Answer: 12 Tbsp
Step-by-step explanation:
Note: 1 Tbsp = 3 tsp
2 tsp x 21 = 42 tsp
42 tsp ÷ 3 = 12 Tbsp
Change Y = 3X to the standard form of the equation of a line.
Answer:
-3x+y=0
Step-by-step explanation:
Standard form= Ax+Bx=C
Add -3x both sides, answer -3x+1y=0
The floor of a rectangular room is to be covered with square floor tiles with
1
-foot sides. The floor of the room is
18
feet long and
12
feet wide. If the square tiles cost
$
4
each, how much would it cost to completely cover the floor with these tiles?
Answer:
Total cost = $864
Step-by-step explanation:
The area of the rectangular room
= 18*12
= 216 ft²
The sides of the square is 1ft
The area of the square= 1ft²
To know how many square tiles it will take= 216/1 = 216 square tiles.
The total cost to completely cover the room with tiles if each tiles cost $4
= 216*4
= $864
Total cost=$864
A meteorologist who sampled 4 thunderstorms found that the average speed at which they traveled across a certain state was 16 miles per hour. The standard deviation of the sample was 4.1 miles per hour. Round the final answers to at least two decimal places.
Required:
Find the 90% confidence interval of the mean. Assume the variable is normally distributed.
Answer:
The 90 % confidence interval for the mean population is (11.176 ; 20.824 )
Rounding to at least two decimal places would give 11.18 , 20.83
Step-by-step explanation:
Mean = x`= 16 miles per hour
standard deviation =s= 4.1 miles per hour
n= 4
[tex]\frac{s}{\sqrt n}[/tex] = 4.1/√4= 4.1/2= 2.05
1-α= 0.9
degrees of freedom =n-1= df= 3
∈ ( estimator t with 90 % and df= 3 from t - table ) 2.353
Using Students' t - test
x`±∈ * [tex]\frac{s}{\sqrt n}[/tex]
Putting values
16 ± 2.353 * 2.05
= 16 + 4.82365
20.824 ; 11.176
The 90 % confidence interval for the mean population is (11.176 ; 20.824 )
Rounding to at least two decimal places would give 11.18 , 20.83
Answer:
[tex]11.18 < \mu <20.82[/tex]
Step-by-step explanation:
From the information given:
A meteorologist who sampled 4 thunderstorms of the sample size n = 16
the average speed at which they traveled across a certain state was 16 miles per hour ; i.e Mean [tex]\bar x[/tex] = 16
The standard deviation [tex]\sigma[/tex] of the sample was 4.1 miles per hour
The objective is to find the 90% confidence interval of the mean.
To start with the degree of freedom df = n - 1
degree of freedom df = 4 - 1
degree of freedom df = 3
At 90 % Confidence interval C.I ; the level of significance will be ∝ = 1 - C.I
∝ = 1 - 0.90
∝ = 0.10
∝/2 = 0.10/2
∝/2 = 0.050
From the tables;
Now the t value when ∝/2 = 0.050 is [tex]t_{\alpha / 2 ,df}[/tex]
[tex]t_{0.050 \ ,\ 3} = 2.353[/tex]
The Margin of Error = [tex]t_{\alpha / 2 ,df} \times \dfrac{s}{\sqrt{n}}[/tex]
The Margin of Error = [tex]2.353 \times \dfrac{4.1}{\sqrt{4}}[/tex]
The Margin of Error = [tex]2.353 \times \dfrac{4.1}{2}[/tex]
The Margin of Error = [tex]2.353 \times 2.05[/tex]
The Margin of Error = 4.82365
The Margin of Error = 4.82
Finally; Assume the variable is normally distributed, the 90% confidence interval of the mean is;
[tex]\overline x - M.O.E < \mu < \overline x + M.O.E[/tex]
[tex]16 -4.82 < \mu < 16 + 4.82[/tex]
[tex]11.18 < \mu <20.82[/tex]
Graph the equation y = 1/2x + 5 on the coordinate plans provided below.
Answer:
Well, of course, i can not graph it in the coordinate plane in the image, but i can try to teach you how to do it.
We have the function y = (1/2)*x + 5
The first step is to generate pairs (x, y)
You can do it by evaluating the function in different values of x.
For example;
if x = 0
y = (1/2)*0 + 5 = 5
then we have the point (0,5)
if x = 2
y = (1/2)*2 + 5 = 6
Then we have the point (1, 6)
Now, with only two points you can graph the line.
First find the points in the coordinate plane, and mark them.
Now, with a ruler, draw a line that connects the two points.
That line is the graph of the function.
An example of the graph is:
Rewrite2(4)(6) in a different way, using the Commutative Law of Multiplication.
Answer:
2(6)(4)
Step-by-step explanation:
The commutative law of multiplication states that the order of the numbers does not affect the answer. To rewrite 2(4)(6) using the commutative law of multiplication, rearrange the order of the numbers.
Help all mathematicians!
Answer: Choice D
Maximums = (0,1) and (2pi, 1)
minimum = (pi, -3)
======================================================
Explanation:
Cosine is a periodic function that bounces up and down forever. The highest y = cos(x) gets is y = 1 and that happens when x = 0, 2pi, etc. Basically anything in the form x = 2pi*n for any integer n will have y = cos(x) maxed out. Consequently, this means y = 2cos(x)-1 maxes out at the same mentioned x values.
Plug in those x values to find that y = 1 is the max y value for y = 2cos(x)-1
A similar situation happens for the mins as well. We have y = cos(x) be the smallest when x = pi+2pi*n for any integer n.
In the given diagram, find the values of x, y, and z.
a. x = 36°, y = 36°, z = 34°
b. x = 44º, y = 44°, z = 44°
c. x = 34º, y = 34°, z = 34°
d. x = 36°, y = 34°, z = 34°
Answer:
a. x = 36°, y = 36°, z = 34°
Step-by-step explanation:
X = 36° because x and 144° are supplementary angles and the sum of supplementary angles = 180°
The sum of interior angles in a triangle is equal to 180° since one of the angle is given as 110° the sum of z and y must be equal to 70° the option that fits these qualities is a. x = 36°, y = 36°, z = 34°
Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
u = -4 A = 1 0 3
-5 -2 -1 -4
3 3 -3 0
1 -1 3 6
A) In Col A, not in Nul A
B) Not in Col A, not in Nul A
C) In Col A and in NulA
D) Not in Col in Nul A
Answer: d) Not in Col in Nul A
Step-by-step explanation: The definition of Column Space of an m x n matrix A is the set of all possible combinations of the columns of A. It is denoted by col A. To determine if a vector is a column space, solve the matrix equation:
A.x = b or, in this case, [tex]A.x=u[/tex].
To solve, first write the augmented matrix of the system:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\-2&-1&-4&-5\\3&-3&0&3\\-1&3&6&1\end{array}\right][/tex]
Now, find the row-echelon form of matrix A:
1) Multiply 1st row by 2 and add 2nd row;
2) Multiply 1st row by -3 and add 3rd row;
3) MUltiply 1st row by 1 and add 4th row;
4) MUltiply 2nd row by -1;
5) Multiply 2nd row by 3 and add 3rd row;
6) Multiply 2nd row by -3 and add 4th row;
7) Divide 3rd row by -15;
8) Multiply 3rd row by -15 and add 4th row;
The echelon form matrix will be:
[tex]\left[\begin{array}{cccc}1&0&3&-4\\0&1&-2&13\\0&0&1&-\frac{51}{15}\\0&0&0&-13 \end{array}\right][/tex]
Which gives a system with impossible solutions.
But if [tex]A.x=0[/tex], there would be a solution.
Null Space of an m x n matrix is a set of all solutions to [tex]A.x=0[/tex], so vector u is a null space of A, denoted by null (A)
Maricopa's Success scholarship fund receives a gift of $ 230000. The money is invested in stocks, bonds, and CDs. CDs pay 2.5 % interest, bonds pay 2.2 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 15000 more in bonds than in CDs. If the annual income from the investments is $ 12095 , how much was invested in each account?
Maricopa's Success scholarship fund receives a gift of $ 170000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25 % interest, bonds pay 4.4 % interest, and stocks pay 11.4 % interest. Maricopa Success invests $ 25000 more in bonds than in CDs. If the annual income from the investments is $ 10055 , how much was invested in each account?
--------------------------
Equations:
s + b + C = 170000
11.4s + 4.4b + 3.25C = 1005500
b = C + 25000
-----------------------
Rearrange::
s + b + C = 170000
1140s + 440b + 325C = 100550000
0 + b - C = 25000
--------------------------
Use any method you know to solve the system to get:
stocks = 45000
bonds = 75000
CD's = 50000
----------------
Cheers,
Stan H.
--------------
Maricopa Success invested $
in stocks.
Maricopa Success invested $
in bonds.
Maricopa Success invested $
--------------
Hope this helps!
Brainliest would be great!
--------------
With all care,
07x12!
Help, Please. File attached this time. Sorry
Answer:
27 degrees
Step-by-step explanation:
Because there is a straight line, all of the angles shown add up to 180, so if you add up all the given angles and subtract it from 180, you will get your answer.
39+86+28=153
180-153=27
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
someone gud at math plss
Answer:
Mark Me Brainliest !
Answer:
P - 28 = C
Explanation:
P (Regular Price )
C ( Cost Savings )
You Noticed These Jeans You Liked.
You Couldn't Afford Them So You Waited Til The Price Dropped.
When Prices Drop Its Either 1 of 2 Reasons
Holiday Seasons Or Price Elasticity
So These Jeans Become $28 On The Market.
Simply You Figure Out How Much You'll Save By Comparing The Original Price To The Discounted Price.
There For Your Answer Will Be The Following :
Regular Price - Discounted Price = Cost Savings
PLEASE HELP!!! The side lengths of a square are each 5q. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle? a. 10q^2-6 b. 9q^2+25 c. 25q^2-9 d. 25q^2-30q-9
The area of the rectangle is [tex]25q^2-9[/tex].
Area of the rectangleThe area of the rectangle is the product of length and width.
How to determine the area of the rectangle?The length of the sides of the square is 5q.
3 is added and 3 is subtracted to the length and the width of the square so, the dimensions of the new quadrilateral is (5q+3) and (5q-3).
So, the area of the rectangle is-
[tex]A=(5q+3)\times (5q-3)\\=25q^2-9[/tex]
Thus, the area of the rectangle is [tex]25q^2-9[/tex].
Learn more about the area of the rectangle here- https://brainly.com/question/20693059
#SPJ2
Answer:25q^2-9
Step-by-step explanation:
your welcomeeeeeeee
A bag of 20 tulip bulbs purchased from a nursery contains 10 red tulip bulbs, 7 yellow tulip bulbs, and 3 purple tulip bulbs. What is the probability of randomly selecting a purple tulip bulb from the bag
Answer:
3/20
Step-by-step explanation:
since there is a total of 20 tulips that would be your denominator then your numerator would be the number of purple tulips which would be 3 so you probability of randomly selecting a purple tulip would be 3/20
What is the approximate volume of the cone? Use 3.14 for π. radius-16 height-9
Answer:
2411.52
Step-by-step explanation:
1/3(3.14*16*16*9) = 2411.52
Answer:
2411.52 units³Step-by-step explanation:
Given,
Radius ( r ) = 16
Height ( h ) = 9
pi ( π ) = 3.14
Volume of cone = ?
Now, let's find the volume of cone:
[tex]\pi \: {r}^{2} \frac{h}{3} [/tex]
plug the values
[tex]3.14 \times {16}^{2} \times \frac{9}{3} [/tex]
Evaluate the power
[tex]3.14 \times 256 \times \frac{9}{3} [/tex]
Calculate the product
[tex]2411.52 \: {units}^{2} [/tex]
Hope this helps..
Best regards!!
pls help me with all 3 questions! correct answer will get brainliest and a kiss...
Answer:
1.union = {20 21 22 23 25 27 29}
2. intersection = {5 14 22}
3.1/3
Step-by-step explanation:
1. union U of sets a nd b ={20 21 22 23 25 27 29}
2. intersection n of sets a nd b = {5 14 22}
3. probability = one item / total
= 1/3
1.
A. {22, 25, 27, 29}
B. {20, 21, 22, 23}
Answer: A∪B = {22, 25, 27, 29, 20, 21, 23}
2.
A. {1, 5, 10, 14, 22}
B. {5, 14, 20, 22, 27}
Answer: A∩B = {5, 14, 22}
3.
A. {1, 5, 10, 14, 22}
B. {5, 14, 20, 22, 27}
Answer: The three items that are intersecting each have a 1/3 chance of being chosen.
A baseball is hit into the air, and its height h in feet after t seconds is given by h(t)= -16t^2+128t+2. The height of the baseball when it is hit is ? The baseball reaches its maximum height after ? The maximum height of the baseball is ?
Answer:
[tex]\large \boxed{\sf \ \text{2 feet, 4 seconds, 258 feet } \ }[/tex]
Step-by-step explanation:
Hello,
To know the height of the baseball when it is hit we have to compute h(0), as t = 0 is when the baseball is hit into the air.
[tex]h(0)=-16\cdot 0^2+128 \cdot 0+2=2[/tex]
So, the answer is 2 feet.
h(x) is a parabola which can be written as [tex]ax^2+bx+c[/tex], it means that the vertex is the point (-b/2a,h(-b/2a)).
The baseball reached its maximum height after
[tex]\dfrac{-b}{2a}=\dfrac{-128}{-2*16}=\boxed{4 \text{ seconds}}[/tex]
And the maximum height of the baseball is h(4).
[tex]h(0)=-16\cdot 4^2+128 \cdot 4+2=-256+512+2=\boxed{258 \ \text{feet}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A submarine is moving parallel to the surface of the ocean at a depth of 626 m. It begins a
constant ascent so that it will reach the surface after travelling a distance of 4420 m.
a) What angle of ascent, to the nearest tenth of a degree, did the submarine make? (3
marks)
b) How far did the submarine travel horizontally, to the nearest metre, during its ascent to
the surface? (3 marks)
Answer:
a) the angle of ascent is 8.2°
b) the horizontal distance traveled is 4375 m
Step-by-step explanation:
depth of ocean = 626 m
distance traveled in the ascent = 4420 m
This is an angle of elevation problem with
opposite side to the angle = 626 m
hypotenuse side = 4420 m
a) angle of ascent ∅ is gotten from
sin ∅ = opp/hyp = 626/4420
sin ∅ = 0.142
∅ = [tex]sin^{-1}[/tex] 0.142
∅ = 8.2° this is the angle of ascent of the submarine.
b) The horizontal distance traveled will be gotten from Pythagoras theorem
[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]
The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances
[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]
adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]
adj = 4375 m this is the horizontal distance traveled.
The approximate measurements of the Great Pyramid of Khufu are shown below. A square pyramid. The base is 230 meters by 230 meters. The triangular sides have a base of 230 meters and height of 187 meters. The pyramid has a height of 147 meters. What is the surface area of the pyramid? 86,020 meters squared 138,920 meters squared 224,940 meters squared 2,592,100 meters squared
Answer:
138,920 m²
Step-by-step explanation:
A square pyramid has 1 square base and 4 lateral triangular faces.
Area of square pyramid is given as BASE Area (BA) + ½*Perimeter of Base (P) × Slant height
Area of pyramid = [tex] b^2 + \frac{1}{2}*4(b)*l [/tex]
Where,
b = base length = 230 m
l = slant height = 187 m (height of the triangular sides)
Surface area = [tex] 230^2 + \frac{1}{2}*4(230)*187 [/tex]
[tex] = 52900 + 2(230)*187 [/tex]
[tex] = 52900 + 86020 [/tex]
[tex] = 138920 [/tex]
Surface area of the pyramid = 138,920 m²
Answer:
hope i helped thank you
Step-by-step explanation:
Hello, can someone help me with these ones pls? I need it ASAP Find the slope of the line in each figure. If the slope of the line is undefined, indicate it. Then write an equation for the given line
Answer:
slope: -3
equation: y = -3x
Step-by-step explanation:
the slope is "the amount of change in the y direction when you take one step to the right".
In the first graph you can see that (0,0) and (1,-3) are on the graph. So when you step from x=0 to x=1, the graph moves 3 units down. Hence the slope is -3. The minus sign means down.
Sometimes it is difficult to see the change in the y direction when only taking 1 step to the right. That's no problem, if you take e.g., 4 steps to the right, you have to divide the y change that you found by 4.
Written in a formula it is dy/dx, a.k.a: the y change divided by the x change.
So that takes care of the slope.
In a general formula for a line y = ax + b, the slope is the letter a.
b is used to move the graph up and down. The first graph moves through (0,0) so no b needed, hence the equation y = -3x.
If b would be, say, 5, the graph would be lifted up by 5. In fact, the point (0,b) will be the point where the graph crosses the y-axis. So you find b by finding the intersection with the y axis. x must be 0 at this point.
With this approach you can solve all assignments easily.
Help please and thank you
Answer:
1
Cans 4cans 8 cans 12 cans
Cost $2.25 $4.5 $6.75
2
Ice Cream 180 q 360 q 540 q 720q 900q 1080 q
Hours 2 hours 4 hours 6 hours 8 hours 10 hours 12 hours
***q = quarts
3
Distance 650 miles 1300 miles 1950 miles
Hours 3 hours 6 hours 9 hours
Answer:
Question 1 - 8 cans = $4.50, 12 cans = $10.13
Question 2 - 4 hours = 360 quarts, 6 hours = 540 quarts, 8 hours = 720 quarts, 12 hours = 1,170
Question 3 - 1,950 miles in 9 hours
Hope this helps :)
if a drawing of a tree is 5 inches tall and the radio is 1:7 (inches:feet) ,how tall is the tree?
If the drawing is 5 inches tall and the ratio is 1:7, that means that 1 inch will be equal to 7 feet.
Height = 5 x 7 = 35 feet
HELP PLZZZ will give branliesstttttt Triangle congruence with sss asa aas sas
Answer:
1) Not congruent
2) AAS
3) Not congruent
4) SAS
5) SSS
6) ASA
Step-by-step explanation:
In SSS, ASA, AAS, and SAS, S stands for side and A stands for angle. If the sides and angles are congruent in any of those patterns, the triangles are congruent.
Hope it helps <3
Answer:
1. Not congruent
2. AAS, Congruent
3. Not congruent
4. SAS, congruent
5. SSS, congruent
6. ASA, Congruent
Step-by-step explanation:
1. Not congruent
It only shows that there are 3 similar angles. There were no sides described.
2. AAS, Congruent
They are congruent, just rotated in an angle (see proof 2)
3. Not congruent
It only shows 2 sides next to each other and an angle next to one side.
4. SAS, congruent
It shows 2 sides that are congruent and congruent angles between them (see proof 4)
5. SSS, congruent
All 3 sides are congruent (see proof 5,6)
6. ASA, Congruent
2 angles and an adjacent side are congruent(see proof 5,6)
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 − x2 , y = 0, x = 2, x = 4; about the x-axis
Answer: V = 193.25π
Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:
V = [tex]\pi\int\limits^a_b {[f(x)]^{2}} \, dx[/tex]
f(x) is the area is the function that rotated forms the solid.
For f(x)=y= [tex]\frac{5}{36}-x^{2}[/tex] and solid delimited by x = 2 and x = 4:
V = [tex]\pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx[/tex]
V = [tex]\pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4}) } \, dx[/tex]
V = [tex]\pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )[/tex]
V = [tex]\pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296} )[/tex]
V = 193.25π
The volume of a solid formed by y = [tex]\frac{5}{36} - x^{2}[/tex] and delimited by x = 2 and x = 4
is 193.25π cubic units.
Find the length of BC
Answer:
The answer is option AStep-by-step explanation:
To find the length of BC we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the adjacent
So we have
tan 61 = AC / BC
tan 61 = 47/BC
BC = 47/tan 61
BC = 26.05Hope this helps you
A horticulturist is studying the relationship between tomato plant height and fertilizer amount. Thirty tomato plants grown in similar conditions were subjected to various amounts of fertilizer (in ounces) over a four-month period, and then their heights (in inches) were measured.
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
Required:
a. Estimate the model: Height = β0 + β1Fertilizer + ε.
b. Does the y-intercept make practical sense?
c. Use the estimated model to predict, after four months, the height of a tomato plant which received 3.0 ounces of fertilizer.
Answer: hello your table is incomplete here is the complete table
Fertilizer Amount (ounces) Tomato Plant Height (inches)
1.9 20.4
5.0 49.2
4.2 56.1
1.3 24.3
4.9 29.2
5.4 60.8
3.1 24.6
0.0 25.3
2.3 26.2
2.5 25.7
0.9 26.5
1.0 28.6
4.5 62.9
3.8 30.8
5.3 43.2
2.3 33.4
4.0 35.1
1.4 22.1
3.9 40.6
4.0 44.5
3.6 29.7
0.6 21.1
1.6 25.4
2.5 29.6
4.5 27.6
3.6 32.6
2.0 33.5
0.0 22.5
2.5 27.6
3.1 46.4
Answer : a)Height = 18.639 + 5.208 * fertilizer
b) The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
c) 34.263
Step-by-step explanation:
A) Estimating the model
Height = β0 + β1 FERTILIZER + ∈
β0 = 18.639
β1 = 5.208
hence
Height = 18.639 + 5.208 * fertilizer ( using excel )
B) The y- intercept
The Y intercept make practical sense because without fertilizer there will still be an increase in plant height ( y intercept )
C ) using the estimated model to predict after four months
the model = 18.639 + 5.208 * fertilizer
fertilizer ounce given = 3
therefore height of tomato plant after 4 months that received 3 ounces of fertilizer = 18.639 + 5.208 * 3 = 34.263
Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x)= 6x +sinx
Answer:
[tex]f(x) = x^3 -sinx +Cx+D[/tex]
Step-by-step explanation:
Given that:
[tex]f ''(x)= 6x +sinx[/tex]
We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.
We will have to integrate it twice to find the value of f(x).
Let us have a look at the basic formula of integration that we will use in the solution:
[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]
[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]
Now, integrating it again to find f(x):
[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]
Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
Manufacturers are testing a die to make sure that it is fair (has a uniform distribution). They roll the die 66 times and record the outcomes. They conduct a chi-square Goodness-of-Fit hypothesis test at the 5% significance level. (a) The null and alternative hypotheses are: H0: The die has the uniform distribution. Ha: The die does not have the uniform distribution. (b) χ20=15.091. (c) χ20.05=11.070. (d) What conclusions can be made? Select all that apply. Select all that apply: We should reject H0. We should not reject H0. At the 5% significance level, there is sufficient evidence to conclude that the die is not fair. At the 5% significance level, there is not enough evidence to conclude that the die is not fair.
Answer:
We should reject H0
At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
.19 OF JOE'S SALARY GOES FOR TAXES. WHAT PERCENT OF HIS SALARY DOES THIS REPRESENT?
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▹ Answer
19%
▹ Step-by-Step Explanation
0.19 → hundreth's place.
19/100 (since the denominator is 100, that represents 100% while 19 represents 19%)
Final Answer - 19%
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
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This represent 19% of his salary.
Given, Joe's salary goes for tax is 0.19.
We have to represent the value in percent.
Here 0.19 can be written in fraction form as,
[tex]\dfrac{19}{100}[/tex]
It means 19 part from 100 part goes for taxes, means 19% of the Joe's salary goes for taxes.
Hence this represent 19% of his salary.
For more details follow the link:
https://brainly.com/question/8011401
Solve the system. If there is more than one solution, write the general solution. x + y - 2z = 9 3x + y + 2z = 15 x - 5y + 22z = -27 Solution {-2z + 3, 4z + 6, z | z is any real number}
Answer:
x = (12-k)/2, y = k, z = (k-6)/4Step-by-step explanation:
Given the system of equation
x + y - 2z = 9 ... 1
3x + y + 2z = 15 ...2
x - 5y + 22z = -27... 3
First let us reduce the system of equation into two with two unknowns.
Subtracting 1 from 3
y-(-5y) + (-2z-22z) = 9-(-27)
y+5y + (-24z) = 9+27
6y-24z = 36 ... 4
Multiplying equation 1 by 3 and subtracting from equation 2
3x + 3y - 6z = 27
3x + y + 2z = 15
On subtracting both;
(3y-y)+(-6z-2z) = 27-15
2y-8z = 12 ... 5
Equating 4 and 5
6y-24z = 36 ... 4
2y-8z = 12 ... 5
Multiplying equation 5 by 3 the equation becomes;
6y-24z = 36 ... 6
6y-24z = 36 ... 7
We can see that equation 6 and 7 are the same;
let y = k
6k - 24z = 36
k - 4z = 6
4z = k-6
z = k-6/4
Substituting y = k and z = k-6/4 into equation 1 to get x
From 1; x + y - 2z = 9 ... 1
x + k -2( k-6/4) = 9
x + k - (k-6)/2 = 9
x = 9+(k-6)/2-k
x = {18+(k-6)-2k}/2
x = (12-k)/2
The solutions to the system of equations are x = (12-k)/2, y = k, z = (k-6)/4 where k is any constant. This shows that the system of equation has infinite solutions.