The test statistic z is 2.33, the p-value corresponding to the test statistic z value is 0.0099.
What is Probability?Probability is the measure of the likeliness of happening of an event.
The mean of the data is 15.07 centimeters
The standard deviation of the data is 0.26 centimeters.
n = 75
Significance Level ∝ = 0.01
According to the null and alternative hypothesis
Hₐ : [tex]\rm \mu[/tex] ≤15 vs H₁ : [tex]\rm \mu[/tex] >15
The test statistic z is given by
[tex]\rm Z = \dfrac{(X-\mu)}{\sigma/\sqrt{n}}[/tex]
Z = ( 15.07 -15)/(0.26/√75)
Z = 2.33
The p-value corresponding to z value is 0.0099
as p-value < significance level, therefore the H₁ : [tex]\rm \mu[/tex] >15 is acceptable.
No, significant evidence is not present to tell that the length of bolts is actually greater than the mean value at a significance level of 0.01.
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When flipping a fair coin 4 times in a row, which outcome is more likely: HTHT or HHHH.
Justify your answer
Answer:
See below
Step-by-step explanation:
equal probability each occurs 1 time out of 16 possibilities
tttt
ttth
ttht
tthh
thtt
thth
thhh
httt
htth
thth
htht
hthh
hhtt
hhth
hhht
hhhh
Which choice is the correct graph of Ix <3?
A +
-6
B++
-6
C
-6
DH
-4
-5
-5
-6 -5
F++
-6
EH
-6
-4
-3
-4
-3
-3
3
-4
-5
-2
-2 -1
OA. Graph A
OB. Graph B
C. Graph C
-3 -2 -1
-2 -1
-20
-2
-3
0
0 1
0
0
-1 0
1
1
1
1
2
2
2
2
2
2
3
3
e
4
3 4
4 5
01
3
4
3
3 4
5
5
5
5
6
6
6
6
6
5
4
6
Answer:
2347 elevated in the cube
Step-by-step explanation:
nashe
Find the y-intercept of the line on the
graph.
Answer:
The y intercept is the point where the line crosses the y axis.
Step-by-step explanation:
The graph that correctly represents the given system of equations is graph , and the solution to the system is ( ,
what graph would it be, doing this on plato rn.
The question was incomplete. Below you will find the missing content.
Use the system of equations and graphs below to complete the sentence.
x - 2y = 5
3x + 15y = -6
The graph that correctly represents the given system of equations is a graph ( ), and the solution to the system is ( , ).
The correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).
Given the first equation is x-2y=5
in this equation of line, the x-coordinate is:
x-(2.0)=5
⇒ x=5
The x-coordinate will be (5,0).
in this equation of line, the y-coordinate is:
0- 2y=5
⇒y= -5/2
The y-coordinate will be (0,-5/2).
So the first line equation has x-coordinate (5,0) and y-coordinate (0,-5/2).
Similarly,
Given the second equation is 3x+15y=-6
in this equation of line, the x-coordinate is:
3x+(15.0)=-6
⇒ x=6/3=2
The x-coordinate will be (2,0).
in this equation of line, the y-coordinate is:
(3.0)+15y=-6
⇒y= -6/15= -2/5
The y-coordinate will be (0,-2/5).
So the second line equation has x-coordinate (2,0) and y-coordinate (0,-2/5).
Equation-1: x - 2y = 5
⇒x =2y+5
putting the value of x in equation-2
3x + 15y = -6
⇒ 3(2y+5)+15y=-6
⇒6y+15+15y=-6
⇒21y=-6-15=-21
⇒y=-21/21=-1
putting the value of y in equation of x
x= 2(-1)+5= -2+5= 3
The solution of system of equations will be (3,-1)
Checking all the options
In option B one line has x-coordinate (5,0) and y-coordinate (0,-5/2) and another line has x-coordinate (2,0) and y-coordinate (0,-2/5).
And the point of intersection of two lines is (3,-1).
Therefore the correct option will be Option B: Graph B and the solution of the given system of equations will be (3,-1).
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Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.
Fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A
How to compare the energy released?The given parameters are:
Energy A = 5.1 * 10^7
Energy B = 1.5 * 10^11
The amount of energy B in proportion to energy A is calculated as
Proportion = Energy B/Energy A
So, we have:
Proportion = (1.5 * 10^11)/(5.1 * 10^7)
Divide 1.5 by 5.1
Proportion = 0.2941 * 10^11/10^7
Divide 10^11 by 10^7
Proportion = 0.2941 * 10^4
Evaluate
Proportion = 2941
Hence, fission of 1 kg of element B releases 2941 times as much energy as burning 1 kg of element A
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You want to buy a $33,000 car. The company is offering a 3% interest rate for 36 months (3 years). What will your monthly payments be?
Answer:
$959.68
Step-by-step explanation:
The loan amortization formula can be used to find the payment amount.
FormulaA = P(r/n)/(1 -(1 +r/n)^(-nt))
A = payment amount; P = principal borrowed; r = annual interest rate; t = number of years; n = payments per year (and number of times interest is compounded per year).
ApplicationFor a principal amount of $33,000 at an interest rate of 3%, the 36 monthly payments will be ...
A = $33000(0.03/12)/(1 -(1 +0.03/12)^(-12·3)) ≈ $959.68
The monthly payments will be $959.68.
The sale price of a laptop is R3 700,00, which is only 65% of the original price. Calculate the original price.
The original price of a laptop that is 65% of the sales price is R3 1076923.07692
How to find the original price when given the percentage?The sale price of a laptop is R3 700,00,which is only 65% of the original price.
Therefore,
let
x = original price
Hence,
700, 000 = 65% of x
700,000 = 65 / 100 of x
cross multiply
70000000 = 65x
divide both sides by 65
x = 70000000 / 65
x = 1076923.07692
Therefore, the original price of the laptop is R3 1076923.07692
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Hernandez Company issued $380,000, 7%, 10-year bonds on January 1, 2022, for $407,968. This price resulted in an effective-interest rate of 6% on the bonds. Interest is payable annually on January 1. Hernandez uses the effective-interest method to amortize bond premium or discount.
For calculation of the following entries, the bond interest expense will gotten by multiplying the carrying bond value by the market interest rate.
Journal entry to record issuance of the bonds
Date Account titles Debit Credit
Jan. 1. Cash $407,968
Bonds payable $380,000
Premium on bonds payable $27,968
($407,968 - $380,000)
Journal entry to record accrual of interest and the premium amortizationDate Account titles Debit Credit
Dec. 31. Bond interest expense $24,478
Premium bond payable $2,122
Bond interest payable $26,600
Journal entry to record payment of interestDate Account titles Debit Credit
Jan. 1. Bond interest payable $26,600
($380000 * 7%)
Cash $26,600
Missing words "Prepare journal entries to record (a) The issuance of the bonds, (b) The accrual of interest and the premium amortization on December 31, 2022 and (c) The payment of interest on January 1, 2022"
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Consider the following frequency table representing the scores on a test.
Scores on a Test
Class Frequency
20–29 9
30–39 4
40–49 3
50–59 2
60–69 10
Determine the number of scores between 19.5 and 49.5.
The number of scores between 19.5 and 49.5 using the cumulative frequency is 16.
What is the cumulative frequency?The cumulative frequency is the running total of frequencies over some class intervals.
The frequency refers to the number of elements in the set or class.
Therefore, the cumulative frequency is the sum of all previous frequencies up to the required point.
Data and Calculations:Scores on a Test
Class Frequency Cumulative Frequency
20–29 9 9 (0 + 9)
30–39 4 13 (9 + 4)
40–49 3 16 (13 + 3)
50–59 2 18 (16 + 2)
60–69 10 28 (18 + 10)
Thus, the number of scores between 19.5 and 49.5 using the cumulative frequency is 16.
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cual es el proceso de estas operaciones de :<, > o = ... porfavor
El uso de las dadas operaciones es:
a < b significa "a es menor que b"a > b significa "a es mayor que b"a = b significa "a es igual que b".¿Como utilizar las operaciones?Para las operaciones "<", ">", y "=" uso es:
a < b significa "a es menor que b"a > b significa "a es mayor que b"a = b significa "a es igual que b".Entonces simplemente debemos comparar los dos números, si vemos al primer problema, por ejemplo:
3 ___ 17/2
Sabemos que 17/2 = 8.5
8.5 es más grande que 3, entonces el signo que debe ir ahi es:
3 < 17/2.
Todas las operaciones que estan colocados en la hoja ya son correctos.
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I need help please. Trying to get my HS diploma. I did not graduate :(
Find the holes of the function
Answer:
(a) none
Step-by-step explanation:
A "hole" in the graph of f(x) is located at an x-value where the left limit of the function and the right limit are the same finite value, but the function is undefined at that value of x.
ExampleThe function f(x) = (x -2)/(x -2) can be reduced to the function f(x) = 1, which is defined everywhere. That reduction occurs when the numerator factor (x-2) cancels the same binomial denominator factor. A graph of the original function will be a straight horizontal line with a "hole" at (2, 1).
The attachment shows a graph.
Given FunctionThe given function can be reduced, but the reduced function remains undefined at x=1/2. Not all of the denominator factors are cancelled there. The function is graphed in the second attachment. At x=1/2, there is a vertical asymptote, not a hole.
[tex]g(x)=\dfrac{(2x-1)(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^3}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}\\\\g(x)=\dfrac{(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^2}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}[/tex]
There are no holes in the function's graph.
__
Additional comment
A hole can occur for a variety of reasons. In the graph of a rational function, it will generally be found where numerator and denominator zeros cancel each other completely, and the function can be "reduced" to one that is define at the location of those zeros.
It can also occur in piecewise defined functions, where the pieces are defined on adjoining (half) open intervals. For example:
[tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x > 0\end{cases}[/tex]
has a hole at (0, 0).
I have two gold rings weighing 7.534g and 5,300 mg. Which is the heavier ring? By how much?
Answer:
7.534g ring is heavier, by 2.234g
Step-by-step explanation:
Note: mg =
[tex] {10}^{ - 3} grams[/tex]
[tex]5300mg = ( \frac{5300}{ {10}^{3} } )g \\ = ( \frac{5300}{1000} )g \\ = 5.3g[/tex]
From here we can see Ring A (7.534g) is heavier than Ring B(5,300mg)
Difference in Mass = 7.534g - 5.3g
= 2.234g
A bag has green and purple marbles. Two-fifths of the marbles are green, and the rest are purple.
a. Draw a bar model for this situation.
b. If there are 134 green marbles, how many are purple?
The number of purple marbles in the bag are; 201 purple marbles
How to work out fraction of bar model?We are told that Two-fifths of the marbles are green, and the rest are purple.
A) The image attached shows the bar model where the shaded parts denote the purple marble while the unshaded parts denote the green marbles.
B) We are told that there are 134 green marbles.
If the total number of marbles are x. Then;
(2/5)x = 134
x = 134 * 5/2
x = 335 marbles
Thus;
Purple Marbles = (3/5) * 335 = 201 purple marbles
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NEED ANSWER ASAP
The graph of F(x), shown below, resembles the graph of G(x) = x², but it has
been changed somewhat. Which of the following could be the equation of F(x)
[tex]f(x) = - 3(x + 3) {}^{2} + 3[/tex]
Option Dlook at the picture
Answer:
i can't see the picture.
A company in its first year of business produced 150 training manuals for a total cost of $2.350. The following
year, the company produced 50 more manuals at a cost of $ 1,450. Use this information to find a linear equation
that gives the total cost of producing training manuals from the number of manuals produced.
Answer:
y = 9x +1000
Step-by-step explanation:
The relation for the total cost of manuals based on the number produced will be the sum of a base cost and a variable cost. The variable cost is the product of the cost per manual and the number of manuals.
Cost per manualThe cost per manual can be found by looking at the increase in cost relative to the increase in the number of manuals produced:
cost per manual = (increase in cost)/(increase in production)
= ($2350 -1450)/(150 -50) = $900/100 = $9
Base costThe base cost will be added to the product of the cost per manual and the number of manuals. For the 2nd year purchase, this is ...
$1450 = base cost + (50 manuals)×($9/manual)
$1450 = base cost + $450
base cost = $1450 -450 = $1000
EquationThe equation for the cost in dollars (y) of producing x manuals can now be described by ...
y = (cost per manual)x +(base cost)
y = 9x +1000
14 points
Choose the correct graph of the given system of equations.
y − 2x = −1
x + 3y = 4
graph of two lines, one with a positive slope and one with a negative slope, that intersect at the point negative 1, 1 with text on graph that reads One Solution negative 1, 1
graph of two lines that intersect at the point 1, 1 with text on graph that reads One Solution 1, 1
graph of two parallel lines with positive slopes with text on graph that reads No Solution
The graph of the given system of equations is shown below
Graph of simultaneous linear equations
From the question, we are to graph the given system of equations.
The given system of equations are
y − 2x = −1
x + 3y = 4
The graph of the given system of equations is shown below
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What is the slope of the line that contains these points?
x: -7| -4 | -1 | 2
y: -7| 14 | 35 | 56
slope:?
The slope of the given line containing the given points is; 7.
How to Calculate the slope of a Line?
The formula for slope of a line between two coordinates is;
Slope(m) = (y2 - y1)/(x2 - x1)
Now, let us take the last 2 coordinates which are;
(-1, 35) and (2, 56).
Thus, the slope is;
m = (56 - 35)/(2 - (-1))
m = 21/3
m = 7
Thus, the slope of the given line containing the given points is 7.
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Pls help! Geometry
Find the area
Answer:
197.9
Step-by-step explanation:
find the area of the large circle and subtract the area of the small circle
area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
area of large circle = 144[tex]\pi[/tex]
area of small circle = 81[tex]\pi[/tex]
area of shaded region = 63[tex]\pi[/tex]
which is equal to about 197.9
Purdue has 1320 employees and plans to increase the number of employees by 20% each year. Is this linear or exponential? Which equation describes this situation?
Please Help!!!
Answer Quickly!!
The exponential function that describes the situation is:
[tex]A(t) = 1320(1.2)^t[/tex]
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.The parameters for this problem are:
A(0) = 1320, r = 0.2.
Hence the equation is:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 1320(1 + 0.2)^t[/tex]
[tex]A(t) = 1320(1.2)^t[/tex]
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a history book weights 24 oz more than a math book. the marh book is 75% the weight of the history book. how much does each book weight
The weight of the math and the history book are 72 and 96 ounces respectively.
How to find the weight of a book?A history book weights 24 oz more than a math book.
Therefore,
let
x = weight of math book
weight of history book = 24 + x
The math book is 75% the weight of the history book.
Therefore,
math book weight = 75 / 100 (24 + x)
x = 75 / 100 (24 + x)
x = 1800 + 75x / 100
100x = 1800 + 75x
100x - 75x = 1800
25x = 1800
x = 1800 / 25
x = 72
Therefore,
weight of math book = 72 ounces
weight of history book = 72 + 24 = 96 ounces.
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what do both of these functions have in common? f(x)=3/2 (x-7) -2 g(x) = 1.5ln(x-2)+7
(x-7) should be absolute value of that.
Both the function have same vertical stretch of 1.5 , Option B is the correct answer.
What is a Function ?A function is a law that relates a dependent and an independent variable.
The functions given in the question is
f(x) = 3/2 |(x -7)| -2
g(x) = 1.5 ln(x-2)+7
For a function f(x)
f'(x) = a f(x) represents the stretching of a function if a> 1
here the value of a = 1.5 for both the functions , so they have same vertical stretch of 1.5 .
Therefore from the options given , Option B is the correct answer.
The complete question is attached as an Image.
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Choose the function whose graph is given by:
5
OA. y= cos(x-1)
OB. y= sin(x+2)
OC. y=sin(x-2)
OD. y = sinx-2
Answer:
C.y=sin(x-2)
Step-by-step explanation:
Using the topic of transformation of functions(rules shown in picture above)
the the (x-2) moves the graph to places to the right
and as the sine graph goes through 0 and so you add 2 to the right (but there is a problem in the graph should in the picture as it should me labeled 0,90,180,270,360 not these small numbers)
hope it helps!! :)
Raj and Priyanka are playing a game in which each person takes turns to snap open a book at a random page. The LAST TWO DIGITS OF THE PAGE NUMBER ON THE RIGHT SIDE is taken as the person's score.
A player's TOTAL score is calculated by adding each turn's score to the previous total. Which of the following could NOT be Priyanka's score after 4 rounds of the game?
A. 6
B. 88
D. 145
C. 250
After four rounds of the game, it is impossible that Prinyanka's score could be A. 6.
What is the lowest score Priyanka could get at round 4?The numbers of the right side are shown to be odd numbers. the lowest numbers that Priyanka can get are:
= 1, 3, 5, 7
Assuming Priyanka picks 1 and 3 which are the lowet number, the total Priyanka would get i:
= 1 + 1 + 3 + 3
= 8
it is therefore not possible to get 6 points after 4 rounds of the game.
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You want to place stone pavers around the edge of your concrete patio. The patio is 12 ft wide by 14 ft long and each stone paver is 14 inches long . How many stone pavers will you need to go around the patio (not counting the side against the house which is 14 ft long)? (round to the nearest whole number )
33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
12 inch = 1 ft
Total perimeter of patio not counting the side against the house = 12 + 12 + 14 = 38 feet
38 feet = 38 feet * 12 inch per feet = 456 in
Number of stone pavers needed = 456 in / 14 in = 32.57 ≅ 33
33 stone pavers are needed to go around the patio with dimension of 12 ft wide by 14 ft long
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Type the correct answer in each box.
The inverse of the function are respectively; f⁻¹(3) = 2 and f⁻¹(8) = 8.5
How to find the inverse of a Function?The formula to find the equation of this function using two coordinates is;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
Using the first 2 coordinates, we have;
(y - 1)/(x + 1) = (3 - 1)/(2 + 1)
(y - 1)/(x + 1) = 2/3
3y - 3 = 2x + 2
3y = 2x + 5
y = ¹/₃(2x + 5)
Thus, the inverse is;
f⁻¹(x) = (3x - 5)/2
Thus;
f⁻¹(3) = (3*3 - 5)/2
f⁻¹(3) = 2
Similarly;
f⁻¹(x) = (3x - 5)/2
Thus;
f⁻¹(8) = (3*8 - 5)/2
f⁻¹(8) = 8.5
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A jar contains 11 brown and 18 blue marbles. A marble is drawn at random. What is the theoretical probability of NOT drawing a blue marble?
Answer:
come omo-tzzf-ivc In meet I will tell
solve this question in the picture
YOU HAVE TO FIND THE AREA OF THE SHADED REIGON IN THE GIVEN PICTURE
●Give right answers
●please solve fast
●Thank you, please solve this part
●FIND the area of the shaded part
Answer: [tex]64\pi[/tex]
Step-by-step explanation:
Area of the outer circle: [tex](\pi)(10^{2})=100\pi[/tex]
Area of the inner circle: [tex](\pi)(6^{2})=36\pi[/tex]
Subtracting these areas, we get the area of the shaded region is [tex]\boxed{64\pi}[/tex]
Exact volume:
Approximate volume:
Answer: Multiplying these factors gives the approximate volume of the original body
Step-by-step explanation:
The given convex body can be approximated by a sequence of nested bodies, eventually reaching one of known volume (a hypersphere), with this approach used to estimate the factor by which the volume changes at each step of this sequence.
find the surface area of a cylinder with height of 8 feet and base diameter of 6 feet
Answer:
[tex]66\pi[/tex] ft²
Step-by-step explanation:
First find the area of the rectangle surrounding the cylinder.
Since the base diameter is 6 feet, the circumference [tex]=\pi d=6\pi[/tex].
Since the height is 8 feet, the area of the rectangle is [tex]6\pi\times8[/tex] or [tex]48\pi[/tex]
Now the area of the base circle [tex]=\pi r^2 = \pi\times\frac{1}{4}d^2=9\pi[/tex]
There are 2 base circles, so [tex]9\pi\times2=18\pi[/tex]
Surface area = [tex]18\pi+48\pi=66\pi[/tex] ft²