Use the method of Laplace Transforms to solve the following
IVP.
x'+y'=x-y; x(0)=1
x'-y'=x-y; y(0)=0

Using the predicate symbols shown and appropriate quantifiers,
write each English language statement as a predicate wff. (The
domain is the whole world.)
B(x) is “x is a ball.”
R(x) is “x is round.”
S(x) is “x is a soccer ball.”
1) some balls are round but soccer balls are not
2) if soccer balls are round, then all balls are round

Can you write a haiku poem about anything.

he mean age of graduate students at a University is thought to
be 31 years old.
A random sample of 15 graduate students is taken. The sample mean
age is 33 years and the sample standard deviation is three
years.
Does the sample data indicate that the population mean age is
actually greater than 31 years old? Use a 1% level of
significance.
a.) What is α? State the null and alternate
hypotheses. Will you use a left-tailed, right-tailed, or...

Question: Consider a rhombus with equal sides
and point charges Q, Q, -Q, -Q in the four corner sketch the
electric field lines (this structure is called quadrupole)
Question: How many electrons should we transfer
from Earth to Sun in order to match the gravity force between the
two? Suppose we take those electrons from a cube shape piece of
Al, one electron per atom. What would be the size of the
cube?

a-Calculate conventional yield effort at 0.2% (0.002
in./in.)
b- Tensile strength.
c- The modulus of elasticity.
d- Elongation
e- The reduction in area.
f- The engineering effort to fracture
g- The real stress to fracture
h- The modulus of resilience
Copper alloy
Load (N)
Calibrated length (mm)
0
40.00000
25000
20.01850
50000
40.037
75000
40.0555
90000
40.2000
105000
40.6
120000
41.56
131000
44
125000
47.52
- Initial diameter of the test tube: 20mm
- Initial calibrated length: 40mm
- Calibrated...

The solubility-product constant for Zn(OH)2 is
Ksp=3.00×10−16.
The formation constant for the hydroxo complex, Zn(OH)42−, is
Kf=4.60×1017.
When Zn(OH)2(s) was added to 1.00 L of a basic solution,
1.10×10−2 mol of the solid dissolved. What is the concentration of
OH− in the final solution?

Imagine 2 identical capacitors with C = 1F having a charge Q = 1
C. Suppose you connect their terminals, positive to positive,
negative to negative. Now you have an effective capacitance 2C
carrying a charge 2Q, right? Work out the total energy of the two
capacitors before and after the connection and speculate on the
meaning of your result.

HW6#30
Use a normal approximation to find the probability of the
indicated number of voters. In this case, assume that 125 eligible
voters aged 18-24 are randomly selected. Suppose a previous study
showed that among eligible voters aged 18-24, 22% of them voted.
Probability that fewer than 32 voted.
The probability that fewer than 32 of 125 eligible voters voted
is ____?

f(x)= 4x-2+3
Include on the graph the key point (as an ordered pair),
the equation of the Horizontal Asymptote, and the y-intercept (as
an ordered pair). Show Work (algebraic) for the key point or
indicate the transformation (shifts).

a) Complete the table below by classifying the
cost items. You need to repeat an amount if it belongs to more than
one category. You must provide a total for each column.
b) Coffee-Culture Ltd manufactures barista
quality coffee machines. The unit selling price is $900 and the
variable cost per unit is $630. The monthly fixed cost for August
2020 is $27,000. Answer the questions below in the spaces provided.
(Show the formula and workings for each)
Required: Answer...

a tension test was performed on a steel specimen having an
original diameter of 0.503in. and gauge length of 2.00in. using the
data listed in the table, plot the stress-strain diagram and
determine approximately the modulus elasticity
load(kip
elongation(in)
load(kip
elongation
0
0
13.0
0.0400
2.5
0.009
14.0
0.1400
6.50
0.0025
14.5
0.2500
8.00
0.0040
13.5
0.3500
9.2
0.0075
13.0
0.5700
9.80
0.0098

(x+1)y'=y-1 2) dx+(x/y+(e)?)dy=0 3)ty'+2y=sint 4) y"-4y=-3x²e3x
5) y"-y-2y=1/sinx 6)2x2y"+xy'-2y=0 ea)y=x' b) x=0
2dx/dt-2dy/dt-3x=t; 2

1.If 1.80 ? 1020 electrons move through a pocket
calculator during a full day's operation, how many coulombs of
charge moved through it?
C
2.A 53.0 g ball of copper has a net charge of 2.3

What is the effects of drugs in the nervous system and
behavior

a simply supported beam having a span length equivalent to
2008(mm). the beam is carrying uniform distributed load having
intensity of 08(N/mm) that span from the origin to two third of the
entire span, together with concentrated load of 50N at the mid=span
of the beam.
the beam cross-section details are;
-beam type = inverted tee flange beam
- flange lenght = 008mm
flange thickness= 20mm
web height = 171mm
web thickness= 20mm
Answer the following question
a) sketch the...

Decide whether the normal sampling distribution can be used. If
it can be used, test the claim about the difference between two
population proportions p 1 and p 2 at the given level of
significance alpha using the given sample statistics. Assume the
sample statistics are from independent random samples. Claim: p
1equalsp 2, alphaequals0.10 Sample statistics: x 1equals88, n
1equals171 and x 2equals172, n 2equals212

Please explained using formal proofs in predicate logic
In each part below, give a formal proof that the sentence given
is valid or else provided an interpretation in which the sentence
is false.
(a) ∀xP' (x) → ∃x[P(x) → Q' (x)].
(b) ∃x[P(x) → Q' (x)] → QxP' (x).

Participation in the local soccer league is 10% higher
this year than it was last year. Also, from last year to this year,
the number of males increased by 5% and the number of females
increased by 20%. There were 20 males participating in the league
last year. What fraction of the league’s participants is female
this year? Express your answer as a common fraction.

Use a chi-squared-test to test the claim sigma less than 38 at
the alpha equals 0.05 significance level using sample statistics
s=35.4 and n=17. Assume the population is normally distributed.

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