3. Evaluate the expression 18
7+2 - 4
a. 2
b. 1.4
c. 6
d. 18

Answer:

answer below

Step-by-step explanation:

equation with a negative discriminant: negative number under the square root

1. will produce imaginary number "i"

2. the function will get two complex solutions

Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

The conclusion of the hypothesis testing is that; there is not enough evidence to support the claim that the mineral changes a person’s cholesterol level.

Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample.

Let us first define the hypothesis in this problem;

Null Hypothesis; H₀: μ_d = 0

Alternative Hypothesis; Hₐ: μ_d ≠ 0 (Claim)

The degree of freedom is;

DF = n - 1

DF = 6 - 1

DF = 5

At a significance level of α = 0.10, with a DF of 5, the critical values are ±2.015.

Using a computer software, we can calculate the mean from the attached table as;

D' = ∑d/n

D' = 100/6 = 16.7

Similarly, the standard deviation is calculated from the formula;

S_d = √(n∑d² - (∑d)²)/(n(n - 1))

s_d = √(6.489 - 100²)/(6(6 - 1))

s_d = 25.4

The test statistic is gotten from the formula;

t = (D' - μ_d)/(s_d/√n)

t = (16.7 - 0)/(25.4/√6)

t = 1.610

This is less than the critical value and we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mineral changes a person’s cholesterol level.

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Answer:

3/18

Step-by-step explanation:

Answer:

18:3

Step-by-step explanation:

acorns go first then squirrels cause the question says acorns TO squirrels

Answer:

6

Step-by-step explanation:

hope it helps

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

The median cost of a home in 2014 is $480

First, we need to know that the median of a given set of data is expressed as the middle number determined with the data set is arranged in an order from least to greatest or in an ascending order.

Also, note that the median is one of the measures of central tendency.

From the information given, we have that;

The median cost of a home in 2014 traced from the point year to the cost on the graph is;

$480

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Answer:

For the function y = √4-x, we know that the value inside the square root must be non-negative. Therefore, we have the inequality:

4 - x ≥ 0

Solving for x, we get:

x ≤ 4

So the domain of the function is all real numbers less than or equal to 4.

For the range, we know that the square root of any non-negative number is always non-negative. Therefore, the smallest value that y can take is 0, which occurs when x = 4. As x decreases, y increases without bound. So the range of the function is [0,∞).

Step-by-step explanation:

Answer:

10 ft

Step-by-step explanation:

Answer:

Cosine

Step-by-step explanation:

sine = soh=o/h

cos=cah=a/h

tangent=toa=o/a

If you look at right triangle the slanted line is the hypothese. it will always be. so thats h. the adjacent is the line connected the the angle you are looking for. and opposite is the line thats away from the angle.

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

<95141404393>

Answer:

\(P(p>0.43) = 0.0436\)

Step-by-step explanation:

Given

\(p = 40\%\) -- proportion of baseball players

\(n = 781\) --- selected sample

Required

Determine P(p>43%)

First, calculate the z score using:

\(Z = \frac{\^{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\)

This gives:

\(Z = \frac{48\%-40\%}{\sqrt{\frac{40\% *(1 - 40\%)}{781}}}\)

Convert % to decimal

\(Z = \frac{0.43-0.40}{\sqrt{\frac{0.40 *(1 - 0.40)}{781}}}\)

\(Z = \frac{0.43-0.40}{\sqrt{\frac{0.40 *0.60}{781}}}\)

\(Z = \frac{0.43-0.40}{\sqrt{\frac{0.24}{781}}}\)

\(Z = \frac{0.03}{\sqrt{0.00030729833}}\)

\(Z = \frac{0.03}{0.01752992669}\)

\(Z = 1.71\)

So:

\(P(p>0.43) = P(Z>1.71)\)

\(P(p>0.43) = 1 - P(Z<1.71)\)

\(P(p>0.43) = 1 - 0.9564\)

\(P(p>0.43) = 0.0436\)

Answer:

Angle T is congruent to Angle Z

Step-by-step explanation:

Since the 2 triangles are equal, that means that each pair of angles are also congruent. To know which angles are congruent, you check th order of how the triangles are named. Ex. Angle Q is congruent to Angle A, Angle P is congruent to Angle R, and Angle T is congruent to Angle Z.

Answer:

P = QL/200

Step-by-step explanation:

A) A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.

B) frequency of the pitch that is 73 notes up the keyboard is 1760 cycles per second.

A. To find how many notes up the piano keyboard the pitch with a frequency of 440 cycles per second is, solve the formula

n = 1 + 12 × log₂(f/27.5) for n,

where f = frequency of the pitch to find and n = number of notes up the keyboard.

Substituting f = 440:

n = 1 + 12 × log_2(440/27.5)

n = 1 + 12 × log_2(16)

n = 1 + 12 × 4

n = 49

Therefore, the A above middle C with a frequency of 440 cycles per second is 49 notes up the piano keyboard.

B. Using the same formula, n = 1 + 12 × log₂(f/27.5), to find the frequency of the pitch that is 73 notes up the keyboard. Solving for f:

73 = 1 + 12 × log₂(f/27.5)

72 = 12 × log₂(f/27.5)

6 = log₂(f/27.5)

2⁶ = f/27.5

f = 27.5 x 2⁶

Therefore, the frequency of the pitch that is 73 notes up the keyboard is:

f = 27.5 x 2⁶ = 1760 cycles per second.

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Hence Proved N to N is uncountable set by using a diagonalization argument

What is Diagonalization Argument?

Georg Cantor published the Cantor's diagonal argument in 1891 as a mathematical demonstration that there are infinite sets that cannot be put into one-to-one correspondence with the infinite set of natural numbers. It is also known as the diagonalization argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof.

Proof:

We write f as the sequence of value it generates

that is, say f:N-N is defined as f(x) =x then

we write f as : 1,2,3,4........

similarly if f:N-N were f(x) = 2x then we write it as :2,4,6,8.......

now assume on the contrary that the set of functions from N to N is countable

then,

\(f_{1}\)   :     \(f_{11}\)        \(f_{12}\)       \(f_{13}\) , ...........

\(f_{2}\)   :     \(f_{21}\)        \(f_{22}\)       \(f_{23}\) , ...........

\(f_{3}\)   :     \(f_{31}\)        \(f_{32}\)       \(f_{33}\) , ........... and so on

Here \(f_{ij}\) =\(f_{i}(j)\)

consider the function f as :

f : (\({f11}\) +1 ) , (\({f22}\) +1) , (\({f33}\) +1),.........

Then f wouldn't appear in the list of the function we had above since any \(f_{i}\) would disagree with f at the i th place

Therefore the set of the function from N to N is an uncountable set

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Answer:

50%

Step-by-step explanation:

20 is half of 40 so it would be 50%

Answer:

Option A 8 units left and 6 units up

Step-by-step explanation:

3×10-(16/2)

30-8

the answer is 22

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

We take ~p∧~q∨r to mean (~p∧~q)∨r because "and" normally has precedence over "or." The (~p∧~q) term will only come into play when both p and q are false. It will only affect the outcome if r is also false. This condition is the last line of the table.

Answer:

39  shelves needed to build

Step-by-step explanation:

To find the number of shelves needed we need to divide the number of mystery books by 34

We know that. Each shelf can hold 34.

It is given that, There are 1,326 mystery books

So, 1,326/34

39  shelves needed to build

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The graph is of all the points such that y is 1/4 of x. So, for x=4, y=1, for example. Similarly, for x=-4, y=-1.

These, (4, 1) and (-4, -1), are two points on the graph, which is a straight line through those points and through the origin. The graph extends to infinity to the lower left and the upper right. A portion is shown below.

The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

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1. Find the area of the backyard:

2. Find the area of the patio:

3. Find the area of the shaded region:

4. Find the probability that the leaf falls in the shaded region known that the total area (100%) is 2375 suqare feet:

Step-by-step explanation:

\( \frac{1}{4} \boxed{?} \frac{3}{8} \\ \\ \frac{1}{4} = \frac{2}{8} \\ \\ \because \: 2 < 3 \\ \therefore \: \frac{1}{4} \boxed{ < } \frac{3}{8} \)

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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