Answer:
It is A -∞ < x < ∞
m Step-by-step explanation: I hope i am not late.
The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y=-3x + 24,
algebraically are shown in the table.
Answer:
C
Step-by-step explanation:
(3,15) and (4,12)
Answer:
C or (3, 15) and (4, 12)
Step-by-step explanation:
I just took the test on Edge 2020
Find the 7 term of the Gb 2 , -6 , 18
Answer:
The 7th term is 1458Step-by-step explanation:
For a geometric sequence
U(n) = ar^n - 1
Where
n is the number of terms
r is the common ratio
a is the first term
From the sequence
a = 2
r = - 6 /2 = -3
U(n) = 2(-3) ^ n - 1
For the 7th term
U(7) = 2(-3) ^ 7 - 1
= 2(-3)^6
The final answer is
= 1458
Hope this helps you
If y= -3x7+2x3+ x, the derivative of y with respect to x is
Answer:
[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1
Step-by-step explanation:
Differentiate each term using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
Given
y = - 3[tex]x^{7}[/tex] + 2x³ + x , then
[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]
= - 21[tex]x^{6}[/tex] + 6x² + 1
The mean of the data is 44.7. What is the mean average deviation? Round to the nearest tenth, if necessary.
Temp (°F)
29
38
45
31
50
58
62
Distance
from the
Mean
15.7
6.7
0.3
13.7
5.3
13.3
17.3
Answer:
10.3
Step-by-step explanation:
Answer:10.3
Step-by-step explanation:
Please help me. Please....
Answer:
20
Step-by-step explanation:
1/2(a+b)=180
1/2(6+12)=18
1/2(18)=180
9/9=180/9
=20
which of these 3 curves drawn matches the graph of y=2x^2+x
Answer:
Slope: 1
y-intercept: 8
Step-by-step explanation:
x, y
-8,0
0,8
Please help me find the sign of f
Answer: B. f is always negative on the interval
========================================================
Explanation:
-1/5 = -0.2
Pick any number for x that will make the interval -0.2 < x < 2 to be true. I find x = 0 to be easiest.
Plug it into f(x)
f(x) = (5x+1)(4x-8)(x+6)
f(0) = (5(0)+1)(4(0)-8)(0+6)
f(0) = (1)(-8)(6)
f(0) = -48
We get a negative result.
So we can rule out choice A which says that f is always positive. Either f is always negative on this interval, or it's a mix of being positive and negative.
-------------
Note that the roots of f(x) are -1/5, 2 and -6. This is from solving f(x) = 0
Use the zero product property to solve (5x+1)(4x-8)(x+6) to find the three roots mentioned.
The roots of -1/5 and 2 form the boundary of the interval mentioned at the top of the problem. There are no roots in between -1/5 and 2, so this means that f(x) stays entirely negative on this interval. There is no way f(x) becomes positive on this interval because it would have to cross over the x axis, thus forming another root. But again there are no roots between -1/5 and 2.
A graph confirms we have the correct answer. Check out the image attached below. Note the portion from x = -0.2 to x = 2 is entirely below the x axis.
To determine if a particular predictor in a regression analysis is statistically significant, which statistic should one interpret
Answer:
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Step-by-step explanation:
The general form of a regression equation is:
[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]
Here,
α = y-intercept
βi = regression coefficients, (i = 1, 2, ..., n)
A regression analysis is performed to determine whether the predictor variables are statistically significant or not.
The output of the regression analysis consists of two tables.
One is the regression output and the other is the ANOVA table.
The regression output table is used to display which predictor variables are statistically significant and which are not.
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
And the ANOVA table displays overall regression analysis.
The F-test statistic is used to for the overall regression analysis.
Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 5% margin of error at a 97.5% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.
Answer:
The sample size required is, n = 502.
Step-by-step explanation:
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\cdot (1-\hat p)}{n}}[/tex]
The margin of error is:
[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]
Assume that 50% of the people would support this political candidate.
The margin of error is, MOE = 0.05.
The critical value of z for 97.5% confidence level is:
z = 2.24
Compute the sample size as follows:
[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502[/tex]
Thus, the sample size required is, n = 502.
What is the measure of cuz
Answer:
D. 65°
Step-by-step explanation:
The measure of the angle at crossed chords is the average of the measures of the intercepted arcs:
m∠XYZ = (1/2)(arc XZ +arc WV)
m∠XYZ = (1/2)(86° +44°) = 130°/2
m∠XYZ = 65°
plz answer question in screen shot
Answer:
200√3
Step-by-step explanation:
The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.
Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.
Find the first, fourth, and eighth terms of the sequence.
A(n) = -2x2^n-1
Answer:
first term = -2
fourth term = -16
eighth term = -256
Step-by-step explanation:
Given;
A sequence with function;
A(n) = -2x2^(n-1)
The first, fourth, and eighth terms of the sequence can be calculated by substituting their corresponding values of n;
First term A(1); n = 1
A(1) = -2x2^(1-1) = -2×1 = -2
Fourth term A(4); n = 4
A(4) = -2x2^(4-1) = -2×8 = -16
Eighth term A(8); n = 8
A(8) = -2x2^(8-1) = -2×128 = -256
Therefore,
first term = -2
fourth term = -16
eighth term = -256
Point c (2,2) is the center of the circle. what is the ratio of ac to the length of dc?
1) 1:2
2) 2:1
3) 1:1
4) 3:1
What would be the angle of elevation of a tree from the ground, if the height of the
tree and its shadow are equal in length?
Answer:
45°
Step-by-step explanation:
The diagram for this question has been attached to this response. Please check.
The angle of elevation is the angle between a horizontal line from a viewer and the line of sight to an object being viewed which is above the horizontal line.
From the diagram;
θ is the angle of elevation
x = height of the tree
y = length of the shadow of the tree = x
Therefore,
tanθ = [tex]\frac{x}{y}[/tex] [Remember that y = x? Then substitute into the equation]
tanθ = [tex]\frac{x}{x}[/tex]
tanθ = 1
θ = tan⁻¹(1)
θ = 45°
Therefore, the angle of elevation is 45°
Please help with this. Thanks!
Answer:
1/5k-2/3j and -2/3j+1/5k
Step-by-step explanation:
This is because the sign of both of the terms stay the same and the fractions and variables stay the same for each term as well.
I NEED HELP PLEASE, THANKS! :)
Hey there! :)
Answer:
[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]
Step-by-step explanation:
In rectangular coordinates, the form is:
(r·cosθ, r·sinθ)
In this instance:
Polar coordinates: (9, 150°). Use the coordinates above to solve for the rectangular coordinates.
(r · cos 150°, r· sin 150°)
(9 · cos 150°, 9· sin 150°)
cos 150° = -√3/2
sin 150° = 1/2
Plug these values into the equation:
(9 · (-√3/2), 9 · 1/2)
Multiply and simplify:
(-9√3/2, 9/2)
Therefore, the coordinates in rectangular form are:
[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]
Select the correct answer from each drop down menu
In the figure, AB = ____ inches and AC=____
PLEASE HELP!
Picture posted!
Answer:
AB = 8.39 inches
AC = 13.1 inches
(corrected to 3 significant figures.)
Step-by-step explanation:
In a right triangle, AB is the opposite side; BC is the adjacent side, and AC is the hypotenuse side.
since tanθ = opposite / adjacent,
we can use this to find side AB.
tan40° = AB / 10
AB = 8.39 in. (corrected to 3 significant figures.)
since cosθ = adjacent / hypotenuse
we can use this to find AC.
cos40° = 10 / AC
AC = 13.1 in. (corrected to 3 significant figures.)
Answer:
AB= 8.4
AC= 13.1
Step-by-step explanation:
What is the solution to this system of linear equations? x − 3y = −2 x + 3y = 16 (7, 3) (3, 7) (−2, −3) (−3, −2)
The solution to given system of linear equations is (7, 3)
What is linear equation?
A linear equation is defined as an equation in which the highest power of the variable is always one.
Given,
x-3y = -2
x+3y =16
Adding the both equations,
2x=14
So, x=7
Substitute the value of x=7 in equation x+3y =16
7+3y =16
3y =16-7
y=3
Thus, the solution to given system of linear equations is (7, 3)
Learn more about linear equation
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Answer: A. (7,3)
Step-by-step explanation: I just did the quiz and got 100%, hope this helps!
Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12. He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week?
Answer:
20
Step-by-step explanation:
224÷4 = 56+40 = 96÷2 = 48+12 = 60÷3 = 20
If Ronnie goes to the racetrack with his buddies on a weekly basis. How much did he start with the first week is $20.
How much did he start with?Hence:
4 [2 (3x - 12) -40] = 224
4 [6x - 24 - 40] = 224
Collect like term
24x - 256= 224
24x/24 = 480/24
Divide both side by 24
x=480/24
x=$20
Therefore How much did he start with the first week is $20.
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Suppose that a population is known to be normally distributed with £ = 2400 and € = 210. Of a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,500.
Answer:
0.0885 = 8.85% probability that the sample mean will exceed 2,500.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]\mu = 2400, \sigma = 210, n = 8, s = \frac{210}{\sqrt{8}} = 74.25[/tex]
Calculate the probability that the sample mean will exceed 2,500.
This is 1 subtracted by the pvalue of Z when X = 2500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2500 - 2400}{74.25}[/tex]
[tex]Z = 1.35[/tex]
[tex]Z = 1.35[/tex] has a pvalue of 0.9115
1 - 0.9115 = 0.0885
0.0885 = 8.85% probability that the sample mean will exceed 2,500.
For a segment of a radio show a disc jockey can play 10 records. If there are 12 records to select from in how many ways can the program for this segment be arranged
Answer:
66 different waysStep-by-step explanation:
This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.
nCr = n!/(n-r)r!
According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.
12C10 = 12!/(12-10)!10!
= 12!/2!10!
= 12*11*10!/2*10!
= 12*11/2
= 6*11
= 66 different ways
Which equation represents the total cost (c) of purchasing cans of vegetables(v) at a price of $1.18 per can? What is the total cost to purchase 98 cans of vegetables? Question 10 options: A) c = 1.18v; $83.05 B) v = 1.18c; $83.05 C) c = 1.18v; $115.64 D) v = 1.18c; $115.64
Answer:
C
Step-by-step explanation:
The equation must be equal to c since that is the total cost.
c = 1.18v
Plug in 98 for v to find the answer.
c = 1.18(98)
c = $115.64
solve using elimination method x-3y=1 and 2x+5y=6
Answer:
x =23/11, y =4/11
Step-by-step explanation:
subtract equation 1 from equation 2
2x-x + 5y-(-3) =6-1
x + 8y = 5
make x the subject of formula
x = 5-8y(equation#)
substitute x = 5-8y in equation 1
5-8y-3y = 1
5-11y = 1
collect like terms
5-1 = 11y
4= 11y
divide both sides by 11
4/11 = 11y/11
y = 4/11
put y = 4/11 in equation #
x = 5-8(4/11)
x = 5-32/11
LCM= 11
x = 55-32/11
x = 23/11
so, x =23/11, y = 4/11
37. Emma is storing 432 ounces of soup into small
6-ounces containers and medium 8-ounces
containers. If there must be at least 50 small
containers, what is the least possible number
of containers needed to store all the soup
without any leftover soup remaining?
Answer:
15 8 ounce containers and 52 6 ounce containers
Step-by-step explanation:
First figure out how much soup must be in the 50 small containers
50 * 6 = 300
Subtract that from the total amount of soup
432 - 300 = 132
We have to put 132 ounces of soup into 6 ounce and 8 ounce containers
Let x be the number of 6 ounce and y be the number of 8 ounce containers
6x+8y = 132
x+y = minimum
We want to use as many 8 ounce containers as possible
132/8 = 16.5
16*8 = 128 r4 we cannot use 16 because we do not have a 4ounce container
15*8 = 120 r12 12/6 =2 we can do this because we can use 2 6 ounce containers
We need 15 8 ounce containers and 2 6 ounce for the 132 ounces left
We have 50 for the 300 ounces
For a total of
15 8 ounce containers and 52 6 ounce containers
Rafael is saving money to buy a game. So far he has saved $30, which is five-sixths of the total cost of the game. How much does the game cost?
Answer:
$36
Step-by-step explanation:
30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.
If we add another sixth, we get 36, which will be the total cost of the game.
if he allows 40 people to choose a treat from the bag about how many lizard lollis can he expect to give away
Answer:
20 Lizard lollies.
Step-by-step explanation:
There are 10 lizard lollis. This is out of 10+4+6 = 20 total treats. This makes the probability of drawing a lizard lollis 10/20 = 1/2.
This means out of 40 treats handed out, we can expect him to give out 1/2(40) = 20 lizard lollis.
If s=1/2 unit and A=12s^2, what is the value of A, in square unit?
Answer:
3 square units
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
A = 12(1/2)² = 12(1/4) = 3 . . . square units
__
Comment on the working
It might be helpful to you to see how this works when the units of the number are attached to the number.
A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²
I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.
Which first step for solving the given system using substitution results in an equation without fractions?
[3x+y=9
15x-3y = 1
Solve for x in the first equation.
Solve for y in the first equation.
Solve for x in the second equation.
Solve for y in the second equation.
Answer:
Solve for y in the first equation.
Step-by-step explanation:
Given
3x+y=9
15x-3y = 1
Required
Determine the first step to avoid fractions
From the list of given options, the option that best answered the question is to Solve for y in the first equation.
Solving for y will let you substitute the expression for y in the second equation
Going by that:- Solve for y in the first equation.
[tex]3x + y = 9[/tex]
Subtract 3x from both sides
[tex]3x - 3x + y = 9 - 3x[/tex]
[tex]y = 9 - 3x[/tex]
Substitute 9 - 3x for y in the second equation
[tex]15x - 3y = 1[/tex] becomes
[tex]15x - 3(9 - 3x) = 1[/tex]
[tex]15x - 27 + 9x = 1[/tex]
Collect like terms
[tex]15x + 9x = 1 + 27[/tex]
[tex]24x = 28[/tex]
Divide both sides by 24
[tex]\frac{24x}{24} = \frac{28}{24}[/tex]
[tex]x = \frac{28}{24}[/tex]
Divide numerator and denominator by 4
[tex]x = \frac{7}{6}[/tex]
Substitute 7/6 for x in the [tex]y = 9 - 3x[/tex]
[tex]y = 9 - 3 * \frac{7}{6}[/tex]
[tex]y = 9 - \frac{7}{2}[/tex]
Solve fraction
[tex]y = \frac{18-7}{2}[/tex]
[tex]y = \frac{11}{2}[/tex]
Answer:
It's B (the one above is right)
Step-by-step explanation:
In a fish tank the number of orange fish is 1 1/4 times the number of blue fish. Drag the blue fish to represent the number of blue fish in the tank dor every 5 orange fish
Answer:
4 blue fish for every 5 orange fish
Step-by-step explanation:
(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation
(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction
(orange fish)/(blue fish) = 5/4 . . . . . divide by "blue fish"
There are 4 blue fish for every 5 orange fish.
6x - 2y = 18
3x + 4y= -6
Which of the following ordered pairs (x, y) is the
solution to the system of equations shown above?
A. (-3,2)
B. (-2,3)
C. (2, -3)
D. (3,-2)
Answer:
C. (2, -3)
Step-by-step explanation:
Easiest and fastest way to get the solution set is to graph the systems of equations and analyze where the graphs intersect.