which number is larger 0.707 or 0.71?

Answer:

The y-intercepts of the quadratic are (0, 25)

Step-by-step explanation:

Hope I helped, have a good day

Answer:

Choice a : $96,600

Step-by-step explanation:

The net worth of a person is computed as total assets - total liabilities in money terms

Ben's assets are as follows:

Townhome: $195,000

Savings: $5000

Car: $38,000

Total Assets: 195000 + 5000 + 38000 = $238,000

Ben's liabilities

Home Loan: $120,000

Credit Card: $1,400

Car Loan: $20,000

Total Liabilities = 120000 + 1400 + 20000 = $141,400

Net Worth = 238000 - 141400 = $96,600   (Answer is choice a)

Answer:

A

Step-by-step explanation:

The hypothesis in a hypothesis test is an alternative hypothesis a statement about a parameter.

An alternative hypothesis in a hypothesis test is a statement about a parameter, not a statistic. The null hypothesis is typically a statement about a parameter that assumes there is no significant difference or relationship, while the alternative hypothesis is a statement that contradicts the null hypothesis and suggests there is a significant difference or relationship.

The alternative hypothesis can take one of three forms: it can be a one-tailed hypothesis (either greater than or less than the null hypothesis), or a two-tailed hypothesis (not equal to the null hypothesis). In all cases, the alternative hypothesis is a statement about the population parameter, which is typically denoted by a Greek letter such as μ (mean) or σ (standard deviation).

Therefore, the alternative hypothesis is a statement about the parameter being tested.

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Answer:

d = 8t

Step-by-step explanation:

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

f(x) = max{0,x} then f(x)=0 if x<0 and f(x)=x if x≥0.

f(x)=7x-2xlnx

When x tends to -∞, f is the constant function zero, therefore limit n tends to infinity f(x) = 0.

When x tends to ∞, f(x)=x and x grows indefinitely. Thus limit n tends to infinity f(x) = infinity.

f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x) = x and if x<0, f'(0)=0 (the derivative of the constant zero).

In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

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Answer:

74 degrees

Step-by-step explanation:

Assuming we have the following

FD = 14

DE = 52

m<F = 90degrees

Required

m<D

DE = hypotenuse

FD = adjacent

Using the SOH CAH TOA identity

Cos m<D = adj/hyp

Cos m<D = 14/52

m<D = arccos(0.2692)

m<D = 74.38

m<D to the nearest degree is 74degrees

The perimeter of triangle ABC is 3 cm.

Given:- AB is congruent to segment AC  

AB= AC= 1/2x + 1/4

BC= 5/2-x

Perimeter of a triangle = Sum of all sides

                                      = (1/2x + 1/4) + (1/2x + 1/4) + (5/2-x)

                                      = 1/2x +1/2x -x +1/4+1/4+5/2

                                      = 3 cm

Therefore, the perimeter of triangle ABC is 3 cm.

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$a^4 - 3a^2 + 9$ can be factorised as $(a^2 - 3)(a^2 + 3)$

To factor $a^4 - 3a^2 + 9$ as a product of two monic quadratics with integer coefficients, we can use the difference of squares factorization.

When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b).

$a^4 - 3a^2 + 9$ can be factored as $(a^2 - 3)(a^2 + 3)$

Notice that both factors are monic quadratics with integer coefficients.

So, $a^4 - 3a^2 + 9$ = $(a^2 - 3)(a^2 + 3)$

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Answer:

729

Hope you could understand.

If you have any query, feel free to ask.

Step-by-step explanation:

hope it is helpful to you

Step-by-step explanation:

{(-10)-(-15)÷5}

-10+15÷5

-10+3

= -7

The mathematical equation f(w) = w² - 6w provides a representation of the remaining surface area, measured in square meters, of the field following the construction of the basketball court.

The rectangular field has an area of length x width, which can be expressed as (2w)(w) = 2w² square meters.

The basketball court has an area of length x width, which can be expressed as (w)(w+6) = w² + 6w square meters.

To find the remaining area of the field after the basketball court is built, we need to subtract the area of the basketball court from the area of the rectangular field.

So the function f(w) representing the remaining area, in square meters, is:

f(w) = 2w² - (w² + 6w)

f(w) = 2w² - w² - 6w

f(w) = w² - 6w

Therefore, the function f(w) = w² - 6w represents the area, in square meters, remaining of the field once the basketball court is built.

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Complete question:

A grounds committee of a housing community plans to build a basketball court in an empty rectangular field.

1. The rectangular field-has a width of 2w meters and a length that is 13 meters longer than its width.

2. The basketball court has a width of w meters and a length that is 6 meters longer than its width.

Which function, f(w), represents the area, in square meters, remaining of the field once the basketball court is built?

Answer:

120

Step-by-step explanation:

formula:

\(\frac{n!}{(n-h)!}=\frac{5!}{(5-4)!}=120\)

Answer:

1st side= 4m

2nd side= 8m

3rd side= 12m

Step-by-step explanation:

Let the first, second and third side of the triangle be a, b and c meters respectively.

a= b -4 -----(1)

c= 3a -----(2)

Perimeter of triangle

= a +b +c

= 24

a +b +c= 24 -----(3)

From (1): b= a +4 -----(4)

Subst. (2) and (4) into (3):

a +(a +4) +3a= 24

3a +a +a +4= 24

5a +4= 24

5a= 24 -4

5a= 20

Divide both sides by 5:

a= 20 ÷5

a= 4

Substitute a= 4 into (4):

b= 4 +4

b= 8

Substitute a= 4 into (2):

c= 3(4)

c= 12

Thus, the lengths of the first, second, and third side of the triangle are 4m, 8m and 12m respectively.

a)

Values of the given angles  ∠A = 123°  , ∠B = 123° ,∠C = 57.

Given ,

One angle of the figure as 123°.

Now,

∠C and 123° form linear pair.

So,

∠C + 123° = 180°

∠C = 57°

Now,

∠C and ∠B are pairs of interior angles on same side of transversal, thus they are supplementary.

∠C + ∠B = 180°

Substitute the value of ∠C

53° + ∠B = 180°

∠B = 127°

Now,

∠B and ∠A are vertically opposite angles.

Thus,

∠B = ∠A

So,

∠A = 127° .

Hence,

∠A= 127°

∠B = 127°

∠C = 57°

b)

Values of ∠D = 98°, ∠E = 98°, ∠F = 98° .

Given one angle as 82°

Now,

∠F and 82° form linear pair.

So,

∠F + 82° = 180°

∠F = 98°

Now,

∠D and ∠F are corresponding angles. Thus,

∠D = ∠F

∠D = 98° .

Now,

∠D and ∠E are vertically opposite angles.

Thus,

∠D = ∠E

∠E = 98°.

Hence,

∠D = 98°

∠E = 98°

∠F = 98°

c)

Values of ∠G = 75° and ∠H = 75°

Given one angle as 75° .

∠H and 75° are corresponding angles. Thus,

∠H = 75°

Now,

∠H and ∠G are vertically opposite angles.

So,

∠G = 75° .

Hence,

∠G = 75°

∠H = 75°

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Answer:

b

Step-by-step explanation:

eachone got to go there minus 6

The absolute value of change in the predicted value of dependent variable Y is 18.

Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.

Slope = b = -4

Intercept = a = -2.8

So, the equation of the regression line is

y  =  a + bx

y = -2.8 - 4x              ...Equation 1

Now suppose the value of x is changed by adding 4.5

i.e. put x = x + 4.5

So,

y = -2.8 - 4(x + 4.5)

y = -2.8 -4x - 18         ...Equation 2

Comparing 1 and 2 ,

We get the predicted value of dependent variable Y as 18

Therefore The absolute value of change in the predicted value of dependent variable Y is 18

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the direction angle of w=8j is 90.0 degrees. The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

what is direction angle ?

The direction angle, also known as the argument or phase angle, of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

In the given question,

The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

In this case, the complex number is w=8j, which has an imaginary part of 8 and a real part of 0. Therefore, the vector representing w points directly upwards in the complex plane, and the angle between this vector and the positive real axis is 90 degrees.

Rounding this to the nearest tenth of a degree gives 90.0 degrees.

So the direction angle of w=8j is 90.0 degrees.

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ANSWER

EXPLANATION

If x1, x2, x3, ..., xn are the zeros of a polynomial P, then the polynomial can be written as the product of the factors,

In this problem we have a third-degree polynomial function, so it has 3 zeros and thus 3 factors,

We have to find a knowing that the function has to pass through point (2, 7). This means that when x = 2, f = 7,

Replace into the function,

Solve the parenthesis,

Multiply,

And solve for a by dividing both sides by -12,

Hence, the function is

Next, we have to multiply the factors to obtain the function in standard form. Multiply the first two,

Then multiply by the last factor,

Add like terms,

And finally, distribute the coefficient,

This is the polynomial function with zeros -2, -1 and 3 that passes through point (2, 7)

Answer:

8 inches = 120 miles

Step-by-step explanation:

If 2 inches is equivalent to 30 miles, then divide 120 by 30 then times the answer by two.

120 / 30 = 4

4 x 2 = 8

8 inches = 120 miles

To check;

30 x 4 = 120

8 / 2 = 4

Hope this helps!!!

Answer:

The answer is 8in.

Step-by-step explanation:

Calculated 120/30

The mass of the sample after four hours is 6426.5 grams.

Given,

The biologist has an 8535-gram sample of a radioactive substance.

Relative rate of decay = 13% per hour.

Using exponential decay formula :N(t) = N_0*e^(-rt)

Here, N(t) = mass of the sample after t hours = N_0*e^(-rt)

N_0 = initial mass of the sample = 8535 grams

r = relative rate of decay = 13% per hour = 0.13

t = time in hours = 4 hours

We need to find mass of the sample after 4 hours i.e. N(t).

We can use the formula, N(t) = N_0*e^(-rt)

Substituting the given values,

N(t) = 8535*e^(-0.13*4)

≈ 6426.5 grams (rounding off to nearest tenth)

Therefore, the mass of the sample after four hours is 6426.5 grams.

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The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.

It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.

The value for x based on the equation will be:

3(4x + 6) = 9x + 12

Open bracket

12x + 18 = 9x + 12

Collect like terms

12x - 9x = 12 - 18

3x = -6

Divide

x = -6/3

x = -2

Therefore, x is -2.

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Answer:

I'm not sure but I think the awnser is

4 C

8 R

5 D

and 7H

Using the data given in the question, given below is the frequency table for the movie genres liked by the students.

Movie genre      Number of students

  Action                             6

  Comedy                          4    

  Horror                             7

  Drama                             5

  Romance                        8    

A frequency table lists a set of values and how often each one appears. Frequency is the number of times a specific data value occurs in your dataset.

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Answer:

1.) -10

2.) 10

3.) -27

4.) 27

5.) -8

6.) 8

The latest sentence of proof by using the triangle congruence method we can conclude that f+e=c, \(a^{2} + b^{2} = c^{2}\).

Given that ΔABC and ΔCBD are right triangles

Therefore, one angle of both triangle is of 90°

So, ∠B is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Consequently, ∠A is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Similarly, When two triangles are similar then their corresponding angles are equal and their corresponding sides are also equal.

Therefore , the two proportions can be rewritten as

a² = cf ( equation 1 )

b² = ce ( equation 2 )

By adding b² on both side of equation 1 then we can write equation 1 as

\(a^{2} + b^{2} = b^{2}+cf\)

\(a^{2} + b^{2} = ce+cf\)

Because b² and ce are equal and substitute on the right side of equation 1

Using the converse of distributive property  in above equation then we get a new equation. That is,

\(a^{2} +b^{2} = c(f+e)\)

Because distributive property is a(b+c)=a(b+ac)

a² + b² = c²

Because e + f = c²

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The value of z statistics is -1.878,  

Given,

In the question:

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Now, According to the question:

Estimated proportion of return rate;

To find the value of p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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To find two unit vectors that are orthogonal to both j 2k and i -2j 3k, we can use the cross product and normalization techniques. The two unit vectors that satisfy the condition are (2/3)i + (2/3)j + (1/3)k and (2/3)i - (2/3)j - (1/3)k.

First, we need to calculate the cross product of j 2k and i -2j 3k, which is given by:

j 2k × i -2j 3k = (-6) i -3k - (-4)j -6k = (-6) i + 4j -9k

This cross product vector is orthogonal to both j 2k and i -2j 3k, but it is not a unit vector. To find two unit vectors that are orthogonal to both j 2k and i -2j 3k, we need to normalize this cross product vector. We can do this by dividing the cross product vector by its magnitude:

\(||(-6) i + 4j -9k|| = \sqrt{(-6)^2 + 4^2 + (-9)^2) } = 11\\\)

Therefore, the first unit vector that is orthogonal to both j 2k and i -2j 3k is:

\(u1 = (1/11)(-6)i + (4/11)j - (9/11)k\)

To find the second unit vector, we can take the cross product of the first unit vector and either j 2k or i -2j 3k. Let's take the cross product of u1 and j 2k:

\(u1 × j 2k = (-8/11) i - (6/11)j - (2/11)k\)

This vector is also orthogonal to both j 2k and i -2j 3k, but it is not a unit vector. To find the second unit vector, we need to normalize this vector:

\(||(-8/11) i - (6/11)j - (2/11)k|| = \sqrt{(-8/11)^2 + (-6/11)^2 + (-2/11)^2} \\= 2/3\)

Therefore, the second unit vector that is orthogonal to both j 2k and i -2j 3k is:

\(u2 = (2/3)(-8/11)i - (2/3)(6/11)j - (2/3)(-2/11)k \\ = (2/3)i - (2/3)j - (1/3)k\)

Thus, the two unit vectors that are orthogonal to both j 2k and i -2j 3k are (2/3)i + (2/3)j + (1/3)k and (2/3)i - (2/3)j - (1/3)k.

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Answer:

4125000Au

Step-by-step explanation:

my teacher just went over this for our test  

The distance between the star and the sun is 4124966.128 AU and this can be determined by using the trigonometric function.

Given :

The following steps can be used in order to determine the distance between the star and the Sun in astronomical units:

Step 1 - The trigonometric function can be used in order to determine the distance between the star and the Sun in astronomical units.

Step 2 - The sine function can be used to determine the distance.

\(\rm sin\theta=\dfrac{P}{H}\)

where P is the perpendicular and H is the Hypotenuse.

Step 3 - Substitute the known terms in the above expression.

\(\rm sin(0.00001389)=\dfrac{1}{d}\)

Step 4 - Simplify the above expression.

d = 4124966.128

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