Discuss the validity of the following statement. If the statement is always​ true, explain why. If​ not, give a counterexample. If the odds for E equal the odds against​ E', then ​P(E)P(F)=P(E∩F)

Answer:

Total interest = $3.41

Step-by-step explanation:

Since she can pay $72 each month we can divide the payments on monthly basis till all the money is paid.

The annual interest rate is 24.7%, so the monthly rate will be 24.7 ÷ 12= 2.058%

For the first month

With payment of $72 the remaining amount will be 189.56 - 72 = $117.56

Interest paid will be 0.02058 * 117.56 = $2.42

Total amount owed now will be 117.56 + 2.42 = $119.98

For the second month another payment of $72 is made

The remaining will be 119.98 - 72 = $47.98

Interest charged will be 0.02058 * 47.98 = $0.99

The amount owed will be 47.98 + 0.99 = $48.97

In the third month she will pay the remaining $47.98 which is within her monthly limit

Total interest paid = Sum of Amount paid each month - Initial amount spent

Total interest = {(72 * 2) +48.97} - 189.56 = $3.41

Answer: Amount in 5 years( if compounded quarterly) = $11,768.40

Amount in 5 years( if compounded monthly = $11782.54

Step-by-step explanation:

Formula for accumulated amount in t years at annual rate of r% compounded quarterly: [tex]A=P(1+\dfrac{r}{4})^{4t}[/tex]

Formula for accumulated amount in t years at annual rate of r% compounded monthly: [tex]A=P(1+\dfrac{r}{12})^{12t}[/tex], where P= principal amount.

Given: P= $9000, r= 5.4%= 0.054, t= 5 years

Amount in 5 years if compounded quarterly =[tex]9000(1+\dfrac{0.054}{4})^{4\times5}[/tex]

[tex]=9000(1.0135)^{20}\\\\=9000(1.30760044763)\approx11768.40[/tex]

i.e. Amount in 5 years( if compounded quarterly) = $11,768.40

Amount in 5 years if compounded monthly =[tex]9000(1+\dfrac{0.054}{12})^{12\times5}[/tex]

[tex]=9000(1.0045)^{60}\\\\=9000(1.309171267)\approx11782.54[/tex]

i.e.  Amount in 5 years( if compounded monthly = $11782.54

Answer:

  [tex]\displaystyle A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta[/tex]

Step-by-step explanation:

The shaded area is the area of the curve bounded by θ = π and θ = 7π/6.* A differential of area in polar coordinates is ...

  dA = (1/2)r^2·dθ

So, the shaded area is ...

   [tex]\displaystyle\boxed{A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta}[/tex]

_____

* We found these bounds by trial and error using a graphing calculator to plot portions of the curve.

Answer:

10,000

Step-by-step explanation:

The answer is 10*10*10*10 = 10,000

When the power is positive and in the numerator, the number of places moved or zeros added = the power. This has a power of 4. You add 4 zeros to 1 to get the answer.

Answer:

[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]

Step-by-step explanation:

Given that:

[tex]f(t) = 12 cos (t- \dfrac{\pi}{6})[/tex]

recall that:

cos (A-B) = cos AcosB + sin A sin B

∴

[tex]f(t) = 12 [cos\ t \ cos \dfrac{\pi}{6}+ sin \ t \ sin \dfrac{\pi}{6}][/tex]

[tex]f(t) = 12 [cos \ t \ \dfrac{3}{2}+ sin \ t \ sin \dfrac{1}{2}][/tex]

[tex]f(t) = 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t)[/tex]

[tex]L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ][/tex]

[tex]L(f(t)) = 6 \sqrt{3} \ L [cos \ (t) ] + 6\ L [ sin \ (t) ][/tex]

[tex]L(f(t)) = 6 \sqrt{3} \dfrac{S}{S^2 + 1^2}+ 6 \dfrac{1}{S^2 +1^2}[/tex]

[tex]L(f(t)) = \dfrac{6 \sqrt{3} +6 }{S^2+1}[/tex]

[tex]L(f(t)) = \dfrac{6( \sqrt{3} \ S +1 }{S^2+1}[/tex]

[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]

Answer:

$225.54 (hope it help)

Step-by-step explanation:

for 2nd week

$150 for the first week and a raise of 6% each week

which means 150+6%

6% of 150 is 9 (150x0.06)

150+9=159

and it repeats

for 3rd week

6% of 159 is 9.54 (159x0.06)

159+9.54=168.54

for 4th week

6% of 168.54 is 10.1124 (168.54x0.06)

168.54+10.1124=178.652

for 5th week

6% of 178.652 is 10.71912 (178.652x0.06)

178.652+10.71912=189.37112

an easier to do it is to just do 178.652 + 6% on your calculater

and I'll skip all the way to the 8th since you know the formula

212.777390432+6%=225.544033858

225.544033858≈225.54

Hello!

Answer:

[tex]\huge\boxed{\frac{12}{20}}[/tex]

To find the numerator and denominator, we can set up a proportion where:

x = denominator

x -8 = numerator

[tex]\frac{3}{5} = \frac{x-8}{x}[/tex]

Cross multiply:

[tex]3(x) = 5(x - 8)[/tex]

[tex]3x = 5x - 40[/tex]

Simplify:

[tex]3x - 5x = -40\\\\-2x = -40\\\\x = 20[/tex]

Substitute in this value of x to find the numerator and denominator:

[tex]\frac{(20) - 8}{(20)} = \frac{12}{20}[/tex]

Hope this helped you! :)

[tex] \LARGE{ \boxed{ \rm{ \orange{ Solution:}}}}[/tex]

Let the numerator be x

It is given that,

Then,

⇛ Denominator- 8 = x

⇛ Denominator = x + 8

According to condition -2)

⇛ Fraction = 3/5

⇛ x/x + 8 = 3/5

Cross multiplying,

⇛ 3(x + 8) = 5x

⇛ 3x + 24 = 5x

⇛ 24 = 5x - 3x

⇛ 24 = 24

Flipping it out,

⇛ 2x = 24

⇛ x = 24/2 = 12

Then,

⇛ x + 8 = 12 + 8 = 20

[tex] \large{ \therefore{ \boxed{ \rm{ \pink{Then, \: the \: fraction = \dfrac{12}{20} }}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

Answer: 15m²-2m+1

Step-by-step explanation:

To simplify, you want to combine like terms.

15m²-2m+1

Answer:

[tex]\huge\boxed{15m^2-2m+1}[/tex]

Step-by-step explanation:

[tex]6m^2-5m-3+3m+4+9m^2\\\\\text{combine like terms}\\\\=(6m^2+9m^2)+(-5m+3m)+(-3+4)\\\\=(6+9)m^2+(-5+3)m+1\\\\=15m^2-2m+1[/tex]

Answer:

X is uniformly distributed.

Step-by-step explanation:

Uniform Distribution:

This is the type of distribution where all outcome of a certain event have equal likeliness of occurrence.

Example of Uniform Distribution is - tossing a coin. The probability of getting a head is the same as the probability of getting a tail. The have equal likeliness of occurrence.

Answer:

[tex]\large \boxed{\mathrm{-3w + 5(2w + 1)}}[/tex]

Step-by-step explanation:

-2w + 3 + 5w - 2

Combine like terms.

3w + 1

-3w + 5(2w + 1)

Expand brackets.

-3w + 10w + 5

Combine like terms.

7w + 5

Answer:

The answer is C.

-3w +5(2w +1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the equation of a polynomial is,

[tex]y=(x-a)^2(x-b)^1(x-c)^3[/tex]

Zeroes of this polynomial are x = a, b and c.

For the root x = a, multiplicity of the root 'a' is 2 [given as the power of (x - a)]

Similarly, multiplicity of the roots b and c are 1 and 3.

Effect of multiplicity on the graph,

If the multiplicity of a root is even then the graph will touch the x-axis and if it is odd, graph will cross the x-axis.

Therefore, graph will cross x -axis at x = b and c while it will touch the x-axis for x = a.

In this question,

The given polynomial is,

[tex]y=(x-1)^3(x-2)^1(x-4)^1(x-6)^4[/tex]

Degree of the polynomial = 3 + 1 + 1 + 4 = 9

The graph of the function will cross through the x-axis at x = 1, 2, 4 only, The graph will touch to the x-axis at 6 only.

At the zero of 2 , the graph of the function will CROSS the x-axis.

6, 10, 15

15,21,35

35, 55, 77

77, 91, 143

143, 187, 221

I can go on forever

There are different possibilities

Answer:

Yes

Step-by-step explanation:

Yes, and it’s a right triangle.

3²+4²=5²

9+16=25

25=25

Answer:

Yes

Step-by-step explanation:

In order to determine if a triple of values will form a triangle, we must apply the Triangle Inequality Theorem, which states that for a triangle with lengths a, b, and c:

a + b > c

a + c > b

b + c > a

Here, let's suppose that since the ratio of the sides is 3 : 4 : 5, then let the actual side lengths be 3x, 4x, and 5x, where x is simply a real value.

With loss of generality, set a = 3x, b = 4x, and c = 5x. Plug these into the Triangle Inequality to check:

a + b > c  ⇒  3x + 4x  >?  5x  ⇒  7x > 5x  ⇒  This is true

a + c > b  ⇒  3x + 5x  >?  4x  ⇒  8x > 4x  ⇒  This is also true

b + c > a  ⇒  4x + 5x  >?  3x  ⇒  9x > 3x  ⇒  This is true

Since all three conditions are satisfied, we know that a true triangle can be formed given that the ratio of their sides is 3 : 4 : 5.

~ an aesthetics lover

Step-by-step explanation:

f(x) = x² - 5x - 9

To solve both expressions first find f( -4) and f(5)

For f(- 4)

Substitute the value of x that's - 4 into the expression

That's

f(-4) = (-4)² - 5(-4) - 9

= 16 + 20 - 9

= 36 - 9

For f(-5)

Substitute 5 into f (x)

That's

f(5) = 5² - 5(5) - 9

= 25 - 25 - 9

Hope this helps you

Answer:

1. using hand sanitizer with at least 60% alcohol

2. the probability of contracting a disease is lower if you wash your hands than if you don't wash your hands. That is: P (disease if you wash your hands) < P (disease if you don't wash your hands).

Step-by-step explanation:

1. Noteworthy is the fact that alcohol based hand sanitizers provide good protections to germs, viruses as when one washes his hands with soap for 20 seconds. This was indicated in the video as an acceptable alternative to washing your hands for 20 seconds with respect to preventing illness.

2. Remember, probability implies an assumption of possiblity or likelihood of something happening. Thus, the video's message implies that when people wash their hands it reduces the likelihood (that is, the probability) of contracting diseases. One stands a lower chance of : P (disease if you wash your hands) < P (disease if you don't wash your hands).

[tex] \frac{5b^{5}c}{4c^4} \times \frac{8c}{b^4}[/tex]

[tex]\frac{40b^{5}c^2}{4b^{4}c^4}[/tex]

[tex]{10b^{5-4}c^{2-4}}[/tex]

[tex]10bc^-2[/tex]

[tex]\frac{10b}{c^2}[/tex]

Step-by-step explanation:

[tex] \frac{5 {b}^{5} c}{ 4{c}^{4} } \times \frac{8c}{ {b}^{4} } [/tex]

First reduce the expression with b⁴

b⁴ will cancel b^5 remaining with one b

That's

Next reduce 8 and 4 with their GCF which is 4

We have

Reduce the expression with c .

c will go into c⁴ remaining with c³

That's

Simplify the expression again with c

That's

Multiply the expression

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Given that:

[tex]T(x,y) = \dfrac{100}{1+x^2+y^2}[/tex]

This implies that the level curves of a function(f) of two variables relates with the curves with equation f(x,y) = c

here c is the constant.

[tex]c = \dfrac{100}{1+x^2+2y^2} \ \ \--- (1)[/tex]

By cross multiply

[tex]c({1+x^2+2y^2}) = 100[/tex]

[tex]1+x^2+2y^2 = \dfrac{100}{c}[/tex]

[tex]x^2+2y^2 = \dfrac{100}{c} - 1 \ \ -- (2)[/tex]

From (2); let assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.

Now,

[tex]\dfrac{(x)^2}{\dfrac{100}{c}-1 } + \dfrac{(y)^2}{\dfrac{50}{c}-\dfrac{1}{2} }=1[/tex]

This is the equation for the  family of the eclipses centred at (0,0) is :

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

[tex]a^2 = \dfrac{100}{c} -1 \ \ and \ \ b^2 = \dfrac{50}{c}- \dfrac{1}{2}[/tex]

Therefore; the level of the curves are all the eclipses with the major axis:

[tex]a = \sqrt{\dfrac{100 }{c}-1}[/tex]  and a minor axis [tex]b = \sqrt{\dfrac{50 }{c}-\dfrac{1}{2}}[/tex]  which satisfies the values for which 0< c < 100.

The sketch of the level curves can be see in the attached image below.

Answer:

32 one-dollar bills.

Step-by-step explanation:

Let x represent one-dollar bills and y represent two-dollar bills.

He has a total of 49 bills. Therefore:

[tex]x+y=49[/tex]

The total amount of money James has is 66. x is worth one dollar, while y is worth two dollars. Therefore:

[tex]1x+2y=66\\x+2y=66[/tex]

We have a system of equations. Solve by substitution:

[tex]x+2y=66\\x+y=49\\x=49-y\\(49-y)+2y=66\\y=17\\x=49-17=32[/tex]

Therefore, James has 32 one-dollar bills and 17 two-dollar bills.

Checking:

[tex]32(1)+17(2)\stackrel{?}{=}66\\32(1)+17(2)\stackrel{\checkmark}{=}66\\\\32+17\stackrel{?}{=}49\\49\stackrel{\checkmark}{=}49[/tex]

Step-by-step explanation:

42 is your answer according to bodmas

Answer:

The correct answer is:

Stratified (c.)

Step-by-step explanation:

Stratified sampling technique is one in which the groups of data are divided into smaller groups or strata, based on shared common characteristics in these groups, and the samples randomly selected from each group in a proportional way. In this example, the sub-groups used is "times of the day" ie. morning, afternoon or evening. Other strata that can be used are; age, gender, continents etc. Stratification is done when the researcher wants to understand the relationships between the two or more groups. Stratified random sampling is also known as proportional random sampling or quota random sampling.

Answer:

Rational

Step-by-step explanation:

Rational number consists of

-5/6 is a Fraction and we can also simply it to a Decimal.

Hope this helps ;) ❤❤❤

Answer:

b. The students find a p-value less than 0.05

c. Carrie ends up losing the election.

e. The students make the conclusion that Carrie does not have more than 50% of the vote.

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.

Type I error is one in which we reject a true null hypothesis.

In the given scenario Type I error will be the one where students incorrectly estimates the p value and reject the null hypothesis when it was true. This error will result in losing the elections.

[tex]\dfrac{f(x)}{g(x)}=\dfrac{8x^3+16x^2-15}{2x+1}[/tex]

Answer:

it doesnt add up. the question doesnt make sense.

Step-by-step explanation:

Answer:

157

Step-by-step explanation:

To find the average score, add all individual scores and divide the sum by the number of individual scores.

She has 5 individual scores. Let's say her scores are A, B, C, D, and E.

average score = (A + B + C + D + E)/5

Now we plug in the average and the 4 known scores for A through D, and we solve for E.

average score = (A + B + C + D + E)/5

136.8 = (135 + 144 + 116 + 132 + E)/5

E = 157

Answer: 157

Answer:

we could work this out by geometric sequence

Step-by-step explanation:

G1=2, G2=4, we have a formula,Gn=G1r^n-1

G2=G1 (r)^1, 4=2r, r=2

G30=G1 (2)^29=1,073,741,824 bacterium

Answer:

Step-by-step explanation:

Given that:

[tex]x = 5 + In (t)[/tex]

[tex]y = t^2+2[/tex]

At point (5,3)

To find an equation of the tangent to the curve at the given point,

By without eliminating the parameter

[tex]\dfrac{dx}{dt}= \dfrac{1}{t}[/tex]

[tex]\dfrac{dy}{dt}= 2t[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ \dfrac{dy}{dt} }{\dfrac{dx}{dt} }[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ 2t }{\dfrac{1}{t} }[/tex]

[tex]\dfrac{dy}{dx}= 2t^2[/tex]

[tex]\dfrac{dy}{dx}_{ (5,3)}= 2t^2_{ (5,3)}[/tex]

t²  + 5 = 4

t² = 4 - 5

t² = - 1

Then;

[tex]\dfrac{dy}{dx}_{ (5,3)}= -2[/tex]

The equation of the tangent  is:

[tex]y -y_1 = m(x-x_1)[/tex]

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

By eliminating the parameter

x = 5 + In(t)

In(t)  = 5 - x

[tex]t =e^{x-5}[/tex]

[tex]y = (e^{x-5})^2+5[/tex][tex]y = (e^{2x-10})+5[/tex]

[tex]\dfrac{dy}{dx} = 2e^{2x-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2e^{10-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2[/tex]

The equation of the tangent  is:

[tex]y -y_1 = m(x-x_1)[/tex]

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

Answer:

-9

Step-by-step explanation:

4 + (-13)

=> 4 - 13

=> -9

Answer:

YES

Step-by-step explanation:

1 million minutes = 1.9 years

An average man can live upto 78 years.

So, an average man can easily live upto 1,000,000.

Answer:

There will be (365 x 24 x 60) minutes each year.

and that is 525600.

and 525600 x 78 is 40,996,800.

so, It is definitely more than 1 million minutes.

Hop it helps!

Bye!