If a runner jogs 3 miles west and then jogs 8 miles
north, how far is the runner from her starting point
if she plans to run straight back? Remember to
simplify your answer.

Answer:

352

Step-by-step explanation:

I = PRT  where P is the principle, I is the interest rate, T is the time

I = 275 ( .08) ( 16)

I = 352

Answer:

0

Step-by-step explanation:

0

Answer:

464 $

Step-by-step explanation:

Step-by-step explanation:

70 + 45 = 115

180 - 115 = 65

angle c = 65

use sohcahtoa

cos angle = adjacent

hypotenuse

cos 65 = 2.5

b

b cos 65 = 2.5

use the calc for further answers

hope that helped

Answer:

Step-by-step explanation:

Answer:

The 90% confidence interval is (0.0131, 0.0845).

Step-by-step explanation:

Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Old process:

125 out of 580, so:

[tex]p_O = \frac{125}{580} = 0.2155[/tex]

[tex]s_O = \sqrt{\frac{0.2155*0.7845}{580}} = 0.0171[/tex]

New process:

130 out of 780. So

[tex]p_N = \frac{130}{780} = 0.1667[/tex]

[tex]s_N = \sqrt{\frac{0.1667*0.8333}{780}} = 0.0133[/tex]

Distribution of the difference:

[tex]p = p_O - p_N = 0.2155 - 0.1667 = 0.0488[/tex]

[tex]s = \sqrt{s_O^2+s_N^2} = \sqrt{0.0171^2 + 0.0133^2} = 0.0217[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.0488 - 1.645*0.0217 = 0.0131[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.0488 + 1.645*0.0217 = 0.0845[/tex]

The 90% confidence interval is (0.0131, 0.0845).

Kurt Blixen must invest $85,2296.94.

Given the following data;

To find how much money Kurt Blixen must invest;

Mathematically, simple interest is given by the formula;

[tex]S.I = \frac{PRT}{100}[/tex]

Where:

First of all, we would convert the time in days to years.

Conversion:

365 days = 1 year

90 days = x year

Cross-multiplying, we have;

[tex]365 * x = 90\\\\x = \frac{90}{365}[/tex]

x = 0.247 year

Making P the subject of formula;

[tex]P = \frac{S.I(100)}{RT}[/tex]

Substituting the values into the formula, we have;

[tex]P = \frac{10000(100)}{4.75*0.247}\\\\P = \frac{1000000}{1.1733}[/tex]

P = $85,2296.94

Therefore, Kurt Blixen must invest $85,2296.94.

Find more information here; https://brainly.com/question/9352088

Answer:

1107.

You are rounding up because the number in the tenths slot is over 5.

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]

[tex]\\ \sf\longmapsto 10x=1000[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]

[tex]\\ \sf\longmapsto x=100[/tex]

Answer:

About 54

Step-by-step explanation:

To work backwards from average, you need to multiply the average by the total number of cases, which is 4, since there are 3 current cases/seasons and you want the 4th.

59 * 4 =  236

You then subtract the total home runs that you know of from 236.

236 - 55 - 58 - 69 = 54

To find average, you are adding to the total and then dividing by the number of groups, which is essentially mean (mean is basically the average).

[tex]Hello[/tex] [tex]There[/tex]

The answer is...

[tex]5.[/tex]

[tex]HopeThisHelps!![/tex]

[tex]AnimeVines[/tex]

We know that [tex]\log_a(bc)=\log_a(b)+\log_a(c)[/tex].

Using this rule,

[tex]\log_c(A^5B^3)=\log_c(A^5)+\log_c(B^3)[/tex].

We also know that [tex]\log_c(a^b)=b\log_c(a)[/tex].

Using this rule,

[tex]\log_c(A^5)+\log_c(B^3)=5\log_c(A)+3\log_c(B)[/tex]

Now we know that [tex]\log_c(A)=2,\log_c(B)=5[/tex] so,

[tex]5\cdot2+3\cdot5=10+15=\boxed{25}[/tex].

Hope this helps :)

Answer:

- 5 > b

Step-by-step explanation:

- 9 > 3b + 6

- 9 - 6 > 3b

- 15 > 3b

Divide 3 on both sides,

- 5 > b

Answer:

-5 >b

Step-by-step explanation:

-9 > 3b + 6

Subtract 6 from each side

-9-6 > 3b + 6-6

-15 > 3b

Divide each side by 3

-15/3 > 3b/3

-5 >b

Answer:

-85

Step-by-step explanation:

You can use calculator for this question

Answer:

Blablabka

Step-by-step explanation:

Blablabla

9514 1404 393

Answer:

  -1/2

Step-by-step explanation:

The factor outside parentheses multiplies each term inside.

  5/2(-8/5 +7/5)

  = (5/2)(-8/5) +(5/2)(7/5)

  = -8/2 +7/2 = -1/2

Answer:

What is a linear inequality ? A linear inequality has the same condition as a linear equality, but instead of the equal sign, we have for example this one ≤ wish means less than or equal to.

But what are the condition of a linear equality ? There are many ways of writing linear equations but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y") BUT the variables (x and y) on a linear equation do NOT have Exponents (like the 2 in x²) and square roots,

1. y < 3

Yes, this is a linear inequation. Frequently, the term linear equation refers implicitly to the case of just one variable (here y).

2. x ≥ 6

Yes.

3. x² > - 3

No, remember the rule the variable (here x) must not have exponents.

4. x - 3 > 1/2

Yes.

5. xy + 5 ≤ 7

This one is nice. If both x and y are variables then the answer is no, it's not a linear inequation. Why ?The linear equation is a sum of terms like "Ax" where x is a variable, and A is a number or a constant. On the other hand if x or y was a constant (like e or π), it could be treated as a number and the whole expression would become linear.

You can also have fun and write :

xy ≤ 2

for y > 0 we write:

x ≤ 2/y

x ≤ 2[tex]y^{-1}[/tex]

and then simply say exponents are not allowed so not a linear inequation.

Answer:

Converting into metre (1m=100cm)= 5/100=0.05m.. Converting into km. (1km=100000cm). so 5 cm=5/100000=0.00005km.

Answer:

5cm in meters = 0.05 metre

5cm in kilometres = 0.00005km

Answer:

82

Step-by-step explanation:

1/3( x+9/7) + 3^4

Let x = 12/7

1/3( 12/7+9/7) + 3^4

PEMDAS says parentheses first

1/3( 21/7) + 3^4

1/3(3) +3^4

Then exponents

1/3(3)+81

Then multiply

1+81

82

Is this question complete?

Answer: so there are 666 multiples of 3 between 2 and 2000.

Step-by-step explanation:

the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666

multiples of 3 between {2,2000} = 666-1+1 = 666

1) I think 15 choose (d)

2) The choose (C) -4fg+4g

3) The choose (d) 3xy/2

4) The choose (a) ab/6

5) The choose (C) 2p+4q-6

6)

[tex]\pi {r}^{2} h = 3.14 \times {3}^{2} \times 1.5 = 42.39 {m}^{3} = 42.390 {m}^{3} [/tex]

Point 6 I think there is an error because the unit m must be m³ because it is r² (m²) and h(m) becomes m³.

I hope I helped you^_^

Answer:

x = 2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Pytago:

[tex]2^2 + 4^2 = x^2\\x = \sqrt{2^2 + 4^2} \\x = 2\sqrt{5}[/tex]

Answer:

4.47

Step-by-step explanation:

x²= 2² + 4²

x² = 4 + 16

x²= 20

x = √20

x= 4.47

Answer:

Hello,

Very bad written!!!

Step-by-step explanation:

[tex]e^{1-3x}=e^{4x-3}\\\\1-3x=4x-3\\\\7x=4\\\\\boxed{x=\dfrac{4}{7} }\\[/tex]

Answer:

the answer will be 3.........

Answer:

7

Step-by-step explanation:

It looks like the term is [tex]2^3}x^2}yz^4[/tex]

First simplify

[tex]8x^2}yz^4[/tex]

[y has an exponent of 1 btw]

Then to find the degree of a term, just add up the values of all the exponents

2+1+4=7

I hope this helps!

9514 1404 393

Answer:

  6

Step-by-step explanation:

The number of distinct zeros in the product will be the union of the sets of zeros. Duplicated values are not distinct, so show in the union of sets only once.

  F = {-2, 3, 7}

  G = {-3, -1, 4, 7}

  F∪G = {-3, -2, -1, 3, 4, 7} . . . . . . a 6-element set

The product has 6 distinct zeros.

_____

As you may notice in the graph, the duplicated zero has a multiplicity of 2 in the product.

The tangent vector for the given line is

T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩

On its own, this vector points to a single point in space, (-3, -4, -5).

Multiply this vector by some scalar t to get a whole set of vectors, essentially stretching or contracting the vector ⟨-3, -4, -5⟩. This set is a line through the origin.

Now translate this set of vectors by adding to it the vector ⟨-2, -4, 0⟩, which correspond to the given point.

Then the equation for this new line is simply

L(t) = ⟨-3, -4, -5⟩t + ⟨-2, -4, 0⟩ = ⟨-2 - 3t, -4 - 4t, -5t⟩

The vector parametric equation for the line through the point is [tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex].

Give a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩.

Parametric equations of the line segment are defined by its endpoints.

To find the vector equation of the line segment, we’ll convert its endpoints to their vector equivalents.

Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter).

The vector equation of a line is given by:

[tex]\rm v = r_0+tv[/tex]

Where v is the direction vector and [tex]\rm r_0[/tex] is a point of the line.

The tangent vector for the given line is

T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩

Here,

[tex]\rm r_0 = (-2,-4,0) \ and \ v=(-3, \ -4, \ -5)t\\\\[/tex]

Then,

[tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex]

x = -2-3t, y = -4-4t, and z = 0-5t

To know more about the Parametric equation click the link given below.

https://brainly.com/question/14701215