Answer:
H₀: μ = 4 vs. H ₐ: μ > 4
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.
The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.
It is also known as the research hypothesis and is denoted by H ₐ.
In this case we need to test whether the amount is paid after the grace period, on average, more than 4 times in 2018.
The hypothesis can be defined as follows:
H₀: μ = 4 vs. H ₐ: μ > 4
Evaluate each expression for the given values of the variables: |a−b| − |c+d| , if a=−5; b=4; c=1; d=−3
Answer:
11
Step-by-step explanation:
|a−b| − |c+d|
Let = a=−5; b=4; c=1; d=−3
|-5−4| − |1+-3|
|-9| − |-2|
Absolute values means take the non-negative value
9 + 2
11
Answer:
7
Step-by-step explanation:
| a - b | - | c + d |
Plug in the values for the variables.
| -5 - 4 | - | 1 + -3 |
Evaluate.
| - 9 | - | -2 |
Apply rule : | -a | = a
9 - 2
Subtract the numbers.
= 7
what is the distance formula
Answer:
14.42 units
Step-by-step explanation:
Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:
AB² = AC² + BC²
AB² = 12² + 8²
AB = √(12² + 8²)
AB = 14.42 units
if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6
Answer:
d. 20
Step-by-step explanation:
To answer the question given, we will follow the steps below:
we need to first find p(3)
p(x) = x+ 7/ x-1
we will replace all x by 3 in the equation above
p(3) = 3+7 / 3-1
p(3) = 10/2
p(3) = 5
Similarly to find q(2)
q (x) = x^2 + x - 2,
we will replace x by 2 in the equation above
q (2) = 2^2 + 2 - 2
q (2) = 4 + 0
q (2) = 4
The product of p(3) and q(2) = 5 × 4 = 20
What is the domain of the function shown on the graph? A. -10
Answer:
Option (C)
Step-by-step explanation:
Domain of any graph is defined by the x-values or the input values of a function.
Similarly, y-values on the graph of a function define the Range.
In the graph attached, x-values varies from (-∞) to (+∞).
Therefore, Domain of the graphed function will be (-∞, ∞)
Or -∞ < x < ∞
Similarly, y-values of the graph varies from (-∞) to (1)
Therefore, range of the graphed function will be (-∞, 1).
Or -∞ < y < 1
Option (C) will be the answer.
Using leaner combination method what is the solution to the system of linear equations 7x-2y=-20 and 9x+4y=-6
Answer:
x = -2 and y = 3
Step-by-step explanation:
In linear combination method we try one of the variables from bopth of equations by
first making the variable equal in vlaue
then either subtracting or adding the two equation as required to eliminate the variable.
_____________________________________________
7x-2y=-20 equation 1
and 9x+4y=-6 equation 2
we see that y has
has value -2 and +4
4 = 2*2
thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.
7x-2y=-20
multiplying the LHS and RHS with 2
2(7x-2y)=-20 *2
=> 14x - 4y = -40 eqaution 3
now that we have got 4y
lets add equation 2 and equation 3
9x +4y= -6
+14x - 4y = -40
________________________________
=> 23x + 0 = -46
x = -46/23 = -2
Thus, x = -2
substituitinng x = -2 in 7x-2y=-20
7*-2 -2y=-20
=> -14 -2y = -20
=> -2y = -20+14 = -6
=> y = -6/-2 = 3
Thus, y = 3
solution is x = -2 and y = 3
Chris purchased a tablet for $650. The tablet depreciates at a rate of $25 per month.
Write and simplify an equation that models the value V(m) of the tablet after m months.
Let d equal the final amount it depreciates.
Let m equal the number of months.
Since d is the final amount, we put this at the very end of the equation.
Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).
The final equation comes out too: d = 650 - 25m
Best of Luck!
find the hypo when the opposite is 36 and the adjacent is 27
Answer:
45
Step-by-step explanation:
Given the legs of the right triangle.
Then using Pythagoras' identity
The square oh the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is
h² = 36² + 27² = 1296 + 729 = 2025 ( take the square root of both sides )
h = [tex]\sqrt{2025}[/tex] = 45
Answer:
45
Step-by-step explanation:
When you are given the opposite and adjacent sides of a triangle, the easiest way to find the hypotenuse is through the Pythagorean theorem!
The formula is a^2 + b^2= c^2
Plugging in the values, your formula would now look like 36^2 + 27^2= c^2
Once you do square your values and add them up, the result would end up being 2025, but since that is squared, to find the actual value of c you have to take the square root of this number, this will result in 45.
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the origin. A.) a dilation by a scale factor of Two-fifths and then a translation of 3 units up B.) a dilation by a scale factor of Two-fifths and then a reflection across the x-axis C.) a dilation by a scale factor of Five-halves and then a translation of 3 units up D.) a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Answer:
The correct option is;
A.) A dilation by a scale factor of two-fifths and then a translation of 3 units up
Step-by-step explanation:
The given information are;
Square S undergoes transformation into square S'
From the figure, the dimension of S' = 2/5 dimension of S
Therefore, the scale factor of the dilation is two-fifths
The center of dilation = The origin
Therefore, given that the top right edge of S is at the center of dilation, the initial location of the dilated figure will be (0, 0), (2, 0), (2, -2), and (0, -2)
Given that the lowermost coordinates of S' are (0, 1) and (2, 1), and the lowermost coordinates of the initial dilation are (0, -2) and (2, -2), we have that the translation to S' from the initial dilation is T (0 - 0, 1 - (-2)) = T(0, 3) which is 3 units up.
Answer:
A
Step-by-step explanation:
What is the slope of the line through the points (2,8) and (5,7)
Answer:
-1/3
Step-by-step explanation:
The slope of the line can be found by
m = (y2-y1)/(x2-x1)
= ( 7-8)/(5-2)
= -1/3
Answer:
-1/3.
Step-by-step explanation:
The slope can be found by doing the rise over the run.
In this case, the rise is 8 - 7 = 1.
The run is 2 - 5 = -3.
So, the slope is 1 / -3 = -1/3.
Hope this helps!
Simplify $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$
Let [tex]x=\sqrt[3]{3}[/tex] and [tex]x^2=\sqrt[3]{9}[/tex]. Then
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2x^2}{1+x+x^2}[/tex]
Multiply the numerator and denominator by [tex]1-x[/tex]. The motivation for this is the rule for factoring a difference of cubes:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Doing so gives
[tex]\dfrac{2x^2(1-x)}{(1+x+x^2)(1-x)}=\dfrac{2x^2(1-x)}{1-x^3}[/tex]
so that
[tex]\dfrac{2\sqrt[3]{9}}{1+\sqrt[3]{3}+\sqrt[3]{9}}=\dfrac{2\sqrt[3]{9}(1-\sqrt[3]{3})}{1-3}=\sqrt[3]{9}(\sqrt[3]{3}-1)=3-\sqrt[3]{9}[/tex]
please solve this using quadratic formula :")
Answer:
Step-by-step explanation:
The given equation is expressed as
(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12
Simplifying the right hand side of the equation, it becomes
[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)
x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)
(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)
4x/(x - 1)(x + 1)
Therefore,
4x/(x - 1)(x + 1) = 7/12
Cross multiplying, it becomes
4x × 12 = 7(x - 1)(x + 1)
48x = 7(x² + x - x - 1)
48x = 7x² - 7
7x² - 48x - 7 = 0
Applying the quadratic formula,
x = - b ± √(b² - 4ac)]/2a
from our equation,
b = - 48
a = 7
c = - 7
Therefore
x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)
x = [48 ± √(2304 + 196]/14
x = (48 ± √2500)/14
x = (48 ± 50)/14
x = (48 + 50)/14 or x = (48 - 50)/14
x = 98/14 or x = - 2/14
x = 7 or x = - 1/7
Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7
Step-by-step explanation:
I NEED HELP QUICK like very quick
Answer:
2.5 or 2 1/2
Step-by-step explanation:
i caculated do order of operations
A car can go from rest to 90 km⁄h in 10 s. What is its acceleration?
Answer:
2.5 m/s^2
Step-by-step explanation:
Answer:
2.5 m/s²
Step-by-step explanation:
First, convert to SI units.
90 km/h × (1000 m/km) × (1 h / 3600 s) = 25 m/s
a = Δv / Δt
a = (25 m/s − 0 m/s) / 10 s
a = 2.5 m/s²
What is the least common denominator of the rational expressions below?
Answer:
x(x-3) ( x+4)
Step-by-step explanation:
2 5
---------- + ------------
x^2 -3x x^2 + x - 12
Factor the denominator
2 5
---------- + ------------
x(x -3) (x-3) (x+4)
The common denominator is
x(x-3) ( x+4)
The graph shows the distance Ted traveled from the market in miles (y) as a function of time in seconds (x). The graph is divided into four segments labeled P, Q.
R. and S
S
Distance
(mi)
R
P
Time (sec)
Which segment shows Ted waiting for a cab?
A) P
B) Q
C) R
D) S
Explanation:
The flat horizontal portion S is where the distance (y) does not increase or decrease. So Ted is stationary during this time frame.
In terms of speed, we would say speed = distance/time = (change in y)/(change in x). Note how this is the slope.
Rise = 0 because the horizontal line does not go up or down. The run is any positive number, though convention usually has Run = 1. Therefore, slope = rise/run = 0/1 = 0. All flat horizontal lines have a slope of 0 to indicate no upward or downward movement.
Please help I will give out brainliest
Answer:
All the points change, there are no invariant points
Step-by-step explanation:
The given parameters are
To translate the square OABC by the vector [tex]\dbinom{1}{3}[/tex], we have;
The coordinates of the point O is (0, 0)
The coordinates of the point A is (3, 0)
The coordinates of the point B is (3, 3)
The coordinates of the point C is (0. 3)
The translation is by moving 1 step right and three steps up to give;
O' is (0+1, 0+3) which is (1, 3)
A' is (3+1, 0+3) which is (4, 3)
B' is (3+1, 3+3) which gives (4, 6)
C' is (0+1, 3+3) which gives (1, 6)
As all the points change, there are no invariant points and the number of invariant points is zero.
find the value of x in the triangle shown below
Answer:
x=70
Step-by-step explanation:
the angles opposite 3.5 equal 55 degrees
180-55-55=70
Answer:
70°
Step-by-step explanation:
since the both size are equal which is 3.5,it is equal length, so the other angle should be 55 also. Just use the triangle =180° ，180-55-55=70°
If f(x) and g(x) are quadratic functions but (f + g)(x) produces the graph below, which statement must be tru
Answer:
The leading coefficients of f(x) and g(x) are Opposites.Option A is the correct option.
Step-by-step explanation:
As the graph of ( f + g ) ( x ) is a line. So, ( f + g ) ( x ) is linear which means x² of f ( x ) and x² of g ( x ) get cancelled on adding . They must be equal and opposite in sign.
So, Option A is correct.
Hope this helps..
Best regards!!
PLEASE HELP
What is the y-intercept of the given graph? -4 3 4 None of these choices are correct.
Answer:
3
Step-by-step explanation:
the line crosses the y-axis at (0,3)
Answer:
3
Step-by-step explanation:
The y intercept is where the graph crosses the y axis ( where x =0)
The lines crosses at y=3
Y intercept is 3
I need the answers to the questions highlighted with the black rectangles.
Answer:
b) P(more than 10) = 2/9
c) P(less than 7) = 2/9
Step-by-step explanation:
a) Yaniq spins both spinners and then adds up the results together.
The results are as follow:
5
7
9
6
8
10
7
9
10
These are a total of 9 outcomes.
b) What is the probability that Yaniq gets a total of more than 9?
The probability is given by
P = Number of favorable outcomes/Total number of outcomes
For this case, the favorable outcomes are all those outcomes where the total score is more than 9.
Count the number of times Yaniq got a score of more than 9.
Yes right!
2 times (10 and 10)
P(more than 10) = 2/9
c) What is the probability that Yaniq gets a total of less than 7?
For this case, the favorable outcomes are all those outcomes where the total score is less than 7.
Count the number of times Yaniq got a score of less than 7.
Yes right!
2 times (5 and 6)
P(less than 7) = 2/9
GEOMETRY
1.) find the value of z and show work
a) Explain the difference in how an inscribed angle and central angle are draw
b) Explain the difference in how their measures compare to the subtended arc.
Answer:
z = 8.5
Step-by-step explanation:
Let O be the center of the circle, and A, B, C are three points on the circle.
Draw OA and OC are shown in the figure. To make the central angle.
In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is
[tex]\angle AOC=118^{\circ}[/tex]
Subtended angle on arc AC is
[tex]\angle ABC=(6z+8)^{\circ}[/tex]
According to central angle theorem of circle, central angle is twice of angle subtended by the arc.
[tex]\angle AOC=2\times \angle ABC[/tex]
[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]
[tex]118=12z+16[/tex]
[tex]118-16=12z[/tex]
[tex]102=12z[/tex]
[tex]\dfrac{102}{12}=z[/tex]
[tex]8.5=z[/tex]
Therefore, the value of z is 8.5.
Mr rigo bought 49 bags
Answer:
77 bags
Step-by-step explanation:
if he brought 49 bags then he brought 28 more bags49+28=77
The measure of each exterior angle of a regular polygon is 30 degrees. How many sides does the polygon have
Answer:
12 sides
Step-by-step explanation:
To find the number of sides, use a formula.
[tex]\frac{360}{\theta }=n[/tex]
θ is the measure of each exterior angle of the regular polygon.
n is the number of sides of the regular polygon.
[tex]\frac{360}{30} =12[/tex]
An education researcher claims that 58% of college students work year-round. In a random sample of 400 college students, 232 say they work year-round. At alphaequals0.01, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below.
Answer:
The proportion of college students who work year-round is 58%.
Step-by-step explanation:
The claim made by the education researcher is that 58% of college students work year-round.
A random sample of 400 college students, 232 say they work year-round.
To test the researcher's claim use a one-proportion z-test.
The hypothesis can be defined as follows:
H₀: The proportion of college students who work year-round is 58%, i.e. p = 0.58.
Hₐ: The proportion of college students who work year-round is 58%, i.e. p ≠ 0.58. C
Compute the sample proportion as follows:
[tex]\hat p=\frac{232}{400}=0.58[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0[/tex]
The test statistic value is 0.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=2\times P(z<0)=2\times 0.5=1[/tex]
*Use a z-table for the probability.
The p-value of the test is 1.
The p-value of the test is very large when compared to the significance level.
The null hypothesis will not be rejected.
Thus, it can be concluded that the proportion of college students who work year-round is 58%.
Andy spins the spinner and rolls a standard number cube. Find the probability that the spinner will stop on yellow and the cube will show a three or five. Write the probability as a fraction in simplest form.
Answer: 1/5 , 1/2, and 5/6
Step-by-step explanation:
given;
probability that the cube shows a three (3) or five (5).
probability that it stops on yellow.
1. the probability p of the spinner stopping on yello
= 1/5 times
a cube has 6 sides
2. probability that it shows a 3
this is going to be 3 divided by the total sides on the cube which is 6
P = ( 3 ) = 3/6
Divide both side by 3
= 1/2.
3. probability that it shows a 5,
this is going to be 5 divided by the total sides on the cube which is 6
P = ( 5 )
= 5/6.
PLS help ASAP I need help with 13
Answer:
335
Step-by-step explanation:
536/336 = x/210
We're assuming all horizontal lines are parallel. Let x be the distance between A and B
[tex]\dfrac{x}{536}=\dfrac{210}{336}[/tex]
Cross multiply
[tex]336x=536 \times 210[/tex]
Simplifying and solving for x gives us:
[tex]x=335[/tex]
Now, add the distance between A and B and the distance between B and C to find the distance between A and C:
[tex]335+536=871[/tex]
The answer is choice C. Let me know if you need any clarifications, thanks!
Please answer it now in two minutes
Answer:
[tex] C = 28.9 [/tex]
Step-by-step explanation:
Given the right angled triangle, ∆BCD, you are required to find the measure of angle C.
Apply the trigonometric ratio formula to find m < C.
Adjacent side = 7
Hypotenuse = 8
Trigonometric ratio formula to apply would be:
[tex] cos(C) = \frac{7}{8} [/tex]
[tex] cos(C) = 0.875 [/tex]
[tex] C = cos^{-1}(0.875) [/tex]
[tex] C = 28.9 [/tex]
(To nearest tenth)
Please help need this done ASAP
Answer:
a) 56548.7 cm³
b) 13 minutes
Step-by-step explanation:
a) The volume will be 2/3 pi r³ (which is the given formula divided by 2 since we only have half a sphere)
Fill in r=30 gives: 56548.7 cm³
b) 56548.7 cm³ divided by 4500 cm³/min = 12.6 ≈ 13 minutes
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice
Complete question:
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 70% pure fruit juice?
Answer:
Juice A = 15
Juice B = 35
Step-by-step explanation:
Given the following:
Juice A:
Let juice A = a
35% pure fruit juice
Juice B:
Let juice B = b
85% pure fruit juice
We need to make 50 pints of juice from both: that is ;
a + b = 50 -------(1)
In terms of pure fruit:
a = 0.35 ; b = 0.85 ;
Our mixed fruit juice from a and b should be 70% pure fruit = 0.7
Mathematically,
0.35a + 0.85b = 50(0.7)
0.35a + 0.85b = 35 -------(2)
Multiply (2) by 100
35a + 85b = 3500 --------(3)
We can then solve the simultaneous equation:
a + b = 50 -------(1)
35a + 85b = 3500 --------(3)
Multiply (1) by 35
35a + 35b = 1750 -----(4)
35a + 85b = 3500 ---(5)
Subtract (5) from (4)
-50b = -1750
b = 35
Substitute b = 35 into (2)
0.35a + 0.85(35) = 35
0.35a + 29.75 = 35
0.35a = 35 -29.75
0.35a = 5.25
a = 5.25/0.35
a = 15
Juice A = 15
Juice B = 35
Angles α and β are angles in standard position such that: α terminates in Quadrant III and sinα = - 5/13 β terminates in Quadrant II and tanβ = - 8/15
Find cos(α - β)
-220/221
-140/221
140/221
220/221
Answer:
140/221.
Step-by-step explanation:
For the triangle containing angle α:
The adjacent side is -√(13^2-5^2) = -12.
For the triangle containing angle β:
Hypotenuse = √(-8)^2 + (15)^2) = 17.
cos(α - β) = cos α cos β + sin α sin β
= ((-12/13) * (-15/17) + (-5/13)* (8/17)
= 180/221 + - 40/221
= 140/221.