1 year :
[tex]\text{So, Monthly payment = }\frac{161.32}{12}=\$13.43[/tex]
Hence, Bianca need to pay $13.43 monthly to avoid interest capitalization.
If you have 6 circles and 42 hearts what is the simplified ratio
For any positive numbers a, b, and d, with b 1, logb(a d) = _____.
A.logb a - logb d
B.logb a logb d
C.logb a + logb d
D.d logb a
The expression for log_{b} (ad) is log_{b} a + log_{b} d. Option (C) is the correct answer.
What is a logarithm?"Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation".
For the given situation,
The positive numbers are a,b and d.
By product rule of the logarithm,
[tex]log_{b} (ad) = log_{b} a + log_{b} d[/tex]
Hence we can conclude that option (C) is the correct answer.
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john is building a soccer table and wants it to be similar in size to a real soccer field. a full size soccer field is 336 feet long and 210 feet wide. what will be the area of his soccer table if he wants it to be 2.5 feet wide?
Answer:
[tex]10 ft^2[/tex]
Step-by-step explanation:
We are given that
Length of soccer field=336 feet
Width of soccer field=210 ft
Width of soccer table=2.5 feet
We have to find the area of soccer table which is similar to soccer field in size.
Let x be the length of soccer table.
We know that when two figures are similar then ratio of their corresponding sides are equal.
[tex]\frac{336}{x}=\frac{210}{2.5}[/tex]
[tex]x=\frac{336\times 2.5}{210}=4[/tex]
Length of soccer table=4 ft
Area of soccer table=[tex]length\times breadth[/tex]
Area of soccer table=[tex]4\times 2.5=10 ft^2[/tex]
Hence , the area of soccer table=[tex]10 ft^2[/tex]
@mehek14
The table shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days. It also shows the dollar amount taken in each day.
Hamburgers Hot Dogs Total
Day 1 200 150 $1,450
Day 2 200 250 $1,750
What is the cost of a hamburger and the cost of a hot dog?
Enter your answers in the boxes.
Give an example of an even function and explain algebraically why it is even.
Final answer:
An even function has the property f(x) = f(-x), exemplified by the quadratic function f(x) = x². To prove it's even, substituting -x for x results in f(-x) = (-x)², which simplifies to f(-x) = x² equaling the original function, confirming its evenness and y-axis symmetry.
Explanation:
An example of an even function is the quadratic function f(x) = x². An even function is defined by the property that f(x) = f(-x). Here's a step-by-step explanation to show that f(x) = x² is even:
Take the function f(x) = x².Substitute -x for every x in the function, so f(-x) = (-x)².Since (-x)² = x², we see that f(-x) = f(x), which satisfies the criteria of an even function. Therefore, x² is even.This even property shows symmetry about the y-axis since the function's graph appears the same on either side of the y-axis. Understanding this helps in various mathematical applications, such as simplifying expectation-value calculations in quantum mechanics or solving geometry problems using the Pythagorean theorem.
solving system using subsitution
question
a shopper purchased 8 t-shirts and 5 pairs of pants for $220.The next day he purh pair of purchased 5 tshirts and 1 pair of pants for $112.How much does each tshirt and each pair of pants cost? ...?
5. You are making your weekly mean plans and are working with the following constraints: It costs $8 to go out to dinner. It costs $5 to go out to lunch. You want to go out to dinner at least as many times as you go out to lunch. You can spend at most $42.
What is the greatest number of meals you can eat out?
3
4
5
6
Let
x-------> the number of dinner
y-------> the number of lunch
we know that
[tex]8x+5y \leq 42[/tex] -------> equation A
[tex]x=y[/tex] ------> equation B
Substitute equation B in equation A
[tex]8[y]+5y \leq 42[/tex]
[tex]13y \leq 42[/tex]
[tex]y \leq 42/13[/tex]
[tex]y \leq 3.23[/tex]
so
the greatest number of lunch is [tex]y=3[/tex]
[tex]x=y[/tex]
Hence
the greatest number of dinner is [tex]x=3[/tex]
therefore
the greatest number of meals is
[tex]x+y=3+3=6[/tex]
the answer is
[tex]6[/tex]
A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.
What is the range of video games owned for the cluster?
Answer:
8 to 10
Step-by-step explanation:
The population of a town is 18,922 people. Each year the population increases by 3%. What will the town's population be in 17 years? Round your answer to the nearest whole number.
a) 31,275
b) 2,412,376
c)11,274
d) 70,129
Find the missing angle measures. The diagram is not to scale
Please help me? I'm almost certain it is only option A but I want a second opinion.
Aimee is comparing three investment accounts offering different rates.
Option A: APR of 7.79% compounding monthly
Option B: APR of 7.70% compounding quarterly
Option C: APR of 7.685% compounding daily
She would like to earn at least an 8% annual yield. Which account(s) will give Aimee the yield she wants?
Answer: option A only
Step-by-step explanation:
A number close to its actual value is a(n)
Where can the denominator be found in a fraction?
a. above the fraction bar
b. at the fraction bar
c. below the fraction bar
d. either a or c?
solve 2x+3y=10 and 3x-4y=-2
The solution to the system of equations 2x + 3y = 10 and 3x - 4y = -2 is x = 2 and y = 2.
Given the system of equations in the question:
2x + 3y = 10
3x - 4y = -2
To determine the solution to the system of equations, we can use the elimination method:
2x + 3y = 10
3x - 4y = -2
Multiply the first equation by 4 and the second equation by 3:
We have:
8x + 12y = 40
9x - 12y = -6
Now, we add the two equations.
We have:
17x + 0 = 34
x = 34/17
x = 2
Now, plug x = 2 into the first equation and solve for y:
2x + 3y = 10
2(2) + 3y = 10
4 + 3y = 10
3y = 10 - 4
3y = 6
y = 6/3
y = 2
Therefore, the value of x is 2 and the value of y is 2.