Wanda is working on her predictions for the next few days. She calculates that there is a 20% chance of rain on Monday and a 20% chance onf rain on Tuesday. If she is correct, what is the probability that it will rain on at least one of these days?

Answer:

Check the proof below

Step-by-step explanation:

try to verify from RHS to LHS

(Tan a + tan b) / (tan a - tan b)

= (sin a / cos a + sin b /cos b) / ( sin a/ cos a - sin b/ cos b)

= (sin a cos b + cos a sin b)/ (sin a cos b - cos a sin b)

= sin (a+b) / sin (a-b)

Fyi

sin(A+B) = sinAcosB+cosAsinB

sin(A-B) = sinAcosB-cosAsinB

Answer:

Brooklyn's method results in more money after 2 years

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]

where:

Patrick's Method

Given:

Substituting the given values into the formula and solving for A:

[tex]\implies \sf A=300\left(1+\dfrac{0.03}{4}\right)^{4 \times 2}[/tex]

[tex]\implies \sf A=300\left(1.0075\right)^{8}[/tex]

[tex]\implies \sf A=318.4796543...[/tex]

Therefore, using Patrick's method, there would be $318.48 in the account after 2 years.

Brooklyn's Method

Given:

Substituting the given values into the formula and solving for A:

[tex]\implies \sf A=300\left(1+\dfrac{0.05}{12}\right)^{12 \times 2}[/tex]

[tex]\implies \sf A=331.4824007...[/tex]

Therefore, using Brooklyn's method, there would be $331.48 in the account after 2 years.

As $331.48 > $318.48 then Brooklyn's method results in more money after 2 years.

Answer:

3. B

Step-by-step explanation:

Hi!!

Answer:

I'm not 100% sure, but I think it's 3.1.

Step-by-step explanation:

I took your volume, which is 125[tex]\pi[/tex], then a formula, which is

V=[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex], then I just plugged in the 125 and I got 3.1. I'm so sorry if it's wrong! <3

Answer:

(-4,3)

Step-by-step explanation:

the coordinate (4,-3) is just at the 4th quadrant in which the value of x is positive and the value of y is negative

the quadrant (4,3) is on the first quadrant and the value expressed with the letter A

the coordinate (-4,-3) is a coordinate on the quadrant in which both values are negative

Answer:

199.5

Step-by-step explanation:

Answer:

  x = -2

Step-by-step explanation:

The function is decreasing where the first derivative is negative.

That is, the function is decreasing on the interval (-2, 5), except at x=2, where there is a flat spot. That means the maximum value is found at the left end of that interval, at x=-2.

__

The maximum value might be found at x = 6, at the right end of the interval (5, 6) on which the function is increasing. However, we judge the area under the first derivative curve between x=5 and x=6 to be less than the total area under the curve between x=-2 and x=5. That means the function does not increase enough from its minimum at x=5 to make up for the decrease over the longer interval.

__

The attachment shows an approximation of the derivative function given in the problem statement (dashed line) and its integral (solid line). Not all of the curvature of f'(x) is accounted for in the approximation, but the overall result is consistent with the above analysis.

Answer:

10ad+8ac

Step-by-step explanation:

I know trust me.

Answer:

The required number of cups of frozen mango is 1.125.

Step-by-step explanation:  Given that a smoothie recipe calls for cups of frozen mango and the recipe serves two.

We are to find the number of cups of frozen mango that is needed to serve one.

We will be using the UNITARY method to solve the problem.

We have

The number of cups of frozen mango that needs to serve two is

Therefore, the number of frozen mango that needs to serve one is given by

Thus, the required number of cups of frozen mango is 1.125.

Step-by-step explanation:

Answer:

Step-by-step explanation:

General equation for a circle (x - a)² + (y - b)² = r² with (a,b) represents the center, (x,y) represents one of the points lie on the circle, and r represents the radius Determine r² by substituting the points into the general equation (x - a)² + (y - b)² = r² (5 - (-1))² + (-4 - 2)² = r² (5 + 1)² + (-6)² = r² 6² + 36 = r² 36 + 36 = r² 72 = r² Determine the equation of the circle (x - a)² + (y - b)² = r² (x - (-1))² + (y - 2)² = 72 (x + 1)² + (y - 2)² = 72 (This is the equation of the circle)

Answer:

in my wisdom i think x=60 and y=60

Answer:

4th option, (cy+b)/a

Step-by-step explanation:

By algebraic manipulation, we add b to both sides, then divide by a to isolate x.

Answer:

2.5777

Step-by-step explanation:

Answer: 2.5777

Step-by-step explanation:

Given:

2.577681

Find the fourth decimal place:

2.577681

Round:

2.5777

Rounding:

Is the place to the right greater than or less than 5?

If greater than or equal to, round up. If less than, it stays the same.

    In this case, 8 > 5

Answer:

A. 1

Step-by-step explanation:

y-intercept of f(x)

y-intercept of g(x)

Distance

⇒ 3 - 2

⇒ A. 1

r= \frac{q^{2} }{p^{3}} +1

The tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

For a right angle triangle, the trigonometry ratios can be given as,

[tex]\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}[/tex]

Here, a is base side, b is perpendicular side and c is the hypotenuse side of the triangle.

In the given triangle, the length of base side is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.

[tex]a=8\\b=6\\c=10[/tex]

Thus, the  tangent, cosine and sine ratios of angles X & Y are,

[tex]\rm \sin \theta=\dfrac{6}{10}=\dfrac{3}{5}\\\rm \cos \theta=\dfrac{8}{10}=\dfrac{4}{5}\\\rm \tan \theta=\dfrac{6}{8}=\dfrac{3}{4}[/tex]

Thus, the tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.

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8.1. If x is the distance from P to the flagpole and h is the height of the flagpole, then

tan(53°) = h/x

tan(28°) = h/(x + 20)

Solve for the first equation for h in terms of x :

h = x tan(53°)

Substitute this into the second equation and solve for x :

tan(28°) = x tan(53°) / (x + 20)

(x + 20) tan(28°) = x tan(53°)

x tan(28°) + 20 tan(28°) = x tan(53°)

x (tan(28°) - tan(53°)) = -20 tan(28°)

x = 20 tan(28°) / (tan(53°) - tan(28°))

x ≈ 13.4 m

8.2. By the law of cosines,

BD² = 7² + 11² - 2 • 7 • 11 cos(110°)

⇒   BD = √(170 - 154 cos(110°))

⇒   BD ≈ 14.9 cm

and

BC² = BD² + 16² - 2 • BD • 16 cos(40°)

⇒   BC = √(426 - 154 cos(110°) - 32 cos(40°) √(170 - 154 cos(110°)))

⇒   BC ≈ 10.6 cm

Now use Heron's formula. If S is the semiperimeter of ∆ABD and S' is the semiperimeter of ∆BCD, i.e.

S = (AB + BD + AD)/2 ≈ 16.5 cm

S' = (BC + CD + BD)/2 ≈ 20.7 cm

then

area ∆ABD = √(S (S - AB) (S - BD) (S - AD)) ≈ 36.2 cm²

and

area ∆BCD = √(S' (S' - BC) (S' - CD) (S' - BD)) ≈ 76.7 cm²

so that the total area of ABCD is approximately 112.9 cm².

Answer:

150 Naira

Step-by-step explanation:

3 + 5 = 8

Since Ade receives in a 3 to 5 ratio, Ade receives 3/8 of the total.

3/8 × 400 = 150

Answer: 150 Naira

Answer:

B

Step-by-step explanation:

We shift the black graph about the x axis, to do that we divide y by -1,

We then shift over to the left 5 units, to do that's we add 5 to the x value.

So the answer here is B

Answer:

1234

Step-by-step explanation:

If 20% of his pin code was 246.8, we have to multiply 246.8 by 5 to get his pin code, which is 1234 (not safe btw.)

would really appreciate it if you hearted this answer

Answer:

(0, 0).

Step-by-step explanation:

The 2 points with y = 8 is a horizontal side  with (5, 8) 5 units  to the right and  the point (5, 0) lies vertically down from (5, 8) so the fourth  point is 5 to the left of (5, 0) which is (0, 0)

The standard deviation is a measure of a collection of values' variance or dispersion. The true mean bill for a customer at Burger Palace with 95% confidence is $13.38.

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Given that the Sample mean ([tex]\overline x[/tex]) is $14.30, the Sample size(n) is 24 customers, the Standard deviation(σ) is 2.30, while for a 95% confidence interval the Z-score is 1.960. Therefore, the true mean can be written as,

[tex]Z = \dfrac{\overline x- \mu}{\frac{\sigma}{\sqrt n}}\\\\\\1.960 = \dfrac{14.30-\mu}{\frac{2.30}{\sqrt{24}}}\\\\\\1.960 = \dfrac{14.3-\mu}{0.47}[/tex]

μ = 13.3788 ≈ 13.38

Hence,  the true mean bill for a customer at Burger Palace with 95% confidence is $13.38.

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Alex spend $1507.92 in total to buy this stock at 3% charges on each shares.

Shares represent equity ownership in a corporation or financial asset, owned by investors who exchange capital in return for these units.

Alex buys 30 shares of Walmart at the close price of $48.80.

His broker charges him 3% of each share.

Purchasing of 30 shares =48.80 *30

                                         =$1464

Now we have to find the 3% of total purchasing of shares.

So,

Broker's fees =[tex]\frac{3}{100}*1464[/tex]

                      = 0.03 * 1464

                      = 43.92

So, total cost of stock= 1464+43.92

                                   = 1507.92

Hence, Alex spend $1507.92 in total to buy this stock.

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Step-by-step explanation:

65° + 57° + x = 180° ( the sum of angle of triangle is 180° )

122° + x = 180°

x = 180° - 122°

x = 58°

hence the answer is 58°....

Answer:

58 degrees

Step-by-step explanation:

Sum of angles in a triangle is 180 degrees

180 = 65 + 57 + x

180 = 122 +x

x =180 -122

x = 58

The expected value of the assumed probability density function is 3/4 and the variance is 3/80

The probability density function is not properly stated.

So, I will provide a general explanation on how to determine E(x) and V(x) of a probability density function

Assume that the probability density function is given as:

[tex]f(x)= \left[\begin{array}{ccc}3x^2 &0 \le x \le 1\\0&Otherwise\end{array}\right[/tex]

The expression E(x) is calculated using:

[tex]E(x) = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]

So, we have:

[tex]E(x) = \int\limits^1_0 {x \cdot 3x^2 \ d(x)[/tex]

Evaluate the product

[tex]E(x) = \int\limits^1_0 { 3x^3 \ d(x)[/tex]

Integrate

[tex]E(x) = \frac34x^4 |\limits^1_0[/tex]

Expand

[tex]E(x) = \frac34(1-0)^4[/tex]

Evaluate

[tex]E(x) = \frac34[/tex]

The variance is then calculated using:

[tex]Var(x) = E(x^2) - (E(x))^2[/tex]

Calculate [tex]E(x^2)[/tex] using:

[tex]E(x^2) = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]

This gives

[tex]E(x^2) = \int\limits^1_0 {x^2 \cdot 3x^2} \, dx[/tex]

Expand

[tex]E(x^2) = \int\limits^1_0 {3x^4} \, dx[/tex]

Integrate

[tex]E(x^2) = \frac{3}{5}x^5|\limits^1_0[/tex]

Expand

[tex]E(x^2) = \frac{3}{5}(1 - 0)^5[/tex]

Evaluate

[tex]E(x^2) = \frac{3}{5}[/tex]

Substitute [tex]E(x^2) = \frac{3}{5}[/tex] and [tex]E(x) = \frac34[/tex] in [tex]Var(x) = E(x^2) - (E(x))^2[/tex]

[tex]Var(x) = \frac 35 - (\frac{3}{4})^2[/tex]

Evaluate the exponent

[tex]Var(x) = \frac 35 - \frac{9}{16}[/tex]

Evaluate the difference

[tex]Var(x) = \frac{3}{80}[/tex]

Hence, the variance of the probability density function is 3/80

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Answer:

B. 3.114 > 3.112

D. 0.541 > 0.145

E. 0.141 < 0.19

Step-by-step explanation:

In order to determine which decimal is greater or less than another, compare the place values from left to right. First, compare the whole numbers to the left of the decimal point. If they are not the same, the smaller decimal number is the one with the smaller whole number. This applies to the rest of the places.

----------------------------------------------------

32.3 has a greater tenths value than 32.03, so 32.03 < 32.3. Option A is false.

----------------------------------------------------

3.114 has a greater thousandths value than 3.112, so 3.114 > 3.112. Option B is true.

----------------------------------------------------

4.003 has a greater whole number than 3.996, so 4.003 > 3.996. Option C is false.

----------------------------------------------------

0.541 has a greater tenths value than 0.145, so 0.541 > 0.145. Option D is true.

----------------------------------------------------

0.19 has a greater hundredths value than 0.141, so 0.141 < 0.19. Option E is true.

hope this helps!

The inequalities which are truly compared are B, D and E.

Given certain inequalities.

We have to find the true comparisons.

We have to look at the corresponding digits of numbers which are compared from left to right. Greater numbers on the left will be the greater number.

A. 32. 03 > 32. 3

This is false since 32.3 is greater. In 32.03, 0 is in the tenth place, while 3 is in the tenth place for 32.3.

B. 3. 114 > 3. 112

This is true since in the thousandths place, 4 is greater than 2.

C. 4. 003 < 3. 996

This is clearly false, since in the whole part, 4 is greater than 3.

D. 0. 541 > 0. 145

This is true, since in the tenths place, 5 is greater than 1.

E. 0. 141 < 0. 19

This is also true, since in the hundredths place, 9 is greater than 4.

Hence the true comparisons are B, D and E.

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Step-by-step explanation:

P = l.100/t.r = $821.25×100/12.42×1 = $6612.318

hope this helps you.

Answer:

6m + 10

Step-by-step explanation:

Distributive Property

Solving

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-4,7)\qquad B(5,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-4,7)=1(5,1)[/tex]

[tex](\stackrel{x}{-8}~~,~~ \stackrel{y}{14})=(\stackrel{x}{5}~~,~~ \stackrel{y}{1})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-8 +5}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{14 +1}}{1+2} \right)} \\\\\\ P=\left(\cfrac{-3}{3}~~,~~\cfrac{15}{3} \right)\implies P=(-1~~,~~5)[/tex]

now, the segment AB cut by P in a 1:2 ratio, makes 3 thirds, so the ratio AP/AB is

[tex]\cfrac{AP}{AB}\implies \cfrac{1}{1+2}\implies \cfrac{1}{3}[/tex]