Missing number in sequence need help. ALOT OF POINTS

Answer:

always true.

the expression will always be equal to +5 because -p+p is zero

at any given value to p, the value is constantly +5

Answer:

always true.

the expression will always be equal to +5 because -p+p is zero

at any given value to p, the value is constantly +5

Step-by-step explanation:

always true.

the expression will always be equal to +5 because -p+p is zero

at any given value to p, the value is constantly +5

The measure of the larger acute angle of the right triangle is 73.7°. This can be calculated using trigonometry and the Pythagorean theorem.

The larger acute angle of the triangle can be found using trigonometry. First, we can find the length of the other leg using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs. Plugging in the values we get: 4² + b² = 12², solving for b we get b = √(12² - 4²) = 8√3. Now we can use inverse tangent to find the larger acute angle: tan⁻¹(opposite/adjacent) = tan¹⁽⁸√³/⁴⁾ ≈ 73.7°. So, the measure of the larger acute angle is 73.7°.

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Answer:

factors

Step-by-step explanation:

To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.

In this case, we have w as a function of r and θ, and we need to find dw/dε. We can do this by finding the partial derivatives of w with respect to r and θ, and then multiplying these by dr/dε and dθ/dε, respectively.

(dw/dr)(dr/dε) + (dw/dθ)(dθ/dε)

To find w, we can use the arctan function, which is defined as w = arctan(y/x). Substituting the given values of x and y, we get:

w = arctan(r*sin(e) / r*cos(0))

Simplifying this expression, we get:

w = arctan(tan(e)/cos(0))

Now, using the appropriate chain rule, we can differentiate w with respect to e and r separately:

dw/de = 1 / (1 + tan^2(e))

dw/dr = -tan(e) / (r*cos^2(0)*(1 + tan^2(e)))

To express w as a function of " and 9 before differentiating, we need to use the given equations to eliminate x and y. From the equation x = r*cos(0), we can solve for cos(0) to get:

cos(0) = x/r

Similarly, from the equation y = r*sin(e), we can solve for sin(e) to get:

sin(e) = y/r

Substituting these expressions into the equation for w, we get:

w = arctan(sin(e) / cos(0)) = arctan(y/x)

Now, we can differentiate w with respect to " and 9 using the chain rule:

dw/d" = (cos(0) / (x^2 + y^2)) = (r*cos(0) / (r^2*cos^2(0) + r^2*sin^2(e))) = (cos(0) / r)

dw/d9 = (cos(0) / (x^2 + y^2)) = (r*sin(e) / (r^2*cos^2(0) + r^2*sin^2(e))) = (sin(e) / r)

To convert w to a function of " and 9 before differentiating, we can use the following trigonometric identities:

sin(e) = r*sin(e)*cos(0) / (r*cos(0))

cos(0) = r*cos(0)*cos(9) - r*sin(e)*sin(9) / (r*cos(9))

Substituting these expressions into the equation for w, we get:

w = arctan(sin(e) / cos(0)) = arctan((r*sin(e)*cos(0)) / (r*cos(0)*cos(9) - r*sin(e)*sin(9)))

Now, we can differentiate w with respect to " and 9 using the chain rule:

dw/d" = (cos(0)*cos(9) + sin(e)*sin(9)) / (r*cos(0)*cos(9) - r*sin(e)*sin(9))^2

dw/d9 = (-cos(0)*sin(9) + sin(e)*cos(9)) / (r*cos(0)*cos(9) - r*sin(e)*sin(9))^2

We are given the functions x = r cos(θ) and y = r sin(θ). Our goal is to find the derivative of w with respect to another variable, say ε, using the Chain Rule.

First, we need to express w as a function of r and θ. Since w = arctan(y/x), we can write it as:

w = arctan(r sin(θ) / r cos(θ))

Now, let's differentiate w with respect to ε using the Chain Rule. The Chain Rule states that if we have a function composed of two or more other functions, the derivative of the composite function is the product of the derivatives of its constituent functions.

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The solution of the system of equation are,

x = 1/3 and y = 0

We have to given that;

System of equations are,

3x - 4y = 11

y + 3x = 1

From (ii);

y = 1 - 3x

Put above value in (i);

3x - 4 (1 - 3x) = 1

3x - 4 + 12x = 1

15x = 5

x = 1/3

From (i);

y + 3 (1/3) = 1

y + 1 = 1

y = 0

Thus, The solution of the system of equation are,

x = 1/3 and y = 0

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The solution to the system of equations is x = 1 and y = -2.

We have,

3x - 4y = 11

y + 3x = 1

To solve the system of equations:

3x - 4y = 11

y + 3x = 1

We can use the method of substitution or elimination.

Let's solve it using the elimination method.

Multiply equation 2) by -1 to eliminate the term 3x:

-1(y + 3x) = -1(1)

-y - 3x = -1

Now we have the following system of equations:

3x - 4y = 11

-y - 3x = -1

Add equation 1) and equation 2) together:

(3x - 4y) + (-y - 3x) = 11 + (-1)

3x - 4y - y - 3x = 10

-5y = 10

Divide both sides of the equation by -5:

-5y / -5 = 10 / -5

y = -2

Now substitute the value of y = -2 into equation 2):

-2 + 3x = 1

Add 2 to both sides:

3x = 3

Divide both sides by 3:

3x / 3 = 3 / 3

x = 1

Therefore,

The solution to the system of equations is x = 1 and y = -2.

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Answer:

Carle cut 49 pieces.

Step-by-step explanation:

1 foot= 12 inches

Length of piece of string = 24 3/8  inch

Length of string of ball = 100 ft

We have to find number of pieces cut by Carle.

What is perimeter of circle?

The perimeter of circle is twice of product of π with radius.

Now,

Length of piece of string = 24 3/8  inch

Length of string of ball = 100 ft

Since, 1 ft = 12 inch

Therefore, 100 ft = 1200 inches

We can write 24 3/8  inch = 24.3 inches approximately

Now number of pieces cut by Carle = 1200/24.3 = 49

Thus, Carle cut 49 pieces.

Answer:

x² + y² = z²

Step-by-step explanation:

(a)

Using the right triangle altitude theorem,

x/z = p/x

x² = pz

(b)

y/z = q/y

y² = qz

(c)

x² + y² = pz + qz

x² + y² = z(p + q)

z = p + q

x² + y² = z × z

x² + y² = z²

Mrs. Green can serve a total of six different combinations of two vegetables from the given options.

To find out, we can use the combination formula: \(nCr = n! / (r! * (n-r)!)\)

where n is the total number of items to choose from, and r is the number of items to choose. In this case, n = 4 (carrots, peas, okra, and green beans) and r = 2 (the number of vegetables to be served).

Therefore, the formula becomes: 4C2 = 4! / (2! * (4-2)!)

= (4 * 3 * 2 * 1) / [(2 * 1) * (2 * 1)]

= 6

Mrs. Green can serve six different sets of two vegetables with dinner. These are: carrots and peas, carrots and okra, carrots and green beans, peas and okra, peas and green beans, and okra and green beans.

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To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

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Answer:

48 minutes long

Step-by-step explanation:

For a total amount of minutes the lessons are, take 4x60. 4 for the total time in the lessons and 60 for 60 minutes in an hour. 4x60= 240 minutes.

Take 240/5. 240 is the total number of minutes and with the five lessons being the same amount of time, you divide the total number of minutes by the number of lessons. 240/5= 48 minutes

Answer: yes, the value of x is 4 and angle HEB is 36 degrees

Step-by-step explanation:

1a. Find the value of angle CEB

Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees

2a.set up an equation

After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2

3a. Solve the equation

13x+9x+2=90

22x+2=90 | combine like terms

22x=88 | subtract 2 from both sides

x=4 | divide by 22 on both sides

1b. Set up equation

Knowing x=4 and that angle HEB is 9x the equation is 9(4)

2b. Solve the equation

9(4)

36

Answer:

c)12:16​

Step-by-step explanation:

We know

The ratio is 6:8; we times 2 and get the ratio of 12:16

So, the answer is C

Step-by-step explanation:

Let's call the shorter base of the trapezoid "b1", the longer base "b2", and the height "h". We can use the formula for the surface area of a right prism to set up an equation:

Surface area of prism = 2(base area) + (lateral area) = 1280

The base area is the area of the trapezoid, which is given by:

(base area) = (1/2)(b1 + b2)h

The lateral area is the area of the four rectangular faces of the prism, which are all congruent. Each face has an area equal to the product of the height and the length of one of the legs of the trapezoid, so the lateral area is:

(lateral area) = 4hl

where l is the length of one of the legs of the trapezoid.

Substituting these expressions into the formula for the surface area of the prism, we get:

2[(1/2)(b1 + b2)h] + 4hl = 1280

Simplifying and rearranging, we get:

h(b1 + b2) + 2hl = 1280

We also know that the sum of the lengths of the legs of the trapezoid is 52 feet, which means:

l1 + l2 = 52

But we can express l1 and l2 in terms of b1 and b2 using the formula for the area of a trapezoid:

(base area) = (1/2)(b1 + b2)h = (1/2)(l1 + l2)h

Simplifying, we get:

b1 + b2 = (l1 + l2)h

Substituting this into the previous equation, we get:

h[(l1 + l2)h] + 2hl = 1280

Simplifying, we get:

h^2(l1 + l2) + 2hl = 1280

Substituting l1 + l2 = 52, we get:

h^2(52) + 2hl = 1280

This is a quadratic equation in h. We can solve it using the quadratic formula:

h = [-2l ± sqrt(4l^2 + 4h^2(52)(1280 - 2hl))] / 2(52)

Simplifying and factoring out a 2, we get:

h = [-l ± sqrt(l^2 + h^2(1280 - 2hl))] / 52

We have two possible solutions for h, but one of them is negative, which doesn't make sense in the context of the problem. So we can discard the negative solution and focus on the positive one:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

We don't know the exact value of h yet, but we can use this equation to set up a system of equations that we can solve for h. Specifically, we can use the fact that the legs of the trapezoid add up to 52 feet to solve for l in terms of b1 and b2:

l = 52 - (b1 + b2)

Substituting this into the equation for h, we get:

h = [-l + sqrt(l^2 + h^2(1280 - 2hl))] / 52

h = [-52 + (b1 + b2) + sqrt((52 - (b1 + b2))^2 + h^2(1280 - 2h(b1 + b

The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

What is rotation?

The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then

=> (x , y) = (-8,0)

Now 270 degrees counter clockwise rotation then,

=> (y,-x) = (0,-(-8))

=> (y,-x)=(0,8)

Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

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Answer:

-10

Step-by-step explanation:

-8 + n/2 = -13

n/2 = -13 + 8

n/2 = -5

n = -5 * 2

n = -10

Hope it helps!

Answer:

=1.3

Step-by-step explanation:

Combine multiplied terms into a single fraction

0

.

6

5

=

0

.

5

0.65=0.5c

0.65=0.5c

0

.

6

5

=

1

2

0.65=\frac{1c}{2}

0.65=21c​

2

Multiply by 1

3

Multiply all terms by the same value to eliminate fraction denominators

4

Cancel multiplied terms that are in the denominator

5

Multiply the numbers

6

Move the variable to the left

Solution

=1.3

Answer:

c = 1.3

Step-by-step explanation:

0.65 = 0.5c ( divide both sides by 0.5 )

\(\frac{0.65}{0.5}\) = c , that is

c = 1.3

ANSWER

x = 15, y = 30

EXPLANATION

We want to solve the system of equations by substitution method.

We have that:

y = x + 15

y = 2x

Substitute the value of y in the second equation into the first:

=> 2x = x + 15

Collect like terms:

2x - x = 15

x = 15

Recall that:

y = 2x

=> y = 2(15)

y = 30

The solution to the system of equations is: x = 15, y = 30

Answer:

A) . 5(20+4)5(20+4)

Step-by-step explanation:

5(20+4)5(20+4)

5(24) ×5(24)

120 × 120

14400

Answer: D) 59°

Step-by-step explanation:

The series is absolutely convergent.

To determine if the series is absolutely convergent, conditionally convergent, or divergent, we first analyze the absolute value of the series. We consider the series Σ|sin(8n)/6n| from n=1 to infinity. Using the comparison test

since |sin(8n)| ≤ 1, the series is bounded by Σ|1/6n| which is a convergent p-series with p>1 (p=2 in this case).

Since the series Σ|sin(8n)/6n| converges, the original series Σsin(8n)/6n is absolutely convergent. Absolute convergence implies convergence,

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The series sin(8n)/(6n) is divergent (by comparison with the harmonic series), the original series is not convergent.

To determine the convergence of the given series, we need to analyze it using the given terms. The series is:

Σ(sin(8n) / 6n) from n = 1 to infinity.

First, let's check for absolute convergence by taking the absolute value of the series terms: Lim m as n approaches infinity of |(sin(8(n+1))/(6(n+1))) / (sin(8n)/(6n))|

= lim as n approaches infinity of |(sin(8(n+1))/(6(n+1))) * (6n/sin(8n))|

= lim as n approaches infinity of |sin(8(n+1))/sin(8n)|
Σ|sin(8n) / 6n| from n = 1 to infinity.

Since |sin(8n)| is bounded between 0 and 1, we have:

Σ|sin(8n) / 6n| ≤ Σ(1 / 6n) from n = 1 to infinity.

Now, the series Σ(1 / 6n) is a geometric series with a common ratio of 1/6, which is less than 1. Therefore, this geometric series is convergent. By the comparison test, since the original series has terms that are less than or equal to the terms in a convergent series, the original series must be convergent.

In summary, the given series Σ(sin(8n) / 6n) from n = 1 to infinity is convergent.

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Answer:

function

Step-by-step explanation:

I did this math before

Answer:

this relation is a function

Answer:

49π (or ~154) cm²

Step-by-step explanation:

A = area

A = πr²

r = radius

r = 7

A = π(7)²

= 49π

= 153.938040026 → 154 cm²

Answer:

(-4, -2)

Step-by-step explanation:

x-axis is horizontal and y-axis is vetical. The first valye of point A is -4, the second value of point B is -2, therefore, point C = (-4, -2)

The coordinates of C from the given graph are (-4, -2).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of A = (-4, 1)

The coordinates of B = (3, -2)

Now,

Point C has me same x-coordinate as point A and the same y-coordinate as point B

So,

The coordinates of C = -4, -2)

Thus,

The coordinates of C from the given graph are (-4, -2).

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If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization  is sp hybridization , it forms linear molecules with an angle of 180°.

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.

The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:

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Answer:

Edward earned $1300 interest in 4 years.

Step-by-step explanation:

Principal Amount = Initial Investment = $6500

Time t = 4 years

Interest rate r = 5% = 0.05 (it is taken in decimal i.e 5/100 = 0.05)

We need to find interest.

The formula used is: \(Interest= Principal\times r \times t\)

Putting values and finding Interest

\(Interest= Principal\times r \times t\\Interest=6500\times 0.05 \times 4\\Interest= 1300\)

So, the interest = $1300 in 4 years.

Edward earned $1300 interest in 4 years.

There are 21,600 possible groups that the teacher can form.

Combinations is a method of counting the number of ways to select a specific number of items from a larger set without regard to their order.

Specifically, the problem involves finding the number of ways to select three boys and two girls from a group of twenty students.

C(20, 3) * C(17, 2)

Here we have

A teacher wishes to divide her class of twenty students into four groups, each of which will have three boys and two girls.

Assume that there are two equal number of boys and girls

Now we need to choose 3 boys out of 10 and 2 girls out of 10 for each group, as there are 10 boys and 10 girls in the class.

We can do this in the following way:

Number of ways to choose 3 boys out of 10 = C(10,3) = 120

Number of ways to choose 2 girls out of 10 = C(10,2) = 45

Hence,

The number of ways to form a group of 3 boys and 2 girls

= 120 × 45 = 5400

Since we need to form 4 such groups,

The total number of possible groups that the teacher can form is:

=> 4 × 5400 = 21600

Therefore,  

There are 21,600 possible groups that the teacher can form.

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The probability of selecting chocolate of the first type at random is 1/3.

Since there are three types of chocolates with 6 pieces each, there are a total of 18 chocolates in the box.

The probability of selecting chocolate of the first type is the number of chocolates of the first type divided by the total number of chocolates in the box.

Since there are 6 chocolates of the first type, the probability of selecting a chocolate of the first type is:

Probability = (Number of chocolates of the first type) / (Total number of chocolates)

= 6 / 18

= 1/3

Therefore, the probability of selecting chocolate of the first type at random is 1/3.

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