Answer:
B. 3.
Step-by-step explanation:
At the limit we can take the numerator to be √(9x^4) = 3x^2
The function is of the form ∞/ ∞ as x approaches ∞ so we can apply l'hopitals rule:
Differentiating top and bottom we have 6x / 2x - 3. Differentiating again we get 6 / 2 = 3.
Our limit as x approaches infinity is 3.
The limit of [tex]\(\sqrt{9x^4 + 1}/(x^2 - 3x + 5)\)[/tex] as x approaches infinity is 3, after comparing the highest powers of x in both the numerator and the denominator and simplifying.
Explanation:To find the limit of the given function [tex]\(\displaystyle\lim_{x \to \infty} \frac{\sqrt{9x^4+1}}{x^2 -3x + 5}\)[/tex] as x approaches infinity, we can use the property of limits involving infinity. We need to compare the highest powers of x in both the numerator and the denominator. The highest power of x in the numerator under the square root is x⁴, and outside the square root, it will be x². In the denominator, the highest power is x². If we divide the numerator and the denominator by x², we get:
[tex]\[ \frac{\sqrt{9x^4+1}}{x^2 -3x + 5} = \frac{\sqrt{\frac{9x^4}{x^4}+\frac{1}{x^4}}}{\frac{x^2}{x^2} -\frac{3x}{x^2} + \frac{5}{x^2}} = \frac{\sqrt{9+\frac{1}{x^4}}}{1 -\frac{3}{x} + \frac{5}{x^2}} \][/tex]
As x approaches infinity, the terms [tex]\(\frac{1}{x^4}\), \(\frac{3}{x}\), and \(\frac{5}{x^2}\)[/tex] approach zero, and we are left with:
[tex]\[ \frac{\sqrt{9}}{1} = 3 \][/tex]
Therefore, the limit of the given function as x approaches infinity is 3, which corresponds to option (B).
Kim and her two brothers each use one and a half cups of milk for breakfast. How many fluid ounces of milk do they use in four days
Answer: 48 fl oz ( fluid ounces )
Explanation:
1 c = 8 fl oz
1 1/2 c = 12 fl oz
12 fl oz of milk × 4 Days =
48 fl oz in four days
Reggie can line a football field in 120 minutes. Rosalinda can line a football field in 80 minutes. If they work together, how many minutes does it take them to line a football field?40 minutes 48 minutes200 minutes 240 minutes
Answer:
48 minutes.
Step-by-step explanation:
Reggie can line [tex]\frac{1}{120}[/tex] of a football field in one minute.
Rosalinda can line [tex]\frac{1}{80}[/tex] of a football field in one minute.
[tex]\frac{1}{120}[/tex] + [tex]\frac{1}{80}[/tex] = [tex]\frac{1}{48}[/tex], so together, they can line [tex]\frac{1}{48}[/tex] of a football field in one minute.
[tex]\frac{1}{48}[/tex] * 48 = 1
They can line 1 football field together in 48 minutes.
Hat every 2nd visitors backpack every 10th visitor tshirt every 7th visitor how often will a bag contain a 3 items
Answer:
Every 70th visitor
Step-by-step explanation:
Find the least common multiple of 2, 10, and 7.
Write the prime factorization:
2 = 2
7 = 7
10 = 2×5
So the LCM is:
LCM = 2×5×7
LCM = 70
Every 70th visitor will get a bag containing all 3 items.
victor jogged 8 3/7 kilometers on Monday and 7 4/6 kilometers o Tuesday. what is the difference between these two distances?
Answer:
16/21 km
Step-by-step explanation:
The LCD here is 42. Thus, 8 3/7 km = 8 18/42 and 7 4/6 km = 7 28/42 km.
The difference in the two distances is
8 18/42 km
- 7 28/42 km
---------------------
or:
7 60/42 km Here I have borrowed 42/42 from that 8.
- 7 28/42 km
---------------------
32/42 km, or 16/21 km
What are the exact solutions of x2 = 4 − 7x?
x^2 = 4 -7x
Need to rewrite the equation in quadratic form.
Add 7x to each side:
x^2 +7x = 4
Subtract 4 from each side:
x^2 + 7x - 4 = 0
Now using the quadratic formula -b +/-√(b^2-4(ac)) / 2a
We can solve for x.
a = 1, b = 7 and c = -4
Replace the letters with their values:
-7 +/- √(7^2 -4(1-4)) / 2*1
Simplify:
-7 +/- √65 /2
The exact answers are:
X = -7 + √65 / 2 and X = -7 - √65 / 2
Answer:
X = -7 + √65 / 2 and X = -7 - √65 / 2
Step-by-step explanation:
A spinner is separated into 4 equal pieces, as shown below: A spinner is shown with four colors, yellow, pink, white, and black, marked on it. The arrow points towards the black color. Jonathan spins the spinner 10 times. What is the theoretical probability that it stops on the black sector on the last spin?
Answer:
The answer is 1 over 4
Step-by-step explanation:
Answer:
1/4.
Step-by-step explanation:
The spinner has 4 sections, and 1 out of those 4 is the black one, that of which we are seeing the probability of landing on it.
1 chance out of 4 for landing on black.
therefore, your answer is 1/4.
sorry if i'm late but I needed the points :)
Please please help me out
12x18.2/2=109.2 is the area of the big triangle and also the same area could be found 20 x h=109.2 so
h= 109.2/20=5.46 m
Maureen tracks the range of outdoor temperatures over three days. She records the following information.
(picture attached)
Which answer below expresses the intersection of the three days as an inequality in terms of temperature, t. (The Intersection would be the temperatures they have in common.)
0 < t < 40
0 ≤ t ≤ 40
-23 ≤ t ≤ 50
-23 < t < 50
The answer is:
The correct option is the third option;
[tex]-23\leq t\leq 50[/tex]
Why?To find which of the options expresses the intersection of the three days as an inequality in terms of temperature "t" we need to find an inequality which starts at the lowest temperature (greater or equal) and finish at the highest temperature (less or equal).
So, we have that the lowest temperature is -23°F and the highest temperature is 50°F, there are two options for that range, but we need to consider that the temperature will range from -23° to 50°, so, the correct option is the third option;
[tex]-23\leq t\leq 50[/tex]
We can see that the inequality express that the temperature will range from -23°F being greater or equal than that, to 50°F being less or equal than that.
Have a nice day!
What are the angle measures of triangle VUW?
A) m∠V = 30°, m∠U = 60°, m∠W = 90°
B) m∠V = 90°, m∠U = 60°, m∠W = 30°
C) m∠V = 30°, m∠U = 90°, m∠W = 60°
D) m∠V = 60°, m∠U = 90°, m∠W = 30°
Answer:
its option D
Step-by-step explanation:
The angle measures of triangle VUW is D) m∠V = 60°, m∠U = 90°, m∠W = 30°
What are the 3 angles of a triangle?
All three angles in any triangle always upload as many as 180 degrees. So in case you best have of the angles with you, just upload them together, after which subtract the sum from 180. EX: A Triangle has three angles A, B, and C.
What is the angle measure formula?The method for finding the sum of the measure of the indoor angles is (n - 2) * 180. To discover the degree of 1 indoors perspective, we take that method and divide via the range of aspects n: (n - 2) * a hundred and eighty / n.
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You told your friend you could eat 1/3 a large pizza. If you only ate 3/5 of what you said you could, how much pizza did you eat?
Answer:
1/5
Step-by-step explanation:
If you only eat 3/5 of 1/3, you ate 3/5 × 1/3. Multiply fractions straight across the top and straight across the bottom to get 3/15. That reduces down to 1/5. So you ate 1/5 of the large pizza.
Follow below steps:
The question asks how much of a pizza you ate if you initially claimed you could eat 1/3 of a large pizza but ended up eating only 3/5 of that amount. To solve this, you need to multiply the fractions. Multiplying 1/3 by 3/5 gives us:
1/3 of a pizza (the amount you said you could eat) times3/5 (the fraction of the 1/3 you actually ate)When you multiply these two fractions, you get:
(1/3) * (3/5) = 3/15 = 1/5
Therefore, you ate 1/5 of the large pizza.
Please help me out please
Answer:
16.6 in
Step-by-step explanation:
The volume (V) of a pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × h
where h is the perpendicular height and area of base = 14² = 196
here V = 980, so
[tex]\frac{1}{3}[/tex] × 196h = 980 ( multiply both sides by 3 )
196h = 2940 ( divide both sides by 196 )
h = 15
Consider the right triangle formed by the height h from the vertex to the midpoint of the base and the slant height (s) ← the hypotenuse
Using Pythagoras' identity in the right triangle
s² = 15² + 7² = 225 + 49 = 274 ( take the square root of both sides )
s = [tex]\sqrt{274}[/tex] ≈ 16.6
The graph of a linear function has a slope of 1/4 and passes through the point (1,3). What is the y-intercept of the function?
A. b=1/4
B. b=11/4
C. b= -1/4
D. b=4
Answer:
B
Step-by-step explanation:
In slope intercept form, y = mx + b, the m is the slope, the b is the y intercept, and x and y can be subbed in from the point you are given of (1, 3). We are told the slope, so everything we have fills in like this:
[tex]3=\frac{1}{4}(1)+b[/tex]
Now we just need to solve for b:
[tex]3-\frac{1}{4}=b[/tex] and
[tex]\frac{12}{4}-\frac{1}{4}=b[/tex] so
[tex]b=\frac{11}{4}[/tex]
What is the equation of a line passing through (-3, 7) and having a slope of -1/5 ? A. y = -5x + 22 B. y = 5x + 22 C. y=1/5x+32/5 D. y=-1/5x+32/5 E. y=-1/5x+22
Answer:
D. y = -1/5x +32/5
Step-by-step explanation:
The equation of the line passing through point (h, k) with slope m can be written ...
y = m(x -h) +k
Filling in your given values, the equation is ...
y = -1/5(x -(-3)) +7
y = -1/5x -3/5 +7 . . . . eliminate parentheses
y = -1/5x +32/5 . . . . . combine constants
Please please help me out
Answer:
[tex]\frac{15}{17}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
sin²x = 1 - cos²x
sinx = [tex]\sqrt{1-cos^2x}[/tex]
Hence
sinΘ = [tex]\sqrt{1-(8/17)^2}[/tex]
= [tex]\sqrt{1-\frac{64}{289} }[/tex]
= [tex]\sqrt{\frac{225}{289} }[/tex] = [tex]\frac{15}{17}[/tex]
Suppose the line of best fit for some data points has a slope of 1.885. If the mean of the x-coordinates of the data points is 3.448, and the mean of the y-coordinates is 12.318, what is the y-intercept of the line to three decimal places?
Step-by-step Answer:
One of the properties of a least-squares regression line (line of best fit) is that the line always passes through the point (xbar, ybar).
Assuming the given "line of best fit" is a least-squares line, then we are given
a slope m=1.885 passing through (x0,y0)=(3.448,12.318).
Applying the standard point-slope formula:
(y-y0) = m (x-x0)
we get
y-12.318 = 1.885(x-3.448)
Expand and simplify,
y=1.885x -1.885*3.448 + 12.318, or
y=1.885(x) + 5.81852
(numbers to be rounded as precision dictates).
To find the y-intercept of the line of best fit, substitute the mean x and y values and the slope into the equation y = mx + b and solve for b. In this case, the y-intercept is 5.820.
Explanation:To calculate the y-intercept of the line of best fit when you know the slope and the mean values of the x-coordinates and y-coordinates, you can use the formula for the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Given:
Slope (m): 1.885Mean of x-coordinates: 3.448Mean of y-coordinates: 12.318We can substitute the means into the line equation:
12.318 = 1.885(3.448) + b
Now solve for b:
12.318 = 6.49836 + b
b = 12.318 - 6.49836
b = 5.81964
Therefore, the y-intercept b to three decimal places is 5.820.
A hotel in Las Vegas, Nevada, is the largest pyramid in the United States. Prior to the construction of the building, the architects designed a scale model. The height of the scale model is 9 inches less than its length and its base is a square. If the volume of the model is 6300 cubic inches, write an equation describing the situation.
Answer:
The equation that describe the situation is
[tex]b^{3}-9b^{2}-18,900=0[/tex]
Step-by-step explanation:
we know that
The volume of a square pyramid is equal to
[tex]V=\frac{1}{3}b^{2} h[/tex]
where
b is the length side of the square
h is the height of the pyramid
we have
[tex]V=6,300\ in^{3}[/tex]
[tex]h=(b-9)\ in[/tex]
substitute the values and solve for b
[tex]6,300=\frac{1}{3}b^{2} (b-9)\\ \\18,900=[b^{3}-9b^{2}]\\ \\b^{3}-9b^{2}-18,900=0[/tex]
Using a graphing calculator
[tex]b=30\ in[/tex]
[tex]h=(30-9)=21\ in[/tex]
Answer:
A is correct on edge 2022
Step-by-step explanation:
Please help me out please
Answer:
11.7
Step-by-step explanation:
a^2+b^2=c^2
10^2+6^2=c^2
100+36=c^2
add 100+36=136
square root of 136 = 11.6619037897
= 11.7
From the ten books that you've recently bought but not read, you plan to take four with you on vacation. How many different sets of four books can you take
Answer:
Step-by-step explanation:
2 sets of books
if x/5 = 10, then 5 (x/5) = 5(10)
this is an example of which property below?
a. reflexive property
b. commutative property for addition
c. addition property of equality
d. transitive property of equality
e. multiplication property of equality
Answer:
e.
Step-by-step explanation:
Each side is multiplied by 5.
It is the multiplication property of equality.
Identify the measure of arc XY◠. PLEASE HELP!!
Use the intersecting chords theorem: the labeled angle (WVZ) between the given chords has measure that is the average of the two arcs the chords intercept (WZ and XY):
[tex]81^\circ=\dfrac{m\widehat{XY}+52^\circ}2\implies m\widehat{XY}=110^\circ[/tex]
The requried measure of the arc XY is 110°. Option D is correct.
What is an arc?An arc is a portion of the circumference of a circle. It is defined by two endpoints on the circle and all the points on the circle between these endpoints. The length of an arc is proportional to the measure of the central angle that subtends it.
Here,
To use the intersecting chords theorem,
we can state that the measure of the labeled angle (WVZ) between the given chords is equal to the average of the measures of the two arcs intercepted by the chords, namely WZ and XY.
81 = mWZ+ mXY/2
81 = 52 + mXY / 2
mXY = 110°
Thus, the requried measure of the arc XY is 110°. Option D is correct.
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Find the image of A(4, -2) after it is reflected over the line y = 2, then reflected over the line x = 2.
(-8, 6)
(0, -2)
(0, 6)
(-8, -2)
Answer:
(0, 6)
Step-by-step explanation:
The given point A has coordinates (4,-2).
The mapping for a reflection over the line y=k, is given by:
[tex](x,y)\to (x,2k-y)[/tex]
Therefore the line y=2 is
[tex](4,-2)\to (4,2(2)--2)[/tex]
[tex](4,-2)\to (4,4+2)[/tex]
[tex](4,-2)\to (4,6)[/tex]
When this point is again reflected over the line x=2, we use the mapping
[tex](x,y)\to (2k-xx,y)[/tex]
[tex](4,6)\to (2(2)-4,6)[/tex]
[tex](4,6)\to (4-4,6)[/tex]
[tex](4,6)\to (0,6)[/tex]
Answer:
0,6
Step-by-step explanation:
Lena spent less than $20 at the grocery store .Which inequality represents the amount of ,d, that lena spent last the grocery store ?
Answer:
[tex]d < \$20[/tex]
Step-by-step explanation:
Let
d----> the amount of money that Lena spent at the grocery store
we know that
The inequality that represent this situation is
[tex]d < \$20[/tex]
Answer:
d < $20
Step-by-step explanation:
Since they said less than $20 not less than or equal to $20.
please please help! A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec^2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the velocity of the car when t = 6? You must show your work and include units in your answer.
Answer:
42 ft/s
Step-by-step explanation:
The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is (10+4)/2 = 7 ft/s^2, so the change in velocity is ...
(7 ft/s^2)(6 s) = 42 ft/s
The velocity of the car at t=6 is 42 ft/s.
The velocity of the car at t=6 is 42 ft/s.
The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is [tex](10+4)/2 = 7 ft/s^2[/tex], so the change in velocity is ...
[tex](7 ft/s^2)(6 s) = 42 ft/s[/tex]
The velocity of the car at t=6 is 42 ft/s.
Can someone please help me with this??
Answer:
12. v = 013. b = 914. y = 515. z = -816. n = -m and n ≠ 0 and m ≠ 017. x = 3Step-by-step explanation:
[tex]12.\ a^v=1\to a^v=a^0\to v=0\\\\\text{because}\ a^0=1\ \text{for any}\ a\neq0.\\\\13.\ \ b^{-w}=\dfrac{1}{b^9}\to \dfrac{1}{b^w}=\dfrac{1}{b}\to b=9\\\\\text{because}\ a^{-n}=\dfrac{1}{a^n}\ \text{for any}\ a\neq0\\\\14.\ \dfrac{3^3}{3^y}=\dfrac{1}{9}\to\dfrac{3^3}{3^y}=\dfrac{3^0}{3^2}\to 3-y=-2\to y=5\\\\\text{used}\ \dfrac{a^m}{a^n}=a^{n-m}\\\\15.\ 5^8\cdot5^z=1\to5^{8+z}=5^0\to8+z=0\to z=-8\\\\\text{used}\ a^n\cdot a^m=a^{n+m}[/tex]
[tex]16.\ 7^n\cdot 7^m=1\to7^{n+m}=7^0\to n+m=0\to n=-m\\\\17.\ \dfrac{3^x\cdot2^2}{3^4}=\dfrac{4}{3}\to3^{x-4}\cdot2^2=3^{-1}\cdot2^2\to x-4=-1\to x=3[/tex]
Can someone help me out
Answer:
88?
Step-by-step explanation:
Since XPY is a lot smaller and 23 degrees, 88 degrees makes the most sense.
Find the probability an observation is on a Thursday when the temperature is between 90 and 99. Find the probability an observation is on a Monday when the temperature is less than 90. Find the probability an observation is on a Friday when the temperature is greater than 89. Find the probability that the temperature is between 90 and 99, it will be a Thursday. Find the probability that if the temperature is between 110 and 120 and it will be a Sunday.
Answer:
Out of the 6 observations when the temperature is between 90 and 99, 2 are on Thursday.
2/6 = 33%
Out of the 4 observations when the temperature is less than 90, 1 was on Monday.
1/4 = 25%
Out of the 26 observations when the temperature is greater than 89, 4 were on Friday.
4/26 = 15%
Out of the 6 observations when the temperature is between 90 and 99, 2 are on Thursday.
2/6 = 33%
Out of the 1 observation when the temperature is between 110 and 120, none were on Sunday.
0%
To calculate probabilities of certain observations concerning different variables, we need relevant data pertaining to those variables. Without this data, it's challenging to calculate precise probabilities. In such cases, we use the closest available data or make educated assumptions.
Explanation:To find the probability of different observations, we need specific data that relates to those situations. For example, to find the probability that an observation is on a Thursday when the temperature is between 90 and 99, we would need historic data that captures temperature observations on Thursdays. Similarly, other probabilities also need specific data. For instance, to know the probability of an observation being on a Monday with temperature less than 90, or a Friday where the temperature is greater than 89, we would need historic temperature measurements for these specific days. However, since the provided information doesn't include specific data needed to calculate the probabilities asked in the question, we can't provide precise probabilities. Probability in statistics is generally calculated based on relevant data that is representative of the situation of interest. In situations where it is necessary to estimate the probability without access to specific data, we might use available data that is as closely matching as possible, or might make educated assumptions.
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Determine whether the point (1,1) is a solution to the system of equations. Explain your reasoning in complete scentences . Graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one the graphs intersect at the point 0 comma 2
Answer:
(1, 1) is NOT a solution
Step-by-step explanation:
The only point of intersection of the graphs is (0, 2). The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection, so is NOT the solution to the system of equations.
The point (1,1) is not a solution to the system of equations because, when we substitute the coordinates into the equations, it matches the second equation but not the first.
Explanation:To determine whether point (1,1) is a solution to the system of equations, we need to substitute the x and y values of the point into each equation and see if they produce true statements.
The first equation in the system is '3 times x plus 2', which we can write as 3x + 2. Substituting x = 1 in this equation gives us 3*1 + 2 = 5, which is not equal to the y-coordinate (1) of our input point.
The second equation is the |x - 1| + 1, which refers to the absolute value of (x minus 1) plus one. If we input x = 1, we get |1 - 1| + 1 = 1, which equals the y-coordinate (1) of our point. However, because the point didn't satisfy both equations, (1,1) is not a solution to the system.
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The world's largest chocolate bar is a rectangular prism weighing more than a ton! The bar is 9 feet long, 4 feet tall, and 1 foot wide. How many cubic feet of chocolate does it contain? Show your work.
Answer:
36 ft³
Step-by-step explanation:
The volume of a rectangular prism is computed by multiplying the length, width, and height:
V = LWH = (9 ft)(1 ft)(4 ft) = 36 ft³
The 2011 population of manatees in Florida Was 5,067. The animal is thought to be experiencing annual exponential decay of 1.1%. What is the function rule for this scenario?
Answer:
[tex]y=5,067(0.989)^{x}[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y ----> the population of manatees in Florida since 2011
x ----> the time in years
a is the initial value
b is the base
we have
[tex]a=5,067\ manatees[/tex]
[tex]b=(100\%-1.1\%)=98.9\%=0.989[/tex]
substitute
[tex]y=5,067(0.989)^{x}[/tex] ----> exponential function that represent this scenario
Please help me out with this
Value of x is 140
Tangent are present that means those angles are of 90° and 90° + 90° = 180°
One angle is already given 40°
By angle sum property of Quadrilateral
We can get its value
Love from India❤