Answer:
[tex]\lim_{x \to 2} (x+1)(3x^2-9) = 9[/tex]
Step-by-step explanation:
Step 1: Write out limit
[tex]\lim_{x \to 2} (x+1)(3x^2-9)[/tex]
Step 2: Evaluate
(2 + 1)(3(2)² - 9)
3(3(4) - 9)
3(12 - 9)
3(3)
9
Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a six and then selecting a nine.
The probability of selecting a six and then selecting a nine is
(Round to three decimal places as needed.)
Answer:
0.006
Step-by-step explanation:
The probability that the first card is a six is 4/52.
There's one less card now, so the probability that the second card is nine is 4/51.
The total probability is:
P = (4/52) (4/51)
P ≈ 0.006
If Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a six and then selecting a nine. The probability of selecting a six and then selecting a nine is 0.006
Let the probability that the first card is six be 4/52
Let the probability that the second card is nine be 4/51
Now let determine the probability of selecting a six and then selecting a nine
Probability (P)=(4/52×4/51)
Probability (P)=16÷2,652
Probability (P)= 0.006
Inconclusion if Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a six and then selecting a nine. The probability of selecting a six and then selecting a nine is 0.006
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Simplify by using the greatest common factor to the equation in photo. Someone please help it would greatly be appreciated!
(12x^2 - 15x) / 3x
Divide the expression by 3x
4x - 5 is the simplified version of your expression
8a + 4 = 4 + 8a
Property bank
Answer:
x=x
Infinite solutions
Step-by-step explanation:
8a + 4 = 4 + 8a
subtract 4
8a=8a
Factor out the GCF (8)
x=x
when an equation simplifies to x=x, it has Infinite solutions
Answer:
Commutative Property of Addition
Step-by-step explanation:
I don’t understand this. Please help
I'll do problem 5 to get you started.
The answer is choice B and choice DThe reason why choice B is one answer is because we have something in the form y = k/x to indicate an inverse variation. Replace x with H and y with T, and you'll get the same basic equation.
With inverse variation equations, as one variable goes down, the other variable goes up. Think of a see-saw as one way to visualize what's going on.
Or you can think of the T as T/1. So the equation T = L/H is the same as T/1 = L/H. If H were to decrease, then T would increase, and vice versa. T and H are on opposite sides of their respective fractions which may help see this opposite moving nature of each variable.
The reason why choice D is also an answer is because we can multiply both sides of T = L/H by H to get HT = L or TH = L. The equations T = L/H and TH = L are equivalent equations.
Answer:
5. 2nd and 4th boxes
Step-by-step explanation:
These look like proportionality questions. Typically we hear about two main types of proportionalities:
Directly proportional, which means that two variables change in the same way (Ex. one goes up, the other goes up).Inversely proportional, which means that two variables change in opposite ways (Ex. one goes up, the other goes down).Directly proportional variables are, intuitively, on opposite sides of an equation and both in the numerator on their side. Inversely proportional variables are on opposite sides but with one in the numerator and one in the denominator.
I can't see what the top one is asking for nor the bottom of 6., but let me try and use 5. as an example. If H increases as T decreases, then the two are inversely proportional. So the form would either have to be H=1/T or T=1/H. Other variables can be thrown into the mix and not change the outcome, so the 2nd and 4th boxes are your answers for 5.
Seven more than the product of a number and 8 is equal to 6
Answer:
Step-by-step explanation:
7>4n=6 or 7>4+n=6
Tom earns $15.50 per hour at the Yankee Bowling Alley. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 42 hours. What was his gross pay for the week?
Answer:
$666.50
Step-by-step explanation:
Tom worked only 2 hours of overtime, at (1.5)($15.50/hr) = $23.25/hr.
At the regular pay rate of $15.50/hr he earned:
($15.50/hr)(40 hrs) = $620
His overtime pay is (1.5)($15.50/hr)(2 hr) = ($23.25/hr)(2 hr) = $46.50
Additing these two amounts together, we get $666.50 (gross pay for the week).
The weights of 3 puppies at one week old were 6.5 ounces, 7.3 ounces, and 6.4 ounces. If each
puppy gained 2.1 ounces, how much would the puppies weigh?
The first puppy would weigh ounces, the second puppy would weigh ounces, and the third
puppy would weigh ounces.
(Type integers or decimals.)
The answers are 8.6 ounces, 9.4 ounces, and 8.5 ounces
Explanation:
To find how much each puppy weights simply add the weight they gained (2.1 ounces) to the weight of each puppy at one week old. The process to add the weights is shown below:
First Puppy
6.5 ounces (weight at one week old) + 2.1 ounces (weight gained)
Align both numbers using the period as the reference and add
6.5
+ 2.1
8.6
The weigh of the first puppy is 8.6 ounces which can be rounded as 9 ounces (integer)
Second Puppy
Now, repeat the process
7.3 ounces + 2.1 ounces
7.3
+ 2.1
9.4
The weigh of this puppy is 9.4 ounces or 9 ounces (integer) if rounded
Third Puppy
6.4 ounces + 2.1 ounces
6.4
+ 2.1
8.5
The weight of the third puppy is 8.5 ounces which can be rounded as 8 ounces or 9 ounces (integers) depending on the rounding method.
Answer:
The answer to this questions is 8.6
Step-by-step explanation:
I need help with this question
Answer: Choice A) [tex]x > -3[/tex]
There's an open hole at -3 and shading to the right of this hole.
The hole indicates "do not include this endpoint". So we won't have an "or equal to" as part of the inequality sign.
The shading is to the right meaning we are shading everything larger than -3.
is -0.347 a rational number
Answer:
Yes
Step-by-step explanation:
-0.347 is a rational number because all positive and negative numbers are integers
In a linear cost function, the marginal cost is the (additional, abstract or fixed) cost per item.
Answer:
Does this help
Step-by-step explanation:
included in the fixed cost are, for instance, mortgage payments, salaries, and insurance. This allows us to interpret the marginal cost, m = $3.50, as the cost to print each additional books.In general, the marginal cost is the cost per additional item.
abstractAnswer:
additional
Step-by-step explanation:
find the unit rate of 2 1/2 miles in 3/4 hour
HELP PLZZZZ
Answer:
2 1/2 miles per hour
Step-by-step explanation:
A boat that is out in sea is 400m from the bottom of a cliff. A lighthouse is at the top of the cliff. The lighthouse is 52m tall. The distance from the boat to the top of the lighthouse is 610m. What is the height of the cliff?
Answer:
409m
Step-by-step explanation:
Please see attached picture for full solution.
name a rational number between the two given numbers? 7/11ths and 4/7ths explain how you know
Answer:
basically u have to beble gep
Step-by-step explanation:
art
10-mg Atorvastatin Placebo Headache 15 65 No headache 17 3 3. If two different subjects are randomly selected, find the probability that they both had a headache.
Answer:
0.6384
Step-by-step explanation:
Given that:
10-mg Atorvastatin Placebo Headache 15 65 No headache 17 3
Hence the total of number of patients = 15 + 65 + 17 + 3 = 100 patients
The number of patients with headache = 15 + 65 = 80 patients
Also, C(n, x) is the number of combinations in which n items can be chosen taken x at a time it is given by the formula:
[tex]C(n,x)=\frac{n!}{(n-x)!x!}[/tex]
The the probability that if two different subjects they both had a headache = [tex]\frac{C(80,2)}{C(100,2)}=\frac{\frac{80!}{(80-2)!2!} }{\frac{100!}{(100-2)!2!} } =\frac{3160}{4950}=0.6384[/tex]
2 is not a solution for
True
False
Answer:
False
Step-by-step explanation:
2 is a solution because to circle is closed. All answers including 2 and above are solutions.
Answer:
False
Step-by-step explanation:
circle is closed so all awnsers 2 and above is correct
10!•4!/6!•5!
Evaluate
O 1,008
O 4/3
2/3
Answer:
1008
Step-by-step explanation:
10!•4!
---------
6!•5!
Rewriting as
10 * 9*8*7*6! * 4!
---------
6!•5*4!
Canceling like terms
10 * 9*8*7
---------
5
1008
Answer:
1,008
Step-by-step explanation:
The answer is not 4/3 or 2/3. So, it has to be 1,008.
Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1
Answer:
[tex]\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]
Step-by-step explanation:
Given that:
The surface area (S.A) [tex]z = x^2 +y^2[/tex]
Hence the S.A is of form z = f(x,y)
Then the S.A can be represented with the equation
[tex]A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA[/tex]
where :
D = cylinder [tex]x^2 +y^2 =1[/tex]
In polar co-ordinates:
D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)
Similarly, [tex]\dfrac{\partial z}{\partial x} = 2x[/tex] and [tex]\dfrac{\partial z}{\partial y} = 2y[/tex]
Therefore;
[tex]S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA[/tex]
[tex]= \iint_D \sqrt{1+4(x^2+y^2)} \ dA[/tex]
[tex]= \int^{2 \pi}_{0} \int^{1}_{0} \sqrt{1+4r^2} \ r \ dr \d \theta[/tex]
[tex]= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0[/tex]
[tex]= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1][/tex]
[tex]\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]
11.18034 rounded to the nearest tenth
Answer:
11.2
Step-by-step explanation:
Find the number in the tenth place 1 and look one place to the right for the rounding digit 8 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
Hope this helps!
Help me I’m struggling
Answer:
Hey there!
(8^2)^-4=8^2(-4), or 8^-8
8^-8 can be expressed as the third option.
Hope this helps :)
x2 + 10x + 89 = 0
what are the roots of the equation in the simplest a+bi form?
Answer:
The answer is
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]Step-by-step explanation:
x² + 10x + 89 = 0
Using the quadratic formula
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]From the question
a = 1 , b = 10 , c = 89
Substitute the values into the above formula and solve
We have
[tex]x = \frac{ - 10\pm \sqrt{ {10}^{2} - 4(1)(89)} }{2(1)} \\ = \frac{ - 10\pm \sqrt{100 - 356} }{2} \\ = \frac{ - 10\pm \sqrt{ - 256} }{2} \\ = \frac{10\pm 16 \: i}{2} [/tex]Separate the real and imaginary part
That's
[tex]x = - \frac{10}{2} \pm \frac{16}{2} \: i \\ x = - 5\pm8 \: i[/tex]We have the final answer as
[tex]x = - 5 + 8 \: i \: \: \: \: or \: \: \: \: x = - 5 - 8 \: i \\ [/tex]Hope this helps you
I need help I've been suffering on this questiona all day
Answer:
-6.8
Step-by-step explanation:
When your going up you add a number.
How many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 20% antifreeze to get a mixture that is 60% antifreeze?
gallons
The number of gallons that must be mixed is
(Round to the nearest whole number.)
Answer:
360
Step-by-step explanation:
If x is gallons of 70% antifreeze solution, then:
0.70x + 0.20(90) = 0.60(x + 90)
0.70x + 18 = 0.60x + 54
0.10x = 36
x = 360
What is the greatest common
factor) of 105 and 75
Answer: 15
Answer:
What?
Step-by-step explanation:
Desmond and Molly each purchased 5 boxes of tangerines, and each box contains 60 tangerines.
How many tangerines do they have in total?
Answer:
600 tangerines in total
Step-by-step explanation:
If I am reading it correctly, Desmond purchased 5 boxes, and Molly purchased 5 boxes, meaning that would be 10 boxes in total. 10 times 60 is 600.
Consider three siblings:
Amy, Barry, and Clarence. Amy is 3 years older than Barry, and Barry is 4 years older
than Clarence. If the sum of their ages is 62, what are the three ages?
Amy =
Barry =
Clarence =
Answer:
Amy-24
Barry-21
Clarence-17
Step-by-step explanation:
Clarence is the youngest and so you add 4 to that to get Barry, add 3 more to that to get Amy.
Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page
Answer:
Step-by-step explanation:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
A candle maker plans to make 303030 orange candles. She mixes wax to create a specific shade of orange. The ratio of each color in her mixture is shown below:
222 parts red wax
555 parts yellow wax
333 parts white wax
PART A
The candle maker needs 111 quart of orange wax for every 666 candles.
How much yellow wax will the candle maker need to make all 303030 candles?
Choose 1 answer:
Answer:
I would say
Step-by-step explanation:
303030 divided by 666 =455
666x455=303030
455-666=2110
so it would be 2110
1. On the number line, plot and label all numbers with an absolute value of 3/2
Answer:
1 1/3
Step-by-step explanation:
it's unporore
Points [tex]\frac{3}{2} , \frac{-3}{2} , 1.5 , -1.5 , 1 \frac{1}{2} , -1 \frac{1}{2}[/tex] have same absolute value as 3/2
What is an absolute value?The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign.
For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5.
According to the question
numbers with an absolute value of 3/2 are
[tex]absolute value of |\frac{-3}{2}| = \frac{3}{2} \\absolute value of |1.5| = 1.5 or \frac{3}{2} \\\\absolute value of |-1.5| = 1.5 or \frac{3}{2} \\\\absolute value of |1\frac{1}{2} | = \frac{3}{2} \\\\\\[/tex]
[tex]absolute value of |-1\frac{1}{2} | = \frac{3}{2}[/tex]
Number line is attached below
Hence, Points [tex]\frac{3}{2} , \frac{-3}{2} , 1.5 , -1.5 , 1 \frac{1}{2} , -1 \frac{1}{2}[/tex] have same absolute value as 3/2 .
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# SPJ2
I need the domain range and function. With an explanation
Problem 1
Domain = [tex]-3 < x \le 3[/tex], interval notation (-3, 3]Range = [tex]-3 \le y < 3[/tex], interval notation [-3, 3)Is it a function? YesProblem 2
Domain = [tex]x \ge -2[/tex], interval notation [tex][-2, \infty)[/tex]Range = All real numbers, interval notation [tex](-\infty, \infty)[/tex]Is it a function? NoProblem 3
Domain = [tex]-4 \le x < 3[/tex], interval notation [-4, 3)Range = [tex]-4 < y \le 3[/tex], interval notation (-4, 3]Is it a function? YesProblem 4
Domain = All real numbers, interval notation [tex](-\infty, \infty)[/tex]Range = [tex]y \le 4[/tex], interval notation [tex](-\infty, 4][/tex]Is it a function? Yes==================================================
Explanations:
The left most point is when x = -3, and we are not including this value due to the open hole. The other endpoint is included because it is a filled in circle. The domain is therefore [tex]-3 < x \le 3[/tex] which in interval notation is (-3, 3]. We have the curved parenthesis meaning "exclude endpoint" and the square bracket says "include endpoint". The range is a similar story but we're looking at the smallest and largest y values. Though be careful about which endpoint is open/closed. We have a function because it passes the vertical line test.The smallest x value is x = -2. There is no largest x value because the arrows say to go on forever to the right. We can say the domain is [tex]x \ge -2[/tex] which in interval notation is [tex][-2, \infty)[/tex]. The range is [tex](-\infty, \infty)[/tex] to indicate "all real numbers". This graph fails the vertical line test, so it is not a function. The vertical line test is where we check to see if we can pass a vertical line through more than one point on the curve. In this case, such a thing is possible which is why it fails the test.This is the same idea as problem 1, though note the endpoints are flipped in terms of which has an open circle and which doesn't. It is not possible to draw a single vertical line to have it pass through more than one point on the curve, so it passes the vertical line test and we have a function.This is a function because it passes the vertical line test. The domain is the set of all real numbers due to the arrows in both directions. Any x value is a possible input. The range is [tex]y \le 4[/tex] which is the same as saying [tex](-\infty, 4][/tex] in interval notation. This is because y = 4 is the largest y value possible. There is no smallest y value due to the arrows.desperate i need help on this
Complementary angles are two angles which sum is equal to 90 degrees
angle DFG and angle JKL are complementary angles
DFG = x + 3
JKL = x - 5
x-5 +x + 3 = 90
Add like terms
2x - 2 = 90
Add 2 to each side
2x = 92
Divide each side by 2
x = 46
Let's plug 46 into x for angle DFG
46 + 3 = 49
Since they add up to 90, we can subtract 49 from 90 to get angle JKL
90 - 49 = 41
DFG = 49
JKL = 41
For question 5, bisecting means cutting something in half. Angles LMO and NMO are equal to each other.
6x - 21 = 2x + 31
Let's subtract 2x from both sides and add 21 to both sides
4x = 52
Divide each side by 4
x = 13
Let's plug 13 in for x
LMO = 6(13) - 21 = 57
Since LMO and NMO are equal, we can multiply 57 by 2
57 * 2 = 114
The measure of LMN is 114
