Answer:
54
Step-by-step explanation:
p(x)=x^2+50, p(2)=2^2+50=54
P(x) = x² + 50
P(2) = 2² + 50
= 54
P(6) = 6²+50
= 86
P(7) = 7²+ 50
= 99
P(8) = 8²+50
= 114
P(9) = 9²+50
= 131
Answered by Gauthmath must click thanks and mark brainliest
A ball thrown upwards hits a roof and returns back to the ground.
The upward movement is modeled by a function [tex]s=-t^2+3t+4[/tex]
s= −(t^2)+3t+4
and the downward movement is modeled by [tex]s=-t^2+3t+4[/tex]
s= −2(t^2)+t+7, where s is the distance (in metres) from the ground and t is the time in seconds.
Find the height of the roof from the ground.
Answer: 6 m
A ball thrown upwards from the altitude 4 m,
hits a roof and returns back to the ground.
upward movement: s= −t²+3t+4
downward movement: s=-2t²+t+7
Step-by-step explanation:
Let's calculate the intersection:
[tex]- t^2+3t+4 =-2t^2+t+7\\\\t^2+2t-3=0\\\\t^2+3t-t-3=0\\\\t(t+3)-(t+3)=0\\\\(t+3)(t-1)=0\\\\t=-3 \ (exclude)\ or\ t=1\\\\if\ t=1 \ then\ s=-1^2+3*1+4=6\\\\height\ is\ 6\ m.\\[/tex]
Sorry, i have forgotten the picture.
can some0ne help me?
Answer:
(x - 2)/3
(x - 4)/-5 or (-x + 4)/5
Step-by-step explanation:
this is an inverse function, and to solve an inverse function you would :
swap x and g(x) without bringing the x coefficient with it, just simply swap the variables. Then, solve for g(x), and that's it
the first question's answer is :
g(x) = 3x + 2
x = 3(g(x)) + 2
x - 2 = 3(g(x))
(x - 2)/3 = g(x)
the second one is:
g(x) = 4 - 5x
x = 4 - 5(g(x))
x - 4 = -5(g(x))
(x-4)/-5 = g(x)
g(x) = 3x + 2
y = 3x + 2
x = 3y + 2
3y = x - 2
y = x/3 - 2/3
inverse g(x) = (x - 2) / 3
g(x) = 4 - 5x
y = 4 - 5x
x = 4 - 5y
5y = 4 - x
y = 4/5 - x/5
inverse g(x) = (4 - x) / 5
Find the slope of the line containing the points (-3, 8) and (2, 4).
Answer:
-4/5
Step-by-step explanation:
The slope of the line is m=(4-8)/(2-(-3))=-4/5
A box with a square base and no top is to be made from a square piece of carboard by cutting 4 in. squares from each corner and folding up the sides. The box is to hold 1444 in3. How big a piece of cardboard is needed
Answer:
[tex]C=27inch\ by\ 27inch[/tex]
Step-by-step explanation:
Squares [tex]h=4inch[/tex]
Volume [tex]v=1444in^3[/tex]
Generally the equation for Volume of box is mathematically given by
[tex]V=l^2h[/tex]
[tex]1444=l^2*4[/tex]
[tex]l^2=361[/tex]
[tex]l=19in[/tex]
Since
Length of cardboard is
[tex]l_c=19+4+4[/tex]
[tex]l_c=27in[/tex]
Therefore
Dimensions of the piece of cardboard is
[tex]C=27inch\ by\ 27inch[/tex]
Solve this equation for x. Round your answer to the nearest hundredth.
1 = In(x + 7)
Answer:
[tex]\displaystyle x \approx -4.28[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural logarithms ln and Euler's number eStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 1 = ln(x + 7)[/tex]
Step 2: Solve for x
[Equality Property] e both sides: [tex]\displaystyle e^1 = e^{ln(x + 7)}[/tex]Simplify: [tex]\displaystyle x + 7 = e[/tex][Equality Property] Isolate x: [tex]\displaystyle x = e - 7[/tex]Evaluate: [tex]\displaystyle x = -4.28172[/tex]e^1 = x+7
e - 7 = x
x = -4.28
in each figure below find m<1 and m < 2 if a||b
please help i don't have a lot of time I will give brainliest if you help
Answer:
m∠1 = 105°
m∠2 = 75°
Step-by-step explanation:
From the picture attached,
Two lines 'a' and 'b' are parallel and a transversal 't' is intersecting these lines at two distinct lines.
Therefore, m∠2 = 75° [Corresponding angles measure the same]
m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]
m∠1 + 75° = 180°
m∠1 = 105°
Amanufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 427 grams with a variance of 324. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?
Answer:
There is not enough evidence to support the claim that the bags are under filled.
Step-by-step explanation:
Given :
Population mean, μ = 433
Sample size, n = 26
xbar = 427
Variance, s² = 324 ; Standard deviation, s = √324 = 18
The hypothesis :
H0 : μ = 433
H0 : μ < 433
The test statistic :
(xbar - μ) ÷ (s/√(n))
(427 - 433) / (18 / √26)
-6 / 3.5300904
T = -1.70
The Pvalue :
df = 26-1 = 25 ; α = 0.05
Pvalue = 0.0508
Since Pvalue > α ; WE fail to reject the Null and conclude that there is not enough evidence to support the claim that the bags are underfilled
?
6.2
Divided by 1/2
Answer:
The answer is 3.1
[tex]6.2 \div \frac{1}{2} = 3.1[/tex]
If we were to convert it into a **FRACTION** the answer would be : 31/10.
And that i an improper fraction, but as a **MIXED NUMBER** : [tex]3 \frac{1}{10}[/tex]
All answers would be : 3.1 , 31/10 and 3 1/10
Answer:
0.5167
Step-by-step explanation:
6.2/12 first rewrite 6.2 as an improper fraction or 36/5 then multiply by 1/12 to get the solution of 0.5167.
Find a pair of polar coordinates for the point with rectangular coordinates (5, –5).
Answer:
(5*sqrt(2), 5pi/4)
Step-by-step explanation:
In Polar coordinates, tan(theta)=y/x and r=sqrt(x^2+y^2)
tan(theta)=-5/5=-1. Theta=5pi/4
r=sqrt(5^2+5^2)=5*sqrt(2)
Hence the Polar coordinate is (5*sqrt(2), 5pi/4)
The polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].
What is polar coordinate system?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
How to convert rectangular coordinates to polar coordinates?To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula
tanθ = y/x and [tex]r =\sqrt{x^{2} +y^{2} }[/tex]
According to the given question
We have
A rectangular coordinate (5, -5).
⇒ x = 5 and y = -5
Therefore,
[tex]r=\sqrt{(5)^{2} +(-5)^{2} } =\sqrt{25+25} =\sqrt{50} =5\sqrt{2}[/tex]
and
tanθ = [tex]\frac{-5}{5} =-1[/tex]
⇒ θ = [tex]tan^{-1} (-1)[/tex] = [tex]-\frac{\pi }{4}[/tex]
Therefore, the polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].
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14
11. The number of kilograms of corn needed
to feed 5000 chickens is 30 less than twice
the number of kilograms needed to feed
2800 chickens. How many kilograms of
corn are needed to feed 2800 chickens?
(A) 70
(B) 110
(C) 140
(D) 190
(E) 250
Answer:
x = 2515
Step-by-step explanation:
5000 = 2x - 30
2800 = x
have a great day! I hope this helps!140 kilograms of corn is needed to feed 2800 chickens.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the number of kilograms of corn needed to feed 5000 chickens is 30 less than twice the number of kilograms needed to feed 2800 chickens.
Assume that [x] kilograms of corn is needed to feed 2800 chickens.
for 2800 chickens → [x] Kg of corn is needed
for 1 chicken → [x/2800] Kg of corn is needed.
So, we can write -
5000 × [x/2800] = 2x - 30
50x/28 = 2x - 30
50x = 28(2x - 30)
50x = 56x - 28 x 30
50x - 56x = - 840
- 6x = - 840
6x = 840
x = 140
Therefore, 140 kilograms of corn is needed to feed 2800 chickens.
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hlo anyone free .... im bo r ed
d
Step-by-step explanation:
Excuse me! Who r u? where r u frm? tell me tht frst.
Answer:
Oop
Step-by-step explanation:
I’m bored
I'm interval notation please
9514 1404 393
Answer:
(-2, 4]
Step-by-step explanation:
-21 ≤ -6x +3 < 15 . . . . given
-24 ≤ -6x < 12 . . . . . . subtract 3
4 ≥ x > -2 . . . . . . . . . . divide by -6
In interval notation, the solution is (-2, 4].
__
Interval notation uses a square bracket to indicate the "or equal to" case--where the end point is included in the interval. A graph uses a solid dot for the same purpose. When the interval does not include the end point, a round bracket (parenthesis) or an open dot are used.
*PLEASE HELP ME ILL GIVE BRAINLIST IF CORRECT*
Noah is playing a game where he must spin two wheels, each with 9 equal slices. There are 3 red slices, 3 green slices, 2 blue slices and 1 yellow slice on each wheel. If Noah spins and lands on a yellow slice on both wheels he wins, but if he lands on any other color, he loses. This information was used to create the following area model.
Is this a fair game? Why or why not?
A. Yes, the game is fair because Noah has equal probabilities of winning or losing.
B. Yes, the game is fair because Noah does not have equal probabilities of winning or losing.
C. No, the game is not fair because Noah has equal probabilities of winning or losing.
D. No, the game is not fair because Noah does not have equal probabilities of winning or losing.
Step-by-step explanation:
Yes, the game is fair because noah has equal probabilities of Winning
Answer:
No, the game is not fair because Noah does not have equal probabilities of winning or losing.
Step-by-step explanation:
what is sqrt 2x-3 = sqrt 3x-9
Answer:
x=6
Step-by-step explanation:
sqrt (2x-3) = sqrt (3x-9)
Square each side
(sqrt (2x-3))^2 = (sqrt (3x-9))^2
2x-3 = 3x-9
Subtract 2x from each side
2x-3-2x = 3x-2x-9
-3 = x-9
Add 9 to each side
-3+9 = x-9+9
6 =x
Check solution
sqrt (2*6-3) = sqrt (3*6-9)
sqrt (9) = sqrt (9)
3=3
Solution is valid
sqrt (2x-3) = sqrt (3x-9)
Square each side
(sqrt (2x-3))^2 = (sqrt (3x-9))^2
2x-3 = 3x-9
Subtract 2x from each side
2x-3-2x = 3x-2x-9
-3 = x-9
Add 9 to each side
-3+9 = x-9+9
6 =x
sqrt (2*6-3) = sqrt (3*6-9)
sqrt (9) = sqrt (9)
3=3
Therefore ans x = 6
Answered by Gauthmath must click thanks and mark brainliest
which of the following is the correct graph of the solution to the inequality -18 > 5x + 2 > -48?
Answer:
good luck
.............
Answer: the third one. filled circle for 4 ,5,6,7,8,9, open circle 10
Step-by-step explanation:
Use absolute value to express the distance between -12 and -15 on the number line
A: |-12-(-15)|= -37
B: |-12-(-15)|= -3
C: |-12-(-15)|= 3
D: |-12-(-15)|= 27
In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.23 pounds.
a. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Maine. Assume the population is approximately normal.
b. Find the critical value that should be used in constructing the confidence interval.
Answer:
a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
b) [tex]T_c = 2.4469[/tex]
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 7 - 1 = 6
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469, and the answer to question b is [tex]T_c = 2.4469[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{0.23}{\sqrt{7}} = 0.21[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.
The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.
The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.
use quadratic formula to solve the following equation
9514 1404 393
Answer:
x = 2 or x = 9
Step-by-step explanation:
To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).
2(3) +4(3(x -3)) = (x +4)(x -3)
6 +12x -36 = x² +x -12
x² -11x +18 = 0
Using the quadratic formula to find the solutions, we have ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]
The solutions are x=2 and x=9.
could someone please answer this? :) thank you
Answer:
The last one
Step-by-step explanation:
What we know:
We have a total of 16 coins
The 16 coins consist of dimes and quarters
The value of the coins is 3.10
The value of a dime is .10
The value of a quarter is .25
Using this information we can create a system of linear equations
First off we know that we have a total of 16 coins which consist of dimes and quarters
The number of Quarters can be represented by q and then number of dimes can be represented by d.
If we have a total of 16 coins then q + d must equal 16
So equation 1 is q + d = 16
Now we need to create a second equation
We know that the total value of the coins is 3.10 and we know that the coins consist of dimes and quarters
As you may know a quarter has a value of .25 cents and a dime has a value of 10 cents
If the total value of the coins is 3.10 the the number of dimes (d) times .10 + the number of Quarters times .25 must equal 3.10
This can also be written as
.25q + .10d = 3.10
So the two equations are
q + d = 16 and .25q + .10d = 3.10
These equations are shown in the last answer choice
Note: b is very similar to d
However the the value of the coins are incorrect in B
In B the value of the dime is represented by 10 which is not correct because the value of a dime is .10 not 10
Is this the correct answer?
Answer:
25.40
Step-by-step explanation:
tickets ( 2 at 10.95 each) = 2* 10.95 = 21.90
popcorn ( 1 at 7.50) = 7.50
Total cost before discount
21.90+7.50=29.40
subtract the discount
29.40-4.00 =25.40
Answer:
Yep! That's correct!
Step-by-step explanation:
We know that Marilyn and her sister are each getting a ticket that cost $10.95. They are also getting a $7.50 popcorn to share. Let's add those values up.
(10.95 * 2) + 7.50 {Multiply 10.95 by 2 to get 21.90.}
21.90 + 7.50 {Add 7.50 to 21.90 to get 29.40}
$29.40 (without the credit) in toal
A credit on a movie reward card functions as a discount, so what we need to do next is subtract 4 from 29.40. That will get us $25.40 as the total cost.
After doing the math, I can deduce that your answer is correct!
In the figure above, AD and BE intersect at point C, and
the measures of angles B, D, and E are 98°, 81°, and 55°,
respectively. What is the measure, in degrees, of
angle A ? (Disregard the degree sign when gridding your
answer.)
answer in screenshot
A man starts repaying a loans with first insfallameny of rs.10 .If he increases the instalment by Rs 5 everything months, what amount will be paid by him in the 30the instalment.
Answer:
30×5=150
so 150+10=160
thus his payment in the 30th installment is
rs.160
11. What is the midpoint of CD?
12. a. What are the exact lengths of
segments AB and CD?
b. How do the lengths of AB and CD
compare?
c. Is the following statement true or
false?
AB=CD
9514 1404 393
Answer:
11. (-1.5, 3)
12. √29, identical lengths, true they are congruent
Step-by-step explanation:
11. The midpoint is halfway between the end points. On a graph, you can count the grid squares between the ends of the segment and locate the point that is half that number from either end.
Points C and D differ by 2 in the y-direction, so the midpoint will be 1 unit vertically different from either C or D. That is, it will lie on the line y = 3. The segment CD intersects y=3 at x = -1.5, so the midpoint of CD is (-1.5, 3).
If you like, you can calculate the midpoint as the average of the end points:
midpoint CD = (C +D)/2 = ((-4, 4) +(1, 2))/2 = (-3, 6)/2 = (-1.5, 3)
__
12. The exact length can be found using the Pythagorean theorem. The segment is the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.
In the previous problem, we observed that the y-coordinates of C and D differed by 2. The x-coordinates differ by 5. Looking at segment AB, we see the same differences: x-coordinates differ by 5 and y-coordinates differ by 2. Then the lengths of each of these segments is ...
AB = CD = √(2² +5²) = √29
a) The exact lengths of segments AB and CD are √29 units.
b) The lengths of the segments are identical
c) It is TRUE that the segments are congruent.
The measure of angle tis 60 degrees.
What is the x-coordinate of the point where the
terminal side intersects the unit circle?
1
2
O
O
Isla Isla
2
DONE
Answer:
Step-by-step explanation:
Not a clear list of options and/or reference frame
Probably 0.5 if angle t is measured from the positive x axis.
I need answering ASAP please
Answer:
The choose (D) 1/3
I hope I helped you^_^
A school has 4 different after school activities planned in the fall Janet has time to participate in 2 of these activities. How many different pairs of after-school activities can Janet choose from the available activities?
Answer:
6
Step-by-step explanation:
Of 4 options, Janet has to choose 2. This is combinations as A and B is the same as B and A.
Combinations formula gives us 4!/ 2!2! , or 6.
please help me on this
Answer:
Median
Step-by-step explanation:
Using the median to measure central tendency, rather than the mean, is better for a skewed data set.
Since a skewed data set will have either very high or low extreme data points, the mean will be less representative and accurate when measuring central tendency.
Using the median will measure this better because it is not as vulnerable as the mean when there are extreme data points.
So, the answer is the median.
If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the computed z-score with a sample mean (x-bar) of 106 from a sample size of 9?
Answer:
Z = 1
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean (mu) that equals 100 with a standard deviation (sigma) of 18
[tex]\mu = 100, \sigma = 18[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]
What will be the computed z-score with a sample mean (x-bar) of 106?
This is Z when X = 106. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{106 - 100}{6}[/tex]
[tex]Z = 1[/tex]
So Z = 1 is the answer.
Twice a number increased by the product of the number and fourteen results in forty eight
Answer:
Let x = the number. Then you have:
2x + 14x = 48 Collect like terms
16x = 48 Divide both sides by 16
x = 3
PLEASE MARK AS BRAINLIEST ANSWER
The number that satisfies the given statement is 3.
We are given that twice a number increased by the product of the number and 14 results in 48.
We will find the value of the number that we used in the given above statement.
Understand the meaning of the keywords used in the statement.Increased means addition.
Product means multiplication.
Results mean equal to sign.
Let's write the given statement in equation form.
Consider P = the number
Twice a number = 2P
Increased = +
Products of the number and 14 = P x 14
Results in 48 = equals 48.
Combining all the above we get,
2P + P x 14 = 48
2P + 14P = 48
16P = 48
P = 48 / 16
P = 3
Thus the number that satisfies the given statement is 3.
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Determine whether the statement below makes sense or does not make sense. Explain clearly. Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 1.9 to 3.5 hours per day. Therefore, there is 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not.
A. The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100%−95% =5%.
B. The statement makes sense. There is 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%.
C.The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5%+5%=10%.
D. The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this.
The correct option is A because
The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100%−95% =5%.
From the question we are told that:
Confidence interval [tex]CI=95\%[/tex]
Mean [tex]\=x =1.9-3.5hours[/tex]
Level of significance (of the alternative hypothesis)
[tex]\alpha=100-95[/tex]
[tex]\alpha=5\%[/tex]
[tex]\alpha=0.05[/tex]
Generally
There is 95% probability that the confidence interval limits actually contain the true value of the population mean.
In conclusion
The it does not fall in this range is Level of significance (of the alternative hypothesis)
100%−95% =5%.
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