Mathematical induction is:

9514 1404 393

Answer:

  f(7) = 154

Step-by-step explanation:

The basic idea is you put 7 where x is and do the arithmetic.

Polynomial evaluation is sometimes easier if you rewrite it to Horner form.

  f(x) = (4x -7)x +7

  f(7) = (4·7 -7)(7) +7 = 21(7) +7 = 147 +7

  f(7) = 154

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Perhaps you want a graph of ...

  x^2/49 +(y +1)^2/4 = 1

This is an ellipse centered at (x, y) = (0, -1) with a major axis in the x-direction of 14, and a minor axis in the y-direction of 4.

Answer:

The zero 1 has a multiplicity of 1.

The zero -2 has a multiplicity of 2.

Hope this clears up any confusion :)

Step-by-step explanation:

Answer:

The zero  1  has a multiplicity of 1.

The zero −2 has a multiplicity of  2 .

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

40 grouped into 5 = 40/5 = 8

Answer:

The required length of AB is 7.28 units.

Answer:

Because it increases the risk of Type 1 error

Step-by-step explanation:

ANOVA is the analysis of the variance .

When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error  .

For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.

This has two disadvantages .

First the procedure is too lengthy  and tediuos.

Second the overall level of significance greatly increases as the number of t- tests increases.

The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.

Answer:

0.30924

Approximately ≈ 0.3092

Step-by-step explanation:

To solve for this question, we use the formula:

z = (x - μ)/σ

where x is the raw score

μ is the sample mean

σ is the sample standard deviation.

From the question,

x is the raw score = 260

μ is the sample mean = population standard deviation = 258

σ is the sample standard deviation

= σ/√N

N = 76 samples

σ = Population standard deviation

= 35/√76

= 4.0146919966

Hence,

z = (x - μ)/σ

= 260 - 258/ 4.0146919966

= 0.4981702212

Approximately = 0.498

We find the Probability using z score table for normal distribution

P(x = z) = P( x = 260)

= P( z = 0.498)

= 0.69076

The probability that a random customer will have more than $260 in his or her wallet is calculated as:

P(x>Z) = 1 - P( z = 0.498)

P(x>Z) = 1 - 0.69076

P(x>Z) = 0.30924

Approximately ≈ 0.3092

Answer:

Below

Step-by-step explanation:

The two given expressions are:

● √(2p-7) = 3

● 7√(3q-1) = 2

We are told to evaluate p+q^2

To do that let's find the values of p and q^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's start with p.

● √(2p-7) = 3

Square both sides

● (2p-7) = 3^2

● 2p-7 = 9

Add 7 to both sides

● 2p-7+7 = 9+7

● 2p = 16

Divide both sides by 2

● 2p/2 = 16/2

● p = 8

So the value of p is 8

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's find the value of q^2

● 7√(3q-1) = 2

Square both sides

● 7^2 × (3q-1) = 2^2

● 49 × (3q-1) = 4

● 49 × 3q - 49 × 1 = 4

● 147q - 49 = 4

Add 49 to both sides

● 147q -49 +49 = 4+49

● 147q = 53

Divide both sides by 147

● 147q/147 = 53/147

● q = 53/ 147

Square both sides

● q^2 = 53^2 / 147^2

● q^2 = 2809/21609

■■■■■■■■■■■■■■■■■■■■■■■■■

● p+q^2 = 8 +(2809/21609)

● p+q^2 = (2809 + 8×21609)/21609

● p+q^2 = 175681 / 21609

● p + q^2 = 8.129

Round it to the nearest unit

● p+ q^2 = 8

Answer:

2m^3 + 3m^2

Step-by-step explanation:

8m^4+12m^3

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

4m

2m^3 + 3m^2

Check

4m(2m^3+3m^2)

8m^4 + 12 m^3

Answer:

15x-9x=6x

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Answer:

6x.

Step-by-step explanation:

15x - 9x = 6x.

Answer:

The answer for this question is 5

Answer:

Tom:

initial money = $ 39000

% increased per annum = 2.9%

money gained per annum = 39000 * 2.9/100 = $1131

Allen:

initial money = $ 39000

% increased per annum = 5.7 %

money gained per annum = 39000 * 5.7/100 = $2223

Allen has $ (2223 - 1131) = $ 1192 more than Tom

Answer:

Complex numbers

Step-by-step explanation:

Given

[tex]a + bi[/tex]

Required

Determine the type of number in that form

Numbers written in [tex]a + bi[/tex] are referred to as complex numbers

Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]

Note that a and b can either integers or non integers and a and be can also be positive or negative

The following are valid examples of complex numbers

[tex]2 + 3i[/tex]

[tex]2.4 - 5i[/tex]

[tex]-3 - i[/tex]

and lots more..

30.8 m

Step-by-step explanation:

Given: [tex]V = 43\:\text{m}[/tex], [tex]V_y = 30\:\text{m}[/tex]

The x-component of vector [tex]\vec{\text{V}}[/tex] is

[tex]V_x = \sqrt{V^2 - V_y^2} = \sqrt{(43)^2 - (30)^2} = 30.8\:\text{m}[/tex]

The x- component of the vector is 30.8meters.

If [tex]v = < a. b >[/tex] be a position vector then the magnitude of vector v is found by  [tex]|v| =\sqrt{a^{2}+b^{2} } }[/tex] , where a and b are the x and y component respectively.

And the direction is equals to the angle formed x- axis or y axis.

According to the given question

We have

Magnitude of the vector, |v| = 43meters

Y- component of the vector, b = 30meters

Since, we know that

[tex]|v| =\sqrt{a^{2} +b^{2} }[/tex]

Substitute the value of |v| = 43 and b = 30 in the above formula of magnitude.

⇒ [tex]43 = \sqrt{a^{2}+30^{2} }[/tex]

⇒ [tex]43 = \sqrt{a^{2}+900 }[/tex]

⇒ [tex]43^{2} =a^{2} + 900[/tex]

⇒ [tex]1849 = a^{2} + 900[/tex]

⇒ [tex]1849-900=a^{2}[/tex]

⇒ [tex]949=a^{2}[/tex]

⇒ [tex]a =\sqrt{949}[/tex]

⇒ [tex]a = 30.8[/tex]

Hence, the x- component of the vector is 30.8meters.

Learn more about magnitude and direction of a vector here:

https://brainly.com/question/13134973

#SPJ2

Answer:

x=3

Step-by-step explanation:

since its a square all sides equal each other

5x-2=x+10

4x -2 =10

4x=12

x = 3

Answer:

  an isosceles right triangle

Step-by-step explanation:

The square of the length of a side can be found from the distance formula:

  d^2 = (x2-x1)^2 +(y2-y1)^2

The square of the length of WX is ...

  WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74

The square of the length of XY is ...

  XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148

The square of the length of YW is ...

  YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74

The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.

Answer:

Hey there!

True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.

Let me know if this helps :)

Answer:

Is answer 22 units sqaure ?

Answer:

D

Step-by-step explanation:

So we have the expression:

[tex]-4-(-7)[/tex]

First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:

[tex]-4-(-7)\\=-4+7[/tex]

When adding on the number line, we move to the right.

Therefore, the correct interpretation is the value 7 digits to the right of -4.

D is the correct answer.

Answer:

D.  the number that is 7 to the right of -4 on the number line

Step-by-step explanation:

interpret -4 - (-7)

=  -4 +7

therefore

the number that is 7 to the right of -4 on the number line

so its D.

Answer:

x = 15.92

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan 53 = x / 12

12 tan 53 = x

x=15.92453

Rounding to the nearest hundredth

x = 15.92

Answer:

15.92

Step-by-step explanation:

Answer:

-7/6

Step-by-step explanation:

-2/3 x 7/4 = -14/12 = -7/6

Answer: -7/6

Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).

Remember that dividing by a fraction is the same thing

as multiplying by the reciprocal of the fraction.

Before multiplying however, notice that we

can cross-cancel the 2 and 4 to 1 and 2.

So multiplying across the numerators and denominator and

remembering our negative in the first fraction, we have -7/6.

Answer:

option a

Step-by-step explanation:

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Answer:

300

Step-by-step explanation:

1100 = 900 [tex]e^{k*20}[/tex]

1.222222 =  [tex]e^{k*20}[/tex]

ln(1.222) = 20k ln(e)

k = ln(1.222)/20

k = .2004

900 = x [tex]e^{15* .20004}[/tex]

900/x =    [tex]e^{15* .20004}[/tex]

 [tex]e^{15*.2004} = 900/x[/tex]

x = 900/   [tex]e^{15*.2004}[/tex]

x = 300

Answer:

20 %

Step-by-step explanation:

The experimental probability is 4/20 = 1/5 = .2 = 20 %

Answer:

The lengths of the sides are 20 cm and 20 cm

Step-by-step explanation:

Given

Perimeter, P = 80cm

Represent the length and width with L and W, respectively;

[tex]P= 2*(L + B)[/tex]

Substitute 80 for P

[tex]80 = 2 * (L + B)[/tex]

Divide through by 2

[tex]40 = L + B[/tex]

[tex]L + B = 40[/tex]

Make L the subject of formula

[tex]L = 40 - B[/tex]

Area of a rectangle is calculated as thus;

[tex]Area = L * B[/tex]

Substitute 40 - B for L

[tex]Area = (40 - B) * B[/tex]

Express this as a function

[tex]A(B) = (40 - B)* B[/tex]

[tex](40 - B)* B = A(B)[/tex]

Set A(B) = 0 to determine the roots

Hence;

[tex](40 - B)* B = 0[/tex]

[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]

[tex]40 = B[/tex] or [tex]B = 0[/tex]

[tex]B = 40[/tex] or [tex]B = 0[/tex]

The maximum area of a rectangle occurs at half the sum of the roots;

So;

[tex]B= \frac{B_1 + B_2}{2}[/tex]

[tex]B= \frac{40+0}{2}[/tex]

[tex]B= \frac{40}{2}[/tex]

[tex]B = 20[/tex]

Recall that [tex]L = 40 - B[/tex]

[tex]L = 40 - 20[/tex]

[tex]L = 20[/tex]

Hence the lengths of the sides are 20 cm and 20 cm

Answer:

3x-2+2x+1+X

3x+2x+x-2+1

6x-1

Answer:

The bearing is N 55.62° W

Step-by-step explanation:

ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots.

It then turns 90° towards the south after one hour.

Still maintain the same speed and direction for two hours.

The bearing is just the angle difference from the ship current location to where it started.

Let the speed be km/h

Distance covered in the first round

= 15*1

= 15km

Distance covered in the second round

=15*2

= 30 km

Angle at C = (90-80)+90

Angle at C = 10+90= 100

Let the distance between the port and the ship be c

C²= a² + b² -2abcos

C²= 15²+30²-2(15)(30)cos 100

C²= 225+900+156.28

C²= 1281.28

C= 35.8 km

Using sine formula

30/sin x= 35.8/sin 100

30/35.8 * sin 100 = sinx

0.838*0.9848= sin x

0.8253= sin x

Sin ^-1 0.8253 = x

55.62° = x

The bearing is N 55.62° W

This question is solved using proportions.

Doing this, we get that he should take 3 packs.

How many calories he burns in the hike?

In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?

45 minutes - 345 calories

360 minutes - x calories

Applying cross multiplication:

[tex]45x = 345*360[/tex]

[tex]x = \frac{345*360}{45}[/tex]

[tex]x = 2760[/tex]

He burns 2760 calories in the hike.

How many calories he wants to replace?

Roughly 1/3, so he have to find one third of 2760, that is:

[tex]\frac{2760}{3} = 920[/tex]

How many packs?

One pack recovers 310 calories, how many packs for 920 calories?

1 pack - 310 calories

x packs - 920 calories

Applying cross multiplication:

[tex]310x = 920[/tex]

[tex]x = \frac{920}{310}[/tex]

[tex]x = 2.97[/tex]

Rounding up, he should take 3 packs.

A similar question is found at https://brainly.com/question/14426926

Answer:

The point of intersection is (0,-2).

Step-by-step explanation:

Equation 1: [tex]y=-4x-2[/tex]

Equation 2 : [tex]-2x+y=-2[/tex]

Plot the lines on the graph

Refer the attached figure

Equation 1: [tex]y=-4x-2 ---- Red[/tex]

Equation 2 : [tex]-2x+y=-2 ---- Blue[/tex]

Point of intersection : A point where both the lines intersect is called point of intersection.

So, Both lines intersect at point (0,-2)

So, Point of intersection is (0,-2)

Hence The point of intersection is (0,-2).