Answer:
27.883
Step-by-step explanation:
75.847
-47.964
27.883
Complete the table so that the cost per banana remains the same.
number of
bananas
cost in
dollars
unit price
(dollars per banana)
4
0.50
6
0.50
7
0.50
10
0.50
10.00
0.50
16.50
0.50
Step-by-step explanation:
No. of banana Cost Unit price
4 2 0.50
6 3 0.50
7 3.5 0.50
20 10 0.50
20 10 0.50
33 16.50 0.50
Cost = No of banana x unit price
Cost = 4 x 0.50 = 2
Cost = 6 x 0.50 = 3
Cost = 7 x 0.50 = 3.50
Cost = 20 x 0.50 = 10
No of banana = Cost / Unit price
No of banana = 10 / 0.50 = 20
No of banana = 16.50 / 0.50 = 33
1. A company that produces bread is concerned about the distribution of the amount of sodium in its bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be 103 milligrams of sodium per slice. Assume that the population standard deviation is 10 milligrams. a) Construct a 95% confidence interval estimate for the mean sodium level. b) Construct a 99% confidence interval estimate for the mean sodium level.
Answer:
The 95% confidence interval is [tex] 101.13 < \mu < 104.87 [/tex]
The 99% confidence interval is [tex] 100.54 < \mu < 105.46 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 103 \ mg[/tex]
The population standard deviation is [tex]\sigma = 10 \ mg[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 10 }{\sqrt{110} }[/tex]
=> [tex]E =1.8688 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]103 - 1.8688 < \mu < 103 + 1.8688 [/tex]
=> [tex] 101.13 < \mu < 104.87 [/tex]
Considering question b
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{ 10 }{\sqrt{110} }[/tex]
=> [tex]E =2.4599 [/tex]
Generally 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]103 - 2.4599 < \mu <103 + 2.4599 [/tex]
=> [tex] 100.54 < \mu < 105.46 [/tex]
An infinite solution means the solutions for the algebraic equation are endless
Answer:
Correct
Step-by-step explanation:
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+3y=8te^−t+6e^−t−(9t+6)
with initial values y(0)=2andy′(0)=2.
We're given the ODE,
y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) - (9t + 6)
(where I denote exp(x) = eˣ )
First determine the characteristic solution:
y'' + 4y' + 3y = 0
has characteristic equation
r ² + 4r + 3 = (r + 1) (r + 3) = 0
with roots at r = -1 and r = -3, so the characteristic solution is
y = C₁ exp(-t ) + C₂ exp(-3t )
For the non-homogeneous equation, assume two ansatz solutions
y₁ = (at ² + bt + c) exp(-t )
and
y₂ = at + b
• y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) … … … [1]
Compute the derivatives of y₁ :
y₁ = (at ² + bt + c) exp(-t )
y₁' = (2at + b) exp(-t ) - (at ² + bt + c) exp(-t )
… = (-at ² + (2a - b) t + b - c) exp(-t )
y₁'' = (-2at + 2a - b) exp(-t ) - (-at ² + (2a - b) t + b - c) exp(-t )
… = (at ² + (b - 4a) t + 2a - 2b + c) exp(-t )
Substitute them into the ODE [1] to get
→ [(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c)] exp(-t ) = 8t exp(-t ) + 6 exp(-t )
(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c) = 8t + 6
4at + 2a + 2b = 8t + 6
→ 4a = 8 and 2a + 2b = 6
→ a = 2 and b = 1
→ y₁ = (2t ² + t ) exp(-t )
(Note that we don't find out anything about c, but that's okay since it would have gotten absorbed into the first characteristic solution exp(-t ) anyway.)
• y'' + 4y' + 3y = -(9t + 6) … … … [2]
Compute the derivatives of y₂ :
y₂ = at + b
y₂' = a
y₂'' = 0
Substitute these into [2] :
4a + 3 (at + b) = -9t - 6
3at + 4a + 3b = -9t - 6
→ 3a = -9 and 4a + 3b = -6
→ a = -3 and b = 2
→ y₂ = -3t + 2
Then the general solution to the original ODE is
y(t) = C₁ exp(-t ) + C₂ exp(-3t ) + (2t ² + t ) exp(-t ) - 3t + 2
Use the initial conditions y (0) = 2 and y' (0) = 2 to solve for C₁ and C₂ :
y (0) = C₁ + C₂ + 2 = 2
→ C₁ + C₂ = 0 … … … [3]
y'(t) = -C₁ exp(-t ) - 3C₂ exp(-3t ) + (-2t ² + 3t + 1) exp(-t ) - 3
y' (0) = -C₁ - 3C₂ + 1 - 3 = 2
→ C₁ + 3C₂ = -4 … … … [4]
Solve equations [3] and [4] to get C₁ = 2 and C₂ = -2. Then the particular solution to the initial value problem is
y(t) = -2 exp(-3t ) + (2t ² + t + 2) exp(-t ) - 3t + 2
Solve the system of equations using the elimination method.
(8x +11y = 37
8x+y=7
Dawn purchased 6 quarts of motor oil for $14.12. What is the Unit Price per quart rounded to
the nearest cent?
Answer:
$2.35 per quart (rounded to nearest cent)
Step-by-step explanation:
6 quarts --- $14.12
1 quart --- [tex]\frac{1}{6}[/tex] × $14.12 = $2.35 (rounded to nearest cent)
Can some one help me plz
Answer:
4h
2d
Step-by-step explanation:
the sum of three consecutive multiples of 24 is 288 find these multiples
plzz solve these question now
click on the picture attached to get the answer
hope it helps!
..........
Help Me please
Veronica wants to check her work after evaluating 108 ÷(-6) what steps can she follow to verify her answer?
Divide her answer by -6 and see if the result is -108.
Divide her answer by -108 and see if the result is -6.
Multiply her answer by -6 and see if the result is -108.
Multiply her answer by -108 and see if the result is -6.
Answer:
Its C
Step-by-step explanation:
6) A climber is on a hike. After 2 hours she is at an altitude of 400 feet. After 6 hours, she is at an
altitude of 700 feet. What is her rate of change?
Answer:
Her rate of change is 75 ft/h
Step-by-step explanation:
Rate of Change
It measures how one quantity varies with respect to another. The second variable usually is the time.
The climber is hiking. We are given two points of her progress: At 2 hours, she is at 400 ft. This corresponds to the point (2,400).
At 6 hours, she is at 700 ft. This is the point (6,700)
The rate of change is the slope between these two points or the quotient of the variations of each variable:
[tex]\displaystyle m=\frac{700\ ft-400\ ft}{6\ h-2\ h}[/tex]
[tex]\displaystyle m=\frac{300\ ft}{4\ h}[/tex]
[tex]m=75\ ft/h[/tex]
Her rate of change is 75 ft/h
7 1/2÷3/4 Please help this mom out!!
Answer:
10
Step-by-step explanation:
give me brainly
am i correct? let me know
I need the answer to this test question. We were assigned to correct our test for homework. I cannot think of another solution to this problem, please help.
Answer:
angle 1 = 70 degree and angle 2=95 degree
Step-by-step explanation:
for the first angle
180 -70 = 110
and 180-110 = 70 ( opposite angles )
for the second angle
180-85 =95
and again 180-95 =85(opposite angles)
180-85=95 (the straight line property)
Answer ASAP will give brainliest, thanks.
Answer:
B
Step-by-step explanation:
4x+2y=6
6x-4y=-12
2y=6-4x
y=3-2x
6x-4(3-2x)=-12
6x-12+8x=-12
2x-12=-12
2x=0
x=0
4(0)+2y=6
2y=6
y=3
(0,3)
Carle is cutting pieces of string that are exactly inches long. How many pieces can she cut from a ball of string that has 100 feet?
Answer:
Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet? 1 foot= 12 inches. A) 49 pieces.Oct 14, 2016
Step-by-step explanation:
One batch of cookies requires the following ingredients:
2 1/3 cups of flour
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 1/2cups of brown sugar
3/8of a cup of white sugar
1/2 of a teaspoon of salt
Eric wishes to triple the recipe.
How much of each ingredient should he use? Select all that apply.
A) 9/12 cup of chocolate chips
B) 6/5 cups of chopped almonds
C) 1/6 of a teaspoon of salt
D) 1 1/8 cups of white sugar
E) 6 1/3 cups of flour
F) 2 1/2 cups of brown sugar
Help me please I’m dying
Answer:
[tex]\boxed{x = 2+2\sqrt{6} ~~or~~x = 2 - 2 \sqrt{6} }[/tex]
.
Step-by-step explanation:
To find x, use pythagoras form
[tex]c^2 = a^2 + b^2[/tex]
[tex](x + 4)^2 = x^2 + (x + 1)^2[/tex]
[tex]x^2 + 8x + 16 = x^2 + x^2 + 2x + 1[/tex]
[tex]2x^2 + 2x + 1 - x^2 - 8x - 16 = 0[/tex]
[tex]x^2 - 6x - 15 = 0[/tex]
[tex]x^2 - 6x = 15[/tex]
[tex](x - 3)^2 - 9 = 15[/tex]
[tex](x - 3)^2 = 15 + 9[/tex]
[tex](x - 3)^2 = 24[/tex]
[tex]x - 2 = \pm \sqrt{24}[/tex]
[tex]x = 2 \pm 2\sqrt{6}[/tex]
.
[tex]x_1 = 2 + 2\sqrt{6}[/tex]
[tex]x_2 = 2 - 2\sqrt{6}[/tex]
.
Happy to help :)
Wrote a linear function f with the values f(-4)=0 and f(4)=2
Answer:
y = (1/4)x + 1
Step-by-step explanation:
The points mentioned are (-4,0) and (4,2).
We can find the slope m:
(2-0)/(4-(-4)) = 2/8 = 1/4
We now have the equation y = (1/4)x + b
Now we must find the y-intercept.
Plugging in the first point:
0 = (1/4)*(-4) + b
0 = -1 + b
1 = b
y = (1/4)x + 1
Find the area of the trapezoid below by decomposing the shape into
rectangles and triangles.
6
5
8
3
Answer:
72 square units
Step-by-step explanation:
The area of the rectangle in the middle: 6x8 = 48 square units
The area of the triangle on the left: (5x6)/2 = 30/2 = 15 square units
The area of the triangle on the right: (3x6)/2 = 18/2 =9
(The 6 for the height of the triangle on the right is from the left side of the rectangle in the middle, they have to be the same length)
48+15+9 = 72 square units
URGENT !!
A popular television show recently released a video
preview for the upcoming season on íts website As
fans of the show discover the video, the number of
views of the preview video has grown each day
during the last 2 vweeks. The number of days since
the release of the video and the natural log of the
number of video views ís shown in the scatterplot.
Answer:C
Step-by-step explanation:
You increase your walking speed from 1 m/s to 3 m/s in a period of 1 s.
What is your acceleration?
Answer:
2 m/s
Step-by-step explanation:
Answer:
2m/s²
Step-by-step explanation:
acceleration= v-u/t
=3-1/1
=2m/s²
Find the measurement of
an interior angle of a regular
decagon (10-sided figure).
Answer:
144°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Sum of Angles: 180(n - 2)Step-by-step explanation:
Step 1: Define
Number of sides n = 10
Step 2: Find
Substitute: 180(10 - 2)Subtract: 180(8)Multiply: 1440°Step 3: Find 1 angle
We have 10 sides.
Divide: 1440/10 = 144A string is 5.8 meters long. What is it's length in centimeters
Answer:
a
Step-by-step explanation:
because I said it was jejwjwjeiejehxueh ed uejrhcu
Answer:
580
Step-by-step explanation:
If 100 centimeters are in a meter, then we have to multiply 5.8 by 100 to find out the length of the string in centimeters.
(hope this helped)
Graph the line that passes through the point (0,-7) and (-3,-9) and determine the equation of the line
Answer:
The equation is y=2/3x-7
Step-by-step explanation:
-9-(-7) /-3-0
-2/-3
that's your answer
triangle ABC has veritices A(-2,3), B(0,3), and C (-1,-1). Find the coordinates of the image after a reflection over the x-axis.
Answer:
A' = (-2, -3)
B' = (0, -3)
C' = (-1, 1)
I did this on edg
Step-by-step explanation:
Since it's a reflection over the x axis, the x coordinates will stay the same while the y coordinates will be opposite of what they are.
After reflected: A'(-2,-3), B'(0,-3), C'(-1,1)
18 ≤ -2x = what?? please answer im in class
Answer:
-9
Step-by-step explanation:
Find the volume of the region between the cylinder z=3y^2 and the xy-plane that is bounded by the planes x=0,x=1 ,y=-1 and . z = y2 x = 0 x = 1 y = − 1 y =1
Answer:
The volume of the region V = 2
Step-by-step explanation:
Given that:
[tex]z_1 = 3y^2[/tex] ;
where initially;
[tex]z_o = 0; \ x_o = 0; \ x_1 = 1; \ y_o= -1; \ y_1 = 1[/tex]
The volume of the region is given by a triple which is expressed as:
[tex]V = \int_x \int_y \int_z \ dz \ dy \ dx[/tex]
[tex]V = \int \limits ^{x_1 = 1}_{x_o=0} \int \limits ^{y_1 = 1}_{y_o=-1} \int \limits ^{z_1 = 3y^2}_{z_o=0} \ dz \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \int \limits ^{3y^2}_{0} \ dz \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \Bigg [z \Bigg]^{3y^2}_{0} \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \Bigg [3y^2 \Bigg] \ dy \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \Bigg [\dfrac{3y^3}{3} \Bigg]^1_{-1} \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \Bigg [\dfrac{3(1)^3}{3}- \dfrac{3(-1)^3}{3} \Bigg] \ dx[/tex]
[tex]V = \int \limits ^{1}_{0} \Bigg [1-(-1)\Bigg] \ dx[/tex]
[tex]V =2 \Bigg [x \Bigg] ^1_0[/tex]
V = 2
Thus, the volume of the region is 2
Jared a beekeeper placed 120 hives in a apple orchard
Answer: 20
Step-by-step explanation:
can you help me please
Answer:
Please check the explanation.
Step-by-step explanation:
Given that
|v|=38
Ф = 120°
Finding the horizontal component
The horizontal component can be obtained using the formula
Vx = |v| cos Ф
= 38 cos 120°
= 38 (-0.5)
= -19
Thus, the horizontal component is:
Vx = -19
Finding the vertical component
The vertical component can be obtained using the formula
Vy = |v| sin Ф
= 38 sin 120°
= 38 (0.86)
= 32.68
Thus, the vertical component is:
Vy = -19
A vector 'v' with magnitude |v| and direction Ф can be written as:v = |v| cos Ф i + |v| sin Ф j
As
|v|=38
Ф = 120°
Thus, the vector is
v = 38 cos 120° i + 38 sin 120° j
or
v = -19 i + 32.68 j
winston earns $140.00 by selling 56 hotdogs at a concession stand at school. by using the same rate for the cost of one hotdog , how many more would Winston need to sell to earn $175.00?
can commas be used to separate the ones, tens and hundreds
Answer: no? because the comma goes after every three numbers.