Janice wants to go to the Sadie Hawkins dance. The probability of a random boy saying yes is 45%. How many does she need to be willing to ask to have a 99.7% chance of going?

Answer:

4 hours

Step-by-step explanation:

It take them 1.5 h ÷ 0.5 h to chop down 1 tree, so it would take 0.5 h × 8 = 4 hours to chop down 8 trees

Answer:

what do you need help with??

Step-by-step explanation:

i would be happy to help : )

The equation 1 + cot²(∅) = csc²(∅) is true for ∅ = 45 and the equation sin²(∅) + cos²(∅) = 1 is true for ∅ = 45

Equation 1

The equation is given as:

1 + cot²(∅) = csc²(∅)

Where

∅ = 45 degrees

Substitute ∅ = 45 in 1 + cot²(∅) = csc²(∅)

1 + cot²(45) = csc²(45)

Evaluate the trigonometry ratios

1 + (1)² = (√2)²

Evaluate the exponents

1 + 1 = 2

Evaluate the sum

2 = 2

The above equation is true

Hence, the equation 1 + cot²(∅) = csc²(∅) is true for ∅ = 45

Equation 2

The equation is given as:

sin²(∅) + cos²(∅) = 1

Where

∅ = 45 degrees

Substitute ∅ = 45 in sin²(∅) + cos²(∅) = 1

sin²(45) + cos²(45) = 1

Evaluate the trigonometry ratios

(1/√2)² + (1/√2)²= 1

Evaluate the exponents

1/2 + 1/2 = 1

Evaluate the sum

1 = 1

The above equation is true

Hence, the equation sin²(∅) + cos²(∅) = 1 is true for ∅ = 45

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The solution for the given equation is C) \(x=\frac{-1+-\sqrt{33} }{4}\)

What does a quadratic function mean?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other words, a "polynomial function of degree 2" is a quadratic function.

The formula for the solution of a quadratic equation \(ax^{2} +bx+c=0\) is

\(x=\frac{-b+-\sqrt[2]{b^{2}-4ac } }{2a}\).

So, the solution for the equation \(2x^{2} +x-4=0\) is

\(x=\frac{-1+-\sqrt[2]{1^{2}-4*2*(-4) } }{2*2}\\x=\frac{-1+-\sqrt[2]{1+32 } }{4}\\x=\frac{-1+-\sqrt{33} }{4}\)

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Answer:

2(x²-8+15)

X1/2=8+-(64-60) /2= 8+-2 /2=

10/2=5 or

6/2=3

So the answer is C. 2(x-3)(x-5)

There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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Answer:

therefore, \(\frac{(2n)!}{n!}=(n+1)\cdot (n+2)\dots (2n)\)

Step-by-step explanation:

\(\frac{(2n)!}{n!}\) is interesting

if we write it out for n=4

\(\frac{(2n)!}{n!}=\frac{(2(4))!}{4!}=\frac{8!}{4!}=\frac{1\cdot 2\cdot 3\cdot 4\cdot 5 \cdot 6\cdot 7\cdot 8}{1\cdot 2\cdot 3\cdot 4}=5\cdot 6\cdot 7\cdot 8\)

try for n=3

\(\frac{(2n)!}{n!}=\frac{(2(3))!}{3!}=\frac{6!}{3!}=\frac{1\cdot 2\cdot 3\cdot 4\cdot 5 \cdot 6}{1\cdot 2\cdot 3}=4\cdot 5\cdot 6\)

we notice that the first \(n\) terms cancel out

therefore, \(\frac{(2n)!}{n!}=(n+1)\cdot (n+2)\dots (2n)\)

there is no further information given

Answer:

D

Step-by-step explanation:

The diagram below shows the perpendicular bisector of AB.

Option B is the correct answer.

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

Line DF bisects line AB.

The diagram shows the perpendicular bisector of AB.

Thus,

DF is the perpendicular bisector of AB.

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The relation between mode, mean and median is:

mode=3median-2mean

Now, to find mean:

2mean=3median-mode

mean=7/2 = 3.5

Let we wish to evaluate the mean  μ of a population. In real practice we would typically take just one sample. Imagine still that we take sample after sample, all of the same size n, and compute the sample mean x¯ every time.

The sample mean x is a random variable: it differs from sample to sample in a way that cannot be predicted with sureness. We will write X¯ when the sample mean is idea of as a random variable and write x for the values that it takes.

The random variable X¯ has a mean, denoted  μX¯, and a standard deviation, denoted  σX¯. Here is an example with such a small population and small sample size that we can indeed write down every single sample.

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Answer as an improper fraction:    248/3

Answer as a mixed number:    82  2/3

==========================================================

Work Shown:

b1 and b2 are the parallel bases

b1 = 10

b2 = 6

h = height

h = 10 & 1/3 = 10 + 1/3 = 30/3 + 1/3 = 31/3

\(A = \text{area of the trapezoid}\\\\A = h*\frac{b_1+b_2}{2}\\\\A = \frac{31}{3}*\frac{10+6}{2}\\\\A = \frac{31}{3}*\frac{16}{2}\\\\A = \frac{31*16}{3*2}\\\\A = \frac{31*8}{3}\\\\A = \frac{248}{3}\\\\\)

The area as an improper fraction is 248/3 square miles.

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

If you wanted, follow these steps to convert the improper fraction to a mixed number

248/3 = 82.667 approximately

The whole part is 82 as it's to the left of the decimal point.

The fractional part 0.667 multiplies with the denominator 3 to get 3*0.667 = 2.001 which rounds to 2.

Therefore,

248/3 = 82 & 2/3 or 82  2/3

We have 82 full square miles, plus an additional 2/3 of a square mile, to constitute the area of the trapezoid.

The required cubic model would be y = 1 + x³ for the given set of values.

The cubic model function takes the form:

y = a + bx + cx² + dx³,

where a, b, c, and d are real integers that represent the cubic regression model's coefficients As you can see, we simulate how the value of y changes as x changes.

x₁ = -2, y₁ = -7

x₂ = -1, y₂ = 0

x₃ = 0, y₃ = 1

x₄ = 1, y₄ = 2

x₅ = 2, y₅ = 9

Computing the values in the regression models to get the values of coefficients to which the graph has attached.

y = a + bx + cx² + dx³

Fitted coefficients:

a = 1

b = 0

c = 0

d = 1

Cubic model:

y = 1 + x³

Hence, the required cubic model would be y = 1 + x³ for the given set of values.

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Answer:

2.5 goes in 10 4 times

5x4 = 20

colleen can make 20 bracelets in 10h

The angle of elevation of the ramp is approximately 20.56 degrees.

We can use the trigonometric function tangent to find the angle of elevation of the ramp. The definition of tangent is:

tangent(angle) = opposite / adjacent

where "opposite" is the length of the side opposite the angle (i.e., the vertical height of the ramp), and "adjacent" is the length of the side adjacent to the angle (i.e., the horizontal length of the ramp).

Substituting the given values, we get:

tangent(angle) = 5 / 14

To solve for the angle, we need to take the inverse tangent (or arctangent) of both sides of the equation:

angle = tan^(-1) (5/14)

Using a calculator, we get:

angle ≈ 20.56 degrees

Therefore, the angle of elevation of the ramp is approximately 20.56 degrees.

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The steps that are part of a template for proofs by mathematical induction are:

a) Write "By mathematical induction, P(n) is true for all integers n with n ≥ b."
b) Express the statement to be proved in the form "for all n ≥ b, P(n)" for a fixed integer b.
c) Prove that P(b) is true.
d) Show that if P(k) is true for an arbitrary fixed integer k ≥ b, then P(k + 1) is true.

Options E and F are not correct because E is a repetition of option D and F repetition of option c.

Therefore, the correct options are A, B, C, and D.

In summary, the template for proofs by mathematical induction includes writing the statement to be proved, expressing it in the form "for all n ≥ b, P(n)" for a fixed integer b, proving that P(b) is true, and showing that if P(k) is true for an arbitrary fixed integer k ≥ b, then P(k + 1) is true.

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The correct answer is b, e, and f.

The steps that are part of a template for proofs by mathematical induction are b, e, and f. These steps are essential in proving a statement using mathematical induction.

b) Express the statement to be proved in the form "for all n ≥ b, P(n)" for a fixed integer b.
This step is important because it sets the stage for the rest of the proof. It clearly defines the statement that needs to be proved and the range of integers for which it needs to be proved.

e) Show that if P(k) is true for an arbitrary fixed integer k ≥ b, then P(k + 1) is true.
This step is the inductive step, where you prove that if the statement is true for an arbitrary integer k, then it is also true for the next integer k + 1. This is a crucial step in mathematical induction because it shows that the statement holds for all integers greater than or equal to b.

f) Show that P(b) is true.
This step is the base case, where you prove that the statement is true for the smallest integer in the range, b. This is an important step because it establishes a starting point for the inductive step.

Therefore, the correct answer is b, e, and f.

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Answer:

perpendicular

Step-by-step explanation:

If 2 lines are parallel then their slopes are equal

If 2 lines are perpendicular then the product of their slopes = - 1

Here

- \(\frac{9}{5}\) × \(\frac{5}{9}\) = - 1

Then the 2 lines are perpendicular

The statement that 'Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem' is true as it may violate the problem constraints.

The statement that 'In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project is selected, xj - O, otherwise) the constraint x1 * x2 O implies that if project 2 is selected, project 1 cannot be selected' is false.

The constraint x41 + x42 + x43 + x44 ≤ 3 means Agent 4 can be assigned to a maximum of 3 tasks. Therefore, the correct option is 1.

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. The statement is true. When we round non-integer solution values up to the nearest integer value, it can result in an infeasible solution to an integer programming problem. This is because the rounded solution may violate the problem constraints, leading to an infeasible solution.

In a 0-1 integer programming problem involving a capital budgeting application (where xj = 1, if project is selected, xj - O, otherwise) the constraint x1 * x2 O implies that if project 2 is selected, project 1 cannot be selected. The statement is false. The constraint x1 * x2 = 0 implies that if project 1 is not selected (x1=0), then project 2 must not be selected (x2=0). It does not imply that if project 2 is selected, project 1 cannot be selected.

constraint x41 + x42 + x43 + x44 ≤ 3 means Agent 4 can be assigned to a maximum of 3 tasks. The terms in the constraint represent possible task assignments for agent 4 (x41 is agent 4 assigned to task 1, x42 is agent 4 assigned to task 2, etc.). The constraint ensures that agent 4 is not assigned to more than 3 tasks in total. Hence, the correct answer is option 1.

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Answer: (4, -7) (8, 1) (12, 54)

Step-by-step explanation:

A: u = (4, 8), and v = (4, -7)

B: u + v = (4 + 4, 8 - 7) = (8, 1)

C: 5u - 2u = 5(4, 8) - 2(4, -7)

                    = (20, 40) - (8, -14)

                         = (12, 54)

This helped me, so hopefully it helps you! Good luck!

1. 2 ² x 5b³ =   20b³

2. (3a²) ² x 2 (b ²) ³ = 3\(a^{4}\) x 2\(b^{6}\) 5d

3. 15d ³ divided by 3d ² = 5d

What is Operations?

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's acuity is determined by the number of operands.

The given problems are:

1. 2 ² x 5b³

2. (3a²) ² x 2 (b ²) ³

3. 15d ³ divided by 3d ²

1. 2 ² x 5b³

  = 4 x 5b³

  = 20b³

2. (3a²) ² x 2 (b ²) ³

  By the exponent rule:
         \((x^{n} )^m\) = \(x^{n * m}\)

                   = \(x^{nm}\)

∴ 3\(a^{2*2}\) x 2\(b^{2*3}\)

= 3\(a^{4}\) x 2\(b^{6}\)

3. 15d ³ divided by 3d ²

    15d ³ ÷ 3d ²

By the exponent rule:

         \(a^{m}\)÷\(a^{n}\) = \(a^{m-n}\)

∴  5\(d^{3-2}\) = 5\(d^{1}\)

              = 5d

Hence, The solutions are 20b³, 3\(a^{4}\) x 2\(b^{6}\) and 5d

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Answer:

22°

Step-by-step explanation:

a right angle have 90°

So

x+68°=90°

=>x=90-68

=22°

Answer:

Rosie is 10 years old

Step-by-step explanation:

A)

Rosie is x years old

Rosie's age (R) = x

R = x

Eva is 2 years older

Eva's age (E) = x + 2

E = x + 2

Jack is twice Rosie’s age

Jack's age (J) = 2x

J = 2x

B)

R + E + J = 42

x + (x + 2) + (2x) = 42

x + x + 2 + 2x = 42

4x + 2 = 42

4x = 42 - 2

4x = 40

\(x = \frac{40}{4} \\\\x = 10\)

Rosie is 10 years old

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

The first number is 66.7% less than the second.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


To determine the percent by which the second number is greater than the first, divide the difference between the two numbers by the first number and then multiply the result by 100 to obtain the percent. For example, if the first number is 80 and the second number is 120, the calculation would be (120 - 80) / 80 x 100 = 50%. This means that the second number is 50% greater than the first.

To determine the percent by which the first number is less than the second, divide the first number by the second number and then multiply the result by 100 to obtain the percent. For example, if the first number is 80 and the second number is 120, the calculation would be 80 / 120 x 100 = 66.7%. This means that the first number is 66.7% less than the second.

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The rate at which the y-coordinate of the jogger is changing is \({-\frac{3}{4}}\) times the rate at which the x-coordinate of the jogger is changing.

Given information:

Radius of the circular track = 75 ft

Coordinates of the jogger: (45, 60)

We know that the coordinates of a point in the Cartesian plane can be represented as (x, y), where x represents the horizontal displacement and y represents the vertical displacement.

Let us now consider a jogger who runs around a circular track of radius 75 ft, with the center of the track being the origin. Therefore, the horizontal and vertical displacements of the jogger will be its coordinates, respectively.

Let us now consider a right-angled triangle with the hypotenuse representing the radius of the circular track, and the vertical and horizontal sides representing the y and x coordinates of the jogger, respectively. Since the radius of the circular track is constant, we can use the Pythagorean theorem to relate x and y.

Since we know that the radius of the track is 75 ft, we can say that:

\(\[x^2 + y^2 = 75^2\]\)

Differentiating with respect to time t, we get:

\(\[\frac{d}{dt}(x^2 + y^2)\)

= \(\frac{d}{dt}(75^2)\]\\\2x \cdot \frac{dx}{dt} + 2y \cdot \frac{dy}{dt} = 0\]\)

Now, since we are given that the jogger's coordinates are (45, 60), we can substitute these values to obtain:

\(\[2(45) \cdot \frac{dx}{dt} + 2(60) \cdot \frac{dy}{dt} = 0\]\)

On solving, we obtain:

\(\[\frac{dy}{dt} = -\frac{3}{4}\cdot \frac{dx}{dt}\]\)

Hence, the rate at which the y-coordinate of the jogger is changing is \({-\frac{3}{4}}\) times the rate at which the x-coordinate of the jogger is changing.

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Answer:

2^3

Step-by-step explanation:

Let's call the base number x, the first power a, and the second power b. For any number that follows the pattern:

x  ^a/x^b

To simplify this, you just subtract a from b and make that number the new power of x.

x  ^a/x^b = x^(a-b)

This will work with any equation following this example.

2  ^8/2^5

2 ^ (8-5) = 2^3

:)

The year it will take Mussman to reach a population of 27,000 resident is 10.7 years

Population growth is the increase in the number of people in a population or dispersed group.

We use exponential function when calculating increase in population per time

p(t) =p(o) e^kt

27000 = 13500 e^0.065t

e^0.065t = 27000/13500

0.065t = ln 2

0.065t = 0.693

t = 0.693/0.065

t = 10.7 years

therefore it will take 10.7years for the resident of Mussman to reach a population of 27000

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The Battle of Gettysburg was a significant event in the American Civil War that took place from July 1 to 3, 1863. It was fought between the Union and Confederate forces and is considered a turning point in the war due to the Union's decisive victory.

This battle resulted in heavy casualties on both sides and demonstrated the importance of strong leadership, effective strategies, and the resolve of soldiers fighting for their respective causes. The outcome of the Battle of Gettysburg had lasting effects on the remainder of the war and ultimately contributed to the Union's overall success.

The consequences of the Battle of Gettysburg were far-reaching. It boosted the Union's confidence, leading to increased support for the war effort and President Abraham Lincoln's Emancipation Proclamation. The Confederate Army never fully recovered from the loss, and the Union went on to secure further victories, ultimately leading to the Confederate surrender and the preservation of the United States as a unified nation.

In conclusion, the Battle of Gettysburg was a critical event in the American Civil War, with its outcome significantly impacting the trajectory of the war. It demonstrated the importance of leadership, strategy, and the determination of soldiers, ultimately contributing to the Union's ultimate success in preserving the Union and abolishing slavery.

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Answer:

X=1/14

Step-by-step explanation:

Answer:

1/14

Step-by-step explanation:

Answer:

100

Step-by-step explanation: