Answers
The favorable outcomes in this case are the numbers divisible by 3. So the numerator lists the numbers that are divisible by 3, which are the favorable outcomes.
So, the answer to this question is option C
Related Questions
x-1/x-1=1
Solve the equation.
These are fractions
Answers
A number divided by itself will always yield a result of 1. (x-1) is being divided by (x-1), which means that both the numerator and denominator are identical. This will always produce a result of 1, with one exception:
x cannot equal 1, as division by zero is impossible. (1-1) = 0.
hey can you please help me posted picture of question
Answers
Moving one unit to left is equivalent to adding 1 to x in the base of the expression in given case.
So,
G(x) = F(x+1)
G(x) = (x+1)²
Thus the correct answer is option D
PLEASE HELP The data below shows the scores of some students on a test: 28, 30, 22, 20, 24, 23, 32
Answers
expand in logarithmic expression
Answers
in an experiment, the control variable is r and the response variable is s. which variable is not manipulated, but measured, and represents the data being recorded
Answers
Control variables are kept constant between experiments.
Control variable r is not manipulated, but measured and represents the data being recorded.
What is mean by Variables?
A variable is a value that can change, depending on information.
Given that;
In an experiment, the control variable is r and the response variable is s.
Now,
Control variable is a variable that's always constant in an experiment.
It is not a variable of interest in the study, but its controlled because it could influences the outcomes.
Thus, Control variable r is not manipulated, but measured and represents the data being recorded.
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(K-4)(k+4)=0 quadratic equation
Answers
use:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex]k^2-4^2=0\\\\k^2-16=0\ \ \ \ |+16\\\\k^2=16\to k=\pm\sqrt{16}\\\\\boxed{k=-4\ \vee\ k=4}[/tex]
Other method:
[tex](k-4)(k+4)=0\iff k-4=0\ \vee\ k+4=0\\\\\boxed{k=4\ \vee\ k=-4}[/tex]
please help asap. this circle is centered at the origin and the length of its radius is 8. what is the circles equation
Answers
D is 're correct answer
Answer: [tex]x^2 + y^2 = 64[/tex]
Step-by-step explanation:
Since, the equation of a circle that having the center (h,k) and radius r is,
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Here the circle is centered at the origin,
That is, h = 0 , k = 0
Also, the radius of the circle is 8,
That is, r = 8 unit,
Thus, the equation of the given circle,
[tex](x-0)^2 + (y-0)^2 = 8^2[/tex]
[tex]x^2 + y^2 = 64[/tex]
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x + 12), [−3, 1]
Answers
The absolute maximum and minimum values of the function f(x) = ln(x^2 + 5x + 12) on the interval [-3, 1] are f(1) = ln(18) (maximum) and f(-2) = ln(4) (minimum).
Explanation:
To find the absolute maximum and absolute minimum values of the function f(x) = ln(x2 + 5x + 12) on the interval [-3, 1], we first need to find the critical points of the function within this range. The critical points are those at which the derivative equals zero or does not exist.
The derivative of this function is f'(x) = 2x + 5 / (x2 + 5x + 12). Setting this equal to zero and solving for x, we get the values -1 and -2. Both of these are within our interval, so they are critical points.Next, we evaluate the function at the critical points and at the end points of the given interval. We get f(-3) = ln(6), f(-2) = ln(4), f(-1) = ln(6), and f(1) = ln(18).The absolute maximum value within the interval is ln(18) and the absolute minimum value is ln(4).
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The absolute maximum value of f(X) on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749 ), which occurs at ( x = -5/2).
To find the absolute maximum and minimum values of[tex]\( f(x) = \ln(x^2 + 5x + 12) \)[/tex] on the interval [tex]\([-3, 1]\)[/tex], we first need to find the critical points and check the values of the function at those points and at the endpoints of the interval.
1. Find the critical points: Critical points occur where the derivative of the function is zero or undefined.
First, let's find the derivative of (f(x):
[tex]\[ f'(x) = \frac{1}{x^2 + 5x + 12} \cdot (2x + 5) \][/tex]
Setting ( f'(x)) equal to zero:
2x + 5 = 0
x = -5/2
Since this value x = -5/2 lies within the interval [-3, 1], it's a critical point.
2. Check the endpoints and critical point:
[tex]- \( f(-3) = \ln((-3)^2 + 5(-3) + 12) = \ln(9 - 15 + 12) = \ln(6) \)[/tex]
[tex]- \( f(1) = \ln(1^2 + 5(1) + 12) = \ln(1 + 5 + 12) = \ln(18) \)[/tex]
[tex]- \( f\left(-\frac{5}{2}\right) = \ln\left(\left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 12\right) = \ln\left(\frac{25}{4} - \frac{25}{2} + 12\right) = \ln\left(\frac{25 - 50 + 48}{4}\right) = \ln\left(\frac{23}{4}\right) \)[/tex]
3. Compare the values:
- ln(6) = 1.792
- ln(18) = 2.890
- [tex]ln\left(\frac{23}{4}\right)[/tex] = 1.749
So, the absolute maximum value of f(X) on the interval [-3, 1] is approximately ( 2.890), which occurs at ( x = 1), and the absolute minimum value is approximately (1.749), which occurs at ( x = -5/2).
amelia and 2 of her friends went out to lunch. each girl ordered exactly the same meal. the total cost 55.08, which included 8% sales tax. what was the price of each meal, not including tax?
Answers
108% = 55.08
1% = 55.08 ÷ 108 = $0.51
100% = $51
3 meals = $51
1 meal = $51 ÷ 3 = $17
Answer: $17
Answer:
$16.8912
Step-by-step explanation:
We are given that Amelia and her two friends went out to lunch.
If each girl ordered exactly the same meal.
We have to find out the value of price of each meal without tax.
Total cost of meals=$55.08
Cost of 3 meals with tax=$55.08
Sales tax=8% of $55.08
8% of 55.08=[tex]\frac{8}{100}\times55.08[/tex]
8% of 55.08= $4.4064
Cost of 3 meals without tax=$55.08-$4.4064=$50.6736
Cost of each meal=[tex]\frac{50.6736}{3}=[/tex]$16.8912
Hence, the cost of each meal without tax=$16.8912
what tool or tools would you choose to use to solve this problem?
Answers
Answer:
A tool.
Now I just need to put filler so I'm just gonna copy and paste. Now I just need to put filler so I'm just gonna copy and paste.
who do you write a function
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solve |3z-7|-4=0,|1- 3k/4|=7 plz
thx
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Find the area of 7.1m. Round to the nearest tenth. Use 3.14.
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paula earned a 56% on her test. If she got 14 problems correct. how many did she get incorrect
Answers
In Youngtown the population reach 4420 people in 1993 in 1998 there were 5600 residents what was toe population in the year 2000
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5 years = 1180 people
5n = 1180
n = 236
236*2 = 472
5600 + 472 = 6072
6072 people
(5a-5)(2a+2)
Find each product
Answers
= 5a*2a -5*2a + 2*5a - 5*2
= 10a^2 - 10a + 10a - 10
= 10a^2 - 10
The product of the equation is 10a^2 - 10
[tex](5a - 5)(2a + 2) \\10a {}^{2} + 10a - 10a - 10 \\ 10a {}^{2} - 10[/tex]
You foil and the add like terms.
A group of students recycled 7 2/3 pounds of glass and 9 3/4 pounds of paper. How many pounds of glass and paper did the students recycle alltogether?
Answers
[tex]\bf \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} \\\\\\ \stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}\\\\ -------------------------------\\\\ \cfrac{23}{3}+\cfrac{39}{4}\qquad \stackrel{LCD~of~12}{\implies }\qquad \cfrac{4(23)+3(39)}{12}\implies \cfrac{92+117}{12} \\\\\\ \cfrac{209}{12}\implies 17\frac{5}{12}[/tex]
The students recycle 17 5/12 pounds of glass and paper all together.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now it is given that,
Pounds of glass recycled = 7 2/3
⇒ Pounds of glass recycled = 23/3
Pounds of paper recycled = 9 3/4
⇒ Pounds of paper recycled = 39/4
Thus, total pounds of glass and paper recycled = Pounds of glass recycled + Pounds of paper recycled
⇒ total pounds of glass and paper recycled = 23/3 + 39/4
⇒ total pounds of glass and paper recycled = 209/12
⇒ total pounds of glass and paper recycled = 17 5/12 pounds
Thus, the students recycle 17 5/12 pounds of glass and paper all together.
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A jogger goes 1.5km west and then turns south.If the jogger finishes 1.7 km from the starting point,how far south did the jogger go?
Answers
You can use the Pythagorean Theorem to solve this
[tex] a^{2} + b^{2} = c^{2} [/tex]
c is the hypotenuse
a and b are the legs
Put in the values you know
[tex] 1.5^{2} + b^{2} = 1.7^{2} [/tex]
Square the numbers
[tex]2.25+ b^{2} =2.89[/tex]
Subtract 2.25 from both sides
[tex] b^{2} =0.64[/tex]
Take the square root of both sides
b = 0.8
The answer is 0.8km
Hope this helps!
Final answer:
To find out how far south the jogger went, we use the Pythagorean theorem. Given the distances of 1.5 km west and 1.7 km from the start, the jogger went 0.8 km south.
Explanation:
To determine how far south the jogger went, we can use the Pythagorean theorem, as the jogger's path forms a right-angled triangle where one leg of the triangle is the distance west, the other leg is the distance south, and the hypotenuse is the distance from the starting point.
The question states the jogger goes 1.5 km west and ends up 1.7 km from the starting point. We denote the distance travelled south as y. According to the Pythagorean theorem:
west^2 + south^2 = distance from start^2
y = √0.64
y = 0.8 km
So the jogger went 0.8 km south.
The following figures were entered on a checking-account record. Add or subtract them to keep the running total correct. Balance forward $643.72 Check #5734 to Lupe's Market, for food, for $68.29 $ Deposit of $341.80, a paycheck $ Check #5735 to Broadmoor Community Center in the amount of $34.18 $ Check #5736 to Bill Baughman, for plumbing services, for $60.00 $
Answers
It is given Balance forward $643.72 in the account. An amount of $68.29 is given to to Lupe's Market, for food. In the account a Deposit of $341.80 is made.A Cheque of $34.18 is given to Broadmoor Community Center .Charge for for plumbing services, is $60.00 .
Transactions made in the account = $643.72-68.29+341.80-34.18-60.00
Amount left in the account =$823.05.
Answer:
Running Total = $823.05
Step-by-step explanation :
When the figures were entered on a checking account record to keep the running total correct :
Balance forward = $643.72
Check #5734 to Lupe's Market for food = $68.29
A deposit = $341.80
Check #5735 to Broadmoor Community Center = $34.18
Check #5736 to Bill Baughman for plumbing services = $60.00
Total Transactions :
643.72 - 68.29 + 341.80 - 34.18 - 60 = $823.05
Total balance = $823.05
NEED HELP FAST PLEASE
Evaluate the limit.
a.4
c.1
b.2
d.limit does not exist
Answers
(8n2 + 5n + 2) / (3 + 2n)
Evaluating for n = inf we have:
(8 (inf) 2 + 5 (inf) + 2) / (3 + 2 (inf))
(inf) / (inf)
We observe that we have an indetermination, which we must resolve.
Applying L'hopital we have:
(8n2 + 5n + 2) '/ (3 + 2n)'
(16n + 5) / (2)
Evaluating again for n = inf:
(16 (inf) + 5) / (2) = inf
Therefore, the limit tends to infinity.
Answer:
d.limit does not exist
if the customer's order came to $6.22 and he gave you $20.25 what is his change
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beth wants to buy shelves to hold 38 boxes of photos there is a shelf that will hold 8 boxes of photos beth calculates that 38/8=4 r6 how many shelves will beth need to hold all 38 photo boxes
Answers
38/8
=4.75
~5 shelves
thus the answer is 5 shelves
Which is the graph of f(x) = x2 – 2x + 3? Help its timed, also don't want an verified answers
Answers
to resolve this type of exercise you must in first place to verify The determinant of the function to know if it cuts to the x axis, with the following formula b^2-4ac, if this value is less than zero then the function , do not cut the x axis, now -(2)^2-4(1)(3) = -8, as this value is negative, it means that is less than zero nd the function do not cut the x axis
2) the graph cut the y axis eN Y = 3 for x= o, F(0) = 0+2*0+3 = 3
3) This is the graph
Tony makes an hourly salary of $11.50 for 40 regular hours of work. For any time worked beyond 40 hours, he is paid at a rate of time and a half per hour. Last week, Tony worked 46 hours. Find each of the following for this period. Tony’s gross pay. Social Security Tax (6.2%) Medicare tax (1.45%)
Answers
We are given that:
Tony is paid $11.5 per hour for the first 40 hours of work
Tony is paid 1.5 * 11.5 = $17.25 for each hour beyond the 40 hours.
We know that last week he worked 46 hours.
This means that:
he got the normal payment of $11.5 for the first 40 hours
he got the special payment of $17.25 for the extra 6 hours
Therefore:
Total amount he gained = 40(11.5) + 6(17.25) = $563.5
This means that, before removing any taxes or insurances, Tony had a payment of $563.5
Part (2):
We know that the social security tax is 6.2% of the amount he gained.
This means that:
social security tax = 6.2% * 563.5
social security tax = 0.062 * 563.5
social security tax = $34.937
Part (3):
We know that the medicare tax is 1.45% of the amount he gained.
This means that:
medicare tax = 1.45% * 563.5
medicare tax = 0.0145 * 563.5
medicare tax = $8.17075
Part (4):
To get the amount that Tony has after all the taxes, we will subtract the amount of taxes from what he originally gained as follows:
final amount gained = 563.5 - (34.937+8.17075)
final amount gained after taxes = $520.39225
Hope this helps :)
Tony's gross pay for 46 hours of work, including 6 hours of overtime, is $563.50. The Social Security tax on this amount is $34.94, and the Medicare tax is $8.17.
Explanation:Calculating Tony's Gross Pay
Tony's regular pay for 40 hours at an hourly rate of $11.50 is calculated by multiplying the hourly rate by the number of regular hours he worked. Therefore, his regular pay is 40 hours × $11.50/hour = $460. To calculate the overtime pay, we must first determine the overtime rate. The overtime rate is 1.5 times the normal hourly rate, thus the overtime hourly rate is 1.5 × $11.50/hour = $17.25/hour. Tony worked 6 hours overtime, so his overtime pay is 6 hours × $17.25/hour = $103.50. Tony's gross pay is the sum of his regular pay and overtime pay, which is $460 + $103.50 = $563.50.
Calculating Deductions for Social Security and Medicare
The Social Security tax and Medicare tax are calculated as percentages of the gross pay. The Social Security tax at 6.2% of $563.50 is $563.50 × 0.062 = $34.937, which rounds to $34.94. The Medicare tax at 1.45% of $563.50 is $563.50 × 0.0145 = $8.17075, which rounds to $8.17.
A right triangle has one side, s, and a hypotenuse of 12 meters. Find the area of the triangle as a function of s.
A) A(s) = 2s
144 - s2
B) A(s) = s
144 - s2
C) A(s) = 2s
12 - s2
D) A(s) = 12s
144 - s2
10)
The base of a ladder is placed 5 feet away from a 13 foot tall wall. What is the minimum length ladder needed to reach the top of the wall (rounded to the nearest foot)?
A) 12 ft
B) 13 ft
C) 14 ft
D) 15 ft
Answers
we know that
area of triangle=b*h/2
b=s
applying the Pythagoras theorem
h²=12²-s²--------> h=√(144-s²)
so
A=(1/2)*s*√(144-s²)
Part b)
applying the Pythagoras theorem
c²=a²+b²
in this problem
c is the minimum length ladder needed to reach the top of the wall
a=5 ft
b=13 ft
so
c²=5²+13²-----> c²=194--------> c=13.93 ft-------> c=14 ft
the answer is
14 ft
Farmer Ed has 7000 meters of fencing and wants to enclose a rectangular plot that borders on a river. If farmer Ed does not fence the side along the river, what is the largest are that can be enclosed?
Width = 2x
Length = 7,000-2x
Answers
Chord SR intersects tangent AB to form ∠SRA. Find m∠SRA.
A. m∠SRA = 40°
B. m∠SRA = 80°
C. m∠SRA = 100°
D. m∠SRA = 140°
Answers
we know that
C is the center of the circle
CR=CS-----> is the radius of the circle
CR and AB are perpendicular
the triangle SCR is a isosceles triangle
angle SCR is equal to 80°------> is a central angle
angle CSR and angle CRS are equal to 50°----> because 80+50+50=180
therefore
m∠SRA=90°-m∠CRS------> m∠SRA=90°-50°=40°
the answer is
m∠SRA=40°
Answer:
C.
Step-by-step explanation:
what multiplication problem does the model show? And why? please explain.
Answers
A multiplication problem shows the process of calculating the product when one number is multiplied by another. This can be represented using an array model, an area model, or a multiplication sentence. Specific representation will depend on the model provided.
Explanation:In mathematics, a multiplication problem represents the process of finding the product or result when one number is multiplied by another.
However, without a specific model being given in the question, providing a precise answer becomes challenging. In general terms, a multiplication model could be in the form of an array, an area model, or a multiplication sentence. To understand this better, let's illustrate with an example.
An array model of multiplication might show 4 rows of 3 blocks, representing the problem 4 x 3 = 12.An area model could show a rectangle partitioned into smaller parts, with each representing a multiplication fact.A simple multiplication sentence like 2 x 5 = 10, represents the multiplication fact directly.In all the cases, the multiplication problem is demonstrating how to find the product of two numbers or quantities.
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Q #9. find the volume of the sphere
Answers
= 523 in³
The correct answer is the first
volume of a sphere=(4/3)*pi*r³
for r=5 in
volume of a sphere=(4/3)*pi*5³-------> 523.33 in³-------> volume =523 in³
the answer is
the volume is equal to 523 in³
Evaluate the expression 5a + 5b. Let a = -6 and b = -5.
Answers
n = 5a + 5b
n = 5(-6) + 5(-5)
n = -30 + -25
n = -55
Hope this helps