Answer:
x[tex]\geq[/tex]8
Step-by-step explanation:
in order to make 5800. he would need to sell 8 cars at 725. each (5,800/725.=8) so x would have to be equal to or greater that 8
In this activity, you will test if the distribution of colors from a sample bag of M&Ms candy is the same as the Mars company claims. You will need to purchase a small bag of M&Ms from your local store. M&M Mars Co. claims the following distribution of the number of different colors of M&M's in each bag: Brown 13% Yellow 14% Red 13% Orange 20% Green 16% Blue 24% Suppose we are only interested in the number of Orange, Green, Blue and "Other" colors, which would then have the following claimed distribution: Orange 20% Green 16% Blue 24% Other 40% Take a sample of 35 M & M's and run a hypothesis test to see if you accept Mar's claim. Use α = .05.
Answer:
The claim made by Mar's is correct.
Step-by-step explanation:
In this case we need to test whether M&M Mars Co.'s claim about the proportion of different colored M&Ms in a small bag is correct or not.
The hypothesis is:
H₀: The claim made by Mar's is not correct.
Hₐ: The claim made by Mar's is correct.
The proportions claimed are as follows:
Orange: 20%
Green: 16%
Blue: 24%
Other: 40%
A sample of 35 M&M's are selected.
The observed frequencies are:
Observed = {O = 4, G = 8, B = 5 and Ot = 18}
Compute the expected frequencies as follows:
[tex]E(O)=4\times 20\%=0.80\\\\E(G) = 8\times 16\%=1.28\\\\E(B)=5\times 24\%=1.20\\\\E(Ot)=18\times 40\%=7.20[/tex]
Compute the Chi-square statistic as follows:
[tex]\chi^{2}=\sum[\frac{(O-E)^{2})}{E}][/tex]
[tex]=[\frac{(4-0.80)^{2}}{0.80}]+[\frac{(8-1.28)^{2}}{1.28}]+[\frac{(5-1.20)^{2}}{1.20}]+[\frac{(18-7.20)^{2}}{7.20}]\\\\=12.80+35.28+12.03+16.20\\\\=76.31[/tex]
The Chi-square test statistic value is 76.31.
The degrees of freedom of the test is:
df = n - 1
= 4 - 1
= 3
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{0.05,3}<76.31)<0.00001[/tex]
The p-value < 0.05.
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that the claim made by Mar's is correct.
Please answer this question with how do work it out?
Answer:
Point B coordinates' are: (3.2, 1.6)
Step-by-step explanation:
Since this is a rhomboid the diagonals AC and OB, must be perpendicular to each other. Then we can find first the equation of the line where segment AC lies, seeing that this line will cross the y axis at the point (0,4), and the x axis at the point (2, 0). The line can then be obtained by calculating the slope of the segment that joins the two points, and then using that the line's y-intercept must be at the point (0, 4):
[tex]slope=\frac{0-4}{2-0} =-2[/tex]
then the equation of the line for segment AC must be:
[tex]y=-2x+4[/tex]
Next, we calculate the equation of a perpendicular line to the previous one, and that passes through the point (0, 0) to determine the equation of the line that contains the segment OB. Recall that the perpendicular line to one of slope m must have a slope given by: -1/m (the opposite of the reciprocal of "m". Then this new perpendicular line passing through (0, 0) must be given by:
[tex]y=\frac{1}{2} x+0\\y=\frac{1}{2} x[/tex]
Now we can find the point at which both lines intersect:
[tex]\frac{1}{2} x=-2x+4\\\frac{1}{2} x+2x=4\\\frac{5}{2} x = 4\\x=\frac{8}{5}[/tex]
and therefore the y value of the intersection point can be calculated via:
[tex]y=\frac{1}{2} x\\y=\frac{1}{2} (\frac{8}{5} )\\y=\frac{4}{5}[/tex]
Then, point point B must be located at an x value that doubles the x value of the intersecting point, and similarly the y value of point B must be at the double of the value of the intersection point we just calculated. That is:
Point B = [tex](2\,*\frac{8}{5} ,\,2\,*\frac{4}{5} )=(\frac{16}{5} ,\frac{8}{5}) =(3.2,1.6)[/tex]
We can see the coordinates of point B and the lines we just generated in the attached image.
csc^2 xcos^2 x=csc^2 x-1
prove the identity
Answer:
Step-by-step explanation:
Hello
[tex]csc^2(x)-1=\dfrac{1}{sin^2(x)}-1=\dfrac{1-sin^2(x)}{sin^2(x)}\\=\dfrac{cos^2(x)}{sin^2(x)}=cos^2(x)csc^2(x)[/tex]
hope this helps
Helpppp me answer this please
Answer:
D is the right ans
Step-by-step explanation:
if i write step by step it will take a long time so quick
Answer:
D.
Step-by-step explanation:
Simplify the numerator and denominator separately. Let's do the numerator first. In the numerator, we have: [tex]x^2-8x-9[/tex]. We can factor this.
[tex]x^2-8x-9=(x-9)(x+1)[/tex]
(I did this by picking two numbers that multiply to -9 and add to -8. -9 and 1 are the only possible candidates).
Now, let's simplify the denominator. The denominator is:
[tex]5x^2-45x=5x(x-9)[/tex]
Thus, all together we will have:
[tex]\frac{(x-9)(x+1)}{5x(x-9)}[/tex]
We can cancel the (x-9) term. Thus:
[tex]=\frac{x+1}{5x}[/tex]
solve when x ∈ {-2, 0, 2} and y ∈ {-3, -1, 0, 3} y=1-x^2
Answer:
(-2,-3) and (2,-3).
Step-by-step explanation:
It is given that x ∈ {-2, 0, 2} and y ∈ {-3, -1, 0, 3} .
The given equation is
[tex]y=1-x^2[/tex]
At x=-2,
[tex]y=1-(-2)^2=1-4=-3\in y[/tex]
At x=0,
[tex]y=1-(0)^2=1-0=1\notin y[/tex]
At x=2,
[tex]y=1-(2)^2=1-4=-3\in y[/tex]
Therefore, the solution of given equation are (-2,-3) and (2,-3).
PLEASE HELP QUICK!!!Dante wrote several equations and determined that only one of the equations has infinitely many solutions. Which of these equations has infinitely many solutions?
Answer:
I think its D?
Hope this helped!
Monica bought a car for $x 3 years ago. Due to an inflation rate of 6% p.a. this car is now worth Mexican peso 50,000. Calculate the cat's original purchase price
Answer:
its 60198.6
Step-by-step explanation:
use the formula present price=orginal price(1-rate/100)^years
One root of f(x) = x + 10x2 – 25x – 250 is x = -10. What are all the roots of the function? Use the Remainder Theorem.
x= -25 or x = 10
x = -25, x = 1, or x = 10
x = -10 or x = 5
x = -10, x=-5, or x = 5
Answer:
-10
-5
5
Step-by-step explanation:
From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250
The Remainder Theorem is going to take a bit to solve.
You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.
The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.
However just to get the roots, the graph shows that
x = -10
x = - 5
x = 5
The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give
f((10) = 10^3 + 10*10^2 - 25*10 - 250
f(10) = 1000 + 1000 - 250 - 250
f(10) = 2000 - 500
f(10) = 1500 which is not 0.
==================
f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250
f(1) = 1 + 10 - 25 - 250
f(1) = -264 which again is not zero
Answer:
yes its true
Step-by-step explanation:
just took the test
Which table can be created using the equation below? –2 + 4x = y A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 22, negative 2, 10. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 22, negative 2, 10. Column 2 is labeled y with entries negative 5, 0, 3. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 18, negative 2, 10. Column 2 is labeled y with entries negative 5, 0, 3.
The correct answer is C. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10.
Explanation:
The purpose of an equation is to show the equivalence between two mathematical expressions. This implies in the equation "–2 + 4x = y" the value of y should always be the same that -2 + 4x. Additionally, if a table is created with different values of x and y the equivalence should always be true. This occurs only in the third option.
x y
5 -18
0 -2
3 10
First row:
-2 + 4 (5) = y (5 is the value of x which is first multyply by 4)
-2 + 20 = -18 (value of y in the table)
Second row:
-2 + 4 (0) y
-2 + 0 = -2
Third row:
-2 + 4 (3) = y
-2 + 12 = 10
Answer:
it is c
Step-by-step explanation:
Which rule about the sign of the quotient of positive and negative decimals is correct?
Answer:
Hello!
______________________
Your answer would be (B)
Step-by-step explanation: Because it is all negative when you divide by the positive number.
Hope this helped.
The sign of the quotient of positive and negative decimals correct is (B)
We have determined which rule about the sign of the quotient of positive and negative decimals is correct.
What is the positive question?
A positive question is one that can be falsifiable, or put more simply, has a yes/no answer. Think of a positive question as a how is the world question.
The sign of the quotient of positive and negative decimals is correct Because it is all negative when you divide by the positive number.
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Angle lies in quadrant 4. Without using a calculator, determine which ratio is valid.
1) sin =0.789
2) tan =0.573
3) sin =-1.083
4)tan = 0.841
None of the ratios is valid implies no angle lies in quadrant 4.
Angles lie in quadrant 4. Without using a calculator, it is to determine which ratio is valid from the following 1) sin =0.789, 2) tan =0.573, 3) sin =-1.083 and 4) tan = 0.841.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Since in 4th quadrat only values of cos are positive other else operators tend to give negative value so,
1 ) sin = 0.789, here ratio is positive so it does not lies in quadrant 4.
2) tan = 0.573, it is also positive so it does not lies in quadrant 4.
3) sin = -1.083 this ratio is not possible because sin lies between (-1 to +1).
4) tan =0.841, it is also positive so it does not lie in quadrant 4.
Thus, None of the ratios is valid implies no angle lies in quadrant 4.
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A ladder is placed against a vertical wall at an angle of 45° to the horizontal. If the foot of the ladder is 2.5m away from the wall, how high up the wall does the ladder reach?
Forming a triangle using the 45 degree angle both the horizontal and vertical dimensions need to be identical.
The horizontal dimension is given as 2.5m , so the vertical dimension also has to be 2.5m.
Can calculate it as:
Tan(45) = vertical/ horizontal
Tan(45) = x/2.5
Tan(45) = 1
1 = x/2.5
X = 2.5/1
X = 2.5
7. The Quotient
The quotient of a number divided by five is the same as the number decreased by 400.
Answer:
The number is 500Step-by-step explanation:
Let the number be x
The quotient of a number divided by five is written as
[tex] \frac{x}{5} [/tex]
the number decreased by 400 is written as
x - 400
Equate the two expressions
We have
[tex] \frac{x}{5} = x - 400[/tex]
Multiply through by 5
That's
x = 5x - 2000
x - 5x = - 2000
- 4x = - 2000
Divide both sides by - 4
x = 500
Hope this helps you
Answer:
20
Step-by-step explanation:
they are asking you what divided by 100 is 5 and the answer is 20.
Please help me solve this question with working steps,thanks!!
Answer:
x = 20%
Step-by-step explanation:
The area is the product of side lengths. If the original side is "a", then the one increased by 25% is ...
a + 0.25·a = 1.25a
The one decreased by x is ...
a -x·a = a(1 -x)
We want the area of the square to be the same as that of the rectangle, so we write an equation that says that, then solve for x.
square area = rectangle area
a^2 = (1.25a)(a)(1-x)
1 = 1.25 -1.25x . . . . divide by a^2, eliminate parentheses
1.25x = 0.25 . . . . . add 1.25x -1
x = 0.25/1.25 = 0.20
x = 20% . . . . . . expressed as a percentage
Multiply (4x² + 3y) by (3x² - 4y) and verify the result for x = 1, y = 2
Step-by-step explanation:
(4x² + 3y) by (3x² - 4y)
(4(1)² + 3(2)) by (3(1)² - 4(2))
(4 + 6) and (3 - 8)
10 x (-5) = -50 or 50 if negatives aren't an option
Answer:
22
Step-by-step explanation:
(4×1²+3×2) × (3×1²-4×2)
(16+6)×(9-8)
22×1=22
If Radhika adds these two numbers and represents the sum on an abacus, and if the beads on the ten's place are 2 and the beads on the one's place are 5, how many beads will be there on the hundreds place?
Answer:
Explained below.
Step-by-step explanation:
A standard abacus is a traditional method used to perform basic mathematical calculations, such as addition, subtraction, multiplication and division.
There are 5 rods on a standard abacus.
The shape of the abacus has a series of vertical rods on which a number of beads are placed.
Each bead on a particular rod is considered as 1 unit, i.e. if there are three beads on a rod, the value of that rod is 3.
The last rod on an abacus is for the unit's place, the second last rod is for the ten's place, the third last rod is for the hundredth's place, the fourth last rod is for the thousandth's place and the fifth rod is for the ten thousandth's place.
..............................................
Answer:
h = 40°
Step-by-step explanation:
These 2 angles are congruent due to the Corresponding Angles Theorem.
Answer:
40°
Step-by-step explanation:
The lines are parallel. We know this because of the 2 arrows that are on the lines, indicating they are parallel.
Therefore, the 2 angles are congruent by the Corresponding Angle Theorem.
So, we can set the 2 angles equal to each other.
40=h
Therefore, angle h is 40 degrees.
i promise i will mark as brainiest
Help I’ll give you 30 points
Answer:
a) 16.25 centimeters
b) 6.8 centimeters
Step-by-step explanation:
We can set up a proportion for both of these problems.
a) Look at the longest side of each triangle. We can set up a fraction: 7.2/18. We can also set up a fraction for XZ and PR:
6.5/x
x represents the length you're trying to find.
Since the triangles are similar, we have an equation:
7.2/18=6.5/x
Cross multiply
16.25
XZ is 16.25 centimeters long.
b)
We can do same thing:
7.2/18=x/17
Cross multiply
6.8
QR is 6.8 centimeters long.
Hope this helps!
Answer:
QR = 6.8
XZ = 16.25
Step-by-step explanation:
We can use ratios to solve since the triangles are similar
7.2 QR
------- = ------------
18 17
Using cross products
7.2 *17 = QR*18
Divide by 18
7.2 *17/18 = QR*18/18
QR = 6.8
7.2 6.5
------- = ------------
18 XZ
Using cross products
7.2 XZ = 6.5*18
Divide by 7.2
7.2 XZ = 6.5*18/7.2
XZ = 16.25
Wayne is recording the number of hours he sleeps over different periods of time. The table provided shows the number of hours Wayne sleeps during the respective amount of days.
Answer:
dudes buggin its c he got the right answer but he didnt match with the right answer choice
Step-by-step explanation:
fshhhst
Answer:
It is D= 5 hours per day
Step-by-step explanation:
Why I say that is because 15/3 = 5 that is the same as saying 5 x 3 which is 15
so then if you do 15 x 5 you get 75 therefore your answer would be
= 5 hours per day
For three consecutive numbers, the sum of the first number, twice the second and 7 less than the third is 133. What are the three numbers?
Answer:
34, 35, 36
Step-by-step explanation:
1st number = x
2nd number = x+1
3rd number = x+2
So the equation would be:
x+2(x+1)+(x+2)-7=133
x+2x+2+x+2-7=133
4x-3=133
4x=136
x=34
Three consecutive numbers justifying the condition given in the statement will be 34, 35, 36.
Algebraic expression from a verbal statement: Define the variables to form an algebraic expression from a verbal statement first. Then form the expression or equation as per given verbal statement.Let three consecutive number are,
n, (n + 1), (n + 2)
First statement given,
" The sum of first number, twice the second number"
Expression for the statement → [n + 2(n + 1)]
Second statement → " 7 less than the third number"
Expression for the statement → (n + 2) - 7
Combine the expressions,
"The sum of first number, twice the second number and 7 less than the third number is 133"
Form the equation and simplify,
n + 2(n + 1) + (n + 2) - 7 = 133
n + 2n + 2 + n + 2 - 7 = 133
(n + 2n + n) + (2 + 2 - 7) = 133
4n - 3 = 144
4n = 136
n = 34
Therefore, the numbers are,
1st number → n = 34
2nd number → (n + 1) = 35
3rd number → (n + 2) = 36
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Can someone help me pls
Answer:
H. $12.50
Step-by-step explanation:
Misha wants 1 1/4 yards for each of two straps, for a total of 2 1/2 yards. The ribbon costs $5 per yard, so the total cost for the two straps is ...
(2 1/2 yards)($5 /yard) = $12.50
Recall the equation that modeled the volume of the raised flower bed, y, in terms of the width of the box, y = x3 + 11x2 − 312x. Now, open the graphing tool and graph the equation. Remember, this equation represents the volume of a flower box, so neither the width nor the volume can be negative. Using the pointer, determine the x-intercept where the width is positive and the volume will change to positive as x increases.
Answer:
From the attached graph, the x-intercept is (13, 0)
Step-by-step explanation:
The question equation is y = x³ + 11·x² - 312·x
To graph the equation, we find the value of y for a given value of x and we plot the values on a graph as follows;
x, y
13, 0
14, 532
15, 1170
16, 1920
17, 2788
18, 3780
19, 4902
20, 6160
21, 7560
22, 9108
23, 10810
24, 12672
25, 14700
From the graph, the x-intercept can be found at at x = 13.
The x-intercept can also be obtained by equating the right hand side of the equation to 0 (y = 0 is the x -intercept) as follows;
0 = x³ + 11·x² - 312·x
Therefore, x = 0 is one of the x-intercepts
By dividing by x, we have
x² + 11·x - 312 = 0
By completing the square we have
x² + 11·x + (11/2)² = 312+(11/2)²
(x + 11/2)² = 1369/4
x + 11/2 = ±37/2
x = 37/2 - 11/2 = 13 or x = -37/2 - 11/2 = -24
Which gives the x-intercept as (13, 0).
Which point is not a solution to the system of inequalities?
Thank you:)))
Answer:
(4, -1) is not a solution to the system
Step-by-step explanation:
The first point: (4,-1) doesn't satisfy the first inequality:
[tex]y>x-5\\(-1) > 4-5\\-1>-1[/tex]
since we get to an absurd, because -1 cannot be strictly smaller than -1!
Please help me! I need this answer
Answer:
For the first 3 questions, fill out exactly what you see in the picture. So, the first answer is [tex]9\sqrt{2}[/tex], the second one is x, and the third one is y. Now, since we know this is a 45 - 45 - 90 triangle, we can figure out all of the other sides. AB is the same as AC, so your answer for the fourth one question will be [tex]9\sqrt{2}[/tex]. The hypotenuse in a 45 - 45 - 90 triangle is a side times [tex]\sqrt{2}[/tex], so your last answer will be [tex](9\sqrt{2})(\sqrt{2}) = 18[/tex].
d) The amount earned is a function of the number of years of experience
Answer:
(B)the amount earned is a function of the number of hours worked.
Step-by-step explanation:
Let the time worked (in hours) worked =t
Let the amount earned =A
From the graph
When t=1, A= $10
When t=2, A= $20
When t=3, A= $30
When t=4, A= $40
When t=5, A= $50
We observe that as t increases, the amount increases.
We can, therefore, conclude that the amount earned is a function of the number of hours worked.
Which set of angle measures could be the interior angles of a triangle? Explain why 1) 90°, 90°,90° 2)80°,80°,200° 3)40°,50°,60° 4)15°,30°,135°
Answer: option 4) 15°, 30°, 135°
Step-by-step explanation: because the triangle angle rule says that all the intererior angles of the triangle sum upto 180° always
Answer:
4) 15°,30°,135°
Step-by-step explanation:
The interior angles of a triangle will add up to 180°, so we have to choose an answer choice with angles that all add up to 180.
Answer #4 is correct because 15 + 30 + 135 = 180.
For the quadratic equation 3x^2−7x+4=0, enter the correct values of a, b, and c.
Answer:
since 3x^2-7x+4=0 is in the form ax^2+bx+c=0, a=3, b=-7, c=4
Extra Points! Using the following data, calculate the mean absolute deviation: 1 6 5 8 3 7 1 4 10 9 What is the mean absolute deviation for these data? 9 5.4 5 2.6
Answer: 2.6 for the first one
Step-by-step explanation:
First absolute deviation: 1 6 5 8 3 7 1 4 10 9
Solve using the formula and get 2.6
For the second one I do not understand the digits. Therefore I cannot solve it.
I am very sorry, please forgive me
The mean absolute deviation of the data is M = 2.6
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the total number of points be n
Now , the value of n = 10
And , the number of points on each data is given by set A
Now , the value of set A = { 1 , 6 , 5 , 8 , 3 , 7 , 1 , 4 , 10 , 9 }
So , the total sum of data = 1 + 6 + 5 + 8 + 3 + 7 + 1 + 4 + 10 + 9
The total sum of data = 54
Now , the mean number of data points = 54 / 10 = 5.4
And , the mean deviation is M
M = 1/10 | [ ( 1 - 5.4 ) + ( 6 - 5.4 ) + ( 5 - 5.4 ) + ( 8 - 5.4 ) + | ( 3 - 5.4 ) | + ( 7 - 5.4 ) + ( 1 - 5.4 ) + ( 4 - 5.4 ) + ( 10 - 5.4 ) + ( 9 - 5.4 ) |
M = ( 1/10 ) [ 4.4 + 0.6 + 0.4 + 2.6 + 2.4 + 1.6 + 4.4 + 1.4 + 4.6 + 3.6 ]
M = ( 1/10 ) [ 26 ]
M = 2.6
Therefore , the value of M is 2.6
Hence , the mean deviation is 2.6
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Trae is searching for a treasure on the beach. From point $A$, he is told to walk two meters north, three meters east, and then two meters north to point $B$. In meters, what is the length of $\overline{AB}$?
Answer:A triangle ABC with positive integer side lengths has perimeter 35, centroid G, and incenter I. If ∠GIC=90∘, what is the length of AB¯¯¯¯¯¯¯¯?
We use barycentric coordinates with reference triangle △ABC. Letting k=a+b+c, we have the displacement vectors GI→=(13−ak,13−bk,13−ck) and IC→=(ak,bk,ck−1). EFFT gives us
a2(4b+c3k−13−2bck2)+b2(4a+c3k−13−2ack2)+c2(a+b3k−2abk2)=0
. Multiplying by 3k2, writing k=a+b+c, and expanding out, the equation turns into
a2((a+b+c)(3b−a)−6bc)+b2((a+b+c)(3a−b)−6ac)+c2((a+b)(a+b+c)−6ab)=0.
Expanding further and factoring an a+b+c out, we have
(a+b+c)((a+b)(4ab−a2−b2+c2)−6abc)=0.
Notice that when c=a+b the term (a+b)(4ab−a2−b2+c2)−6abc) vanishes, so we factor further to obtain
(a+b+c)(c−a−b)(a2+b2+c(a+b)−4ab)=0⟹a2+b2+c(a+b)−4ab=0⟹(a+b)2+c(a+b)=6ab⟹35(35−c)=6ab.
From the triangle inequality, we have c≤17 and we also know 6|35−c; it's now easy to find a triple (a,b,c)=(10,14,11) satisfying the equation above, and the answer is 11.
Hope this helps......