Marco can paddle his canoe at a rate of 6 miles per hour on unmoving water. However, today Marco is canoeing down (with the current), and then back up (against the current), a river that's moving at a rate of 1 mile per hour, so the current affects his rate of speed. If it takes Marco 6 total hours to go x miles downstream and then return to his starting point, how far downstream does he travel?
A) 1.25 miles
B) 2.5 miles
C) 5 miles
D) 17.5 miles

Answer:

3.01

Step-by-step explanation:

To Find :-

SOLUTION :-

=> Monthly salary = $ 37.165/12= $ 3.01

Answer:

The answer is "18.087 years".

Step-by-step explanation:

For upper class:

[tex]\mu=15.45 \ years\\\\\alpha=2.98 \ years\\\\[/tex]

[tex]P(Z \leq 1.2)[/tex] from the standard normal distribution on the table:

[tex]P(Z \leq 1.2) =0.8849\\\\x=z_{\alpha}+\mu\\\\[/tex]

  [tex]=0.8849 \times 2.98 +15.45\\\\ = 2.637002+15.45 \\\\=18.087 \ \ years\\[/tex]

Answer:

[tex]hright =12[/tex]

Step-by-step explanation:

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

The formula to find the area of a triangle is  [tex]A=\frac{1}{2}bh[/tex]  where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.

But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.

[tex]72=\frac{1}{2}(12)(h)[/tex]

[tex]72=6h[/tex]

Here, divide both sides by 6

[tex]12=h[/tex]

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

Hope this is helpful.

Answer:

height = 12

Step-by-step explanation:

.............

Answer:

#########

Step-by-step explanation:

Answer:

no it is not compact in R

Answer:

13/5a - 8/5

Step-by-step explanation:

= 35/15a + 4/15a - 8/5

= 39/15a - 8/5

= 13/5a - 8/5

The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,7/3a - 8/5 +4/15a.

We have to simplify the expression.

We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

=7/3a - 8/5 +4/15a

= 35/15a + 4/15a - 8/5

= 39/15a - 8/5

= 13/5a - 8/5

Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ6

Answer:

the volume = 1152cm^2

Step-by-step explanation:

> The volume of cylinder =4 spheres

> Volume of sphere = v= 4/3πr³

> radius =6cm

volume of 4 spheres =

[tex]v \: = 4 \times \frac{4}{3} \times \pi \times {6}^{3} \\ \\ v = 1152cm {2} [/tex]

Answer:

the unused volume is 18095,57cm cubed

Answer:

Where is the diagram though..

Step-by-step explanation:

9514 1404 393

Answer:

  -∞ < y ≤ 12

Step-by-step explanation:

The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...

  -∞ < y ≤ 12

Step-by-step explanation:

We can rewrite the given equation as

[tex]x^2 + \frac{1}{5}x - \frac{12}{25} = (x + \frac{4}{5})(x - \frac{3}{5})[/tex]

As a check, let's multiply out the factors:

[tex](x + \frac{4}{5})(x - \frac{3}{5}) = x^2 - \frac{3}{5}x + \frac{4}{5}x - \frac{12}{25}[/tex]

[tex]= x^2 + \frac{1}{5}x - \frac{12}{25}[/tex]

and this is our original equation.

The picture of the problem has been attached below :

Answer:

13.5

Step-by-step explanation:

Applying the sine rule to solve for x

SinA /a = SinB / b = SinC/ c

Sin 34 / x = Sin 27/11

Cross multiply :

11 * sin34 = x * sin 27

6.1511219 = 0.4539904x

Divide both sides by 0.4539904

6.1511219/0.4539904 = x

13.549 = x

x = 13.5

Answer:

78i+52j

Step-by-step explanation:

8(9i+2j)-6(-i-6j)

72i+16j+6i+36j

=78i+52j

Answer:

First one , 0.0000805

Step-by-step explanation:

With negative exponents the decimal is moved to the left the amount of the exponent. The spaces are filled with zeros.

With positive exponents the opposite occurs.  The decimal moves to the right.

Answer:

sorry I can't help you sorry

Answer:

c

Step-by-step explanation:

A reflection in the x- axis of the parent function is - [tex]\sqrt{x}[/tex]

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here the shift is 3 units up , then

g(x) = - [tex]\sqrt{x}[/tex] + 3

Answer:

Step-by-step explanation:

This appears to be an SSA application of solving the triangle

We have 2 sides, so we will use the law of cosines

The law of cosines defines for a triangle ABC with side a/b/c with corresponding angles A/B/C

a^2 = b^2+c^2 - 2*b*c * (cos A)

this applies to the other 2 sides

first using the pythagorean theorem we find that BC = sqrt(55)

then we substitute all 3 sides into our equation to find angle A

55 = 64 + 9 - 2*8*3* (cos A)

18 = 2*8*3(cos A)

3/8 = (cos A)

and angle A is approximately 68 degrees

Please check if I'm correct

Answer:

67.98°

Step-by-step explanation:

Given 2 sides, you can find the missing angle of a right triangle using basic trig functions.

Since Cos∅=adjacent/ hypotenuse, we can use the adjacent side to the angle, 3 and they hypotenuse, 8 in the ratio by doing 3/8. This is 0.375. Then we use the inverse cosine function to find the angle. This gives 67.98°

Or

Cos∅=0.375

Cos^-1= 67.98

Answer:

The correct answer is = 15.

Step-by-step explanation:

Formula:

The sum of the first n terms of an arithmetic progression with first term a and constant difference d is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d[/tex]

using this formula in this problem

Solution:

The sum of the first ten terms is

[tex]S_{10}=\dfrac{10}{2}[2a+(10-1)d[/tex]

[tex]S_{10}=5(2a+9d)[/tex]

The sum of the 20th, 21st, and 22nd terms is three times the 21st term:

[tex]3a_{21}=3(a+(21-1)d)[/tex]

[tex]3a_{21}=3(a+20d)[/tex]

[tex]3a_{21}=3a+60d[/tex]

The problem then tells us

[tex]S_{10}=3a_{21}[/tex]

[tex]10a+45d=3a+60d[/tex]

[tex]7a=15d[/tex]

there are only positive integers and the first term a is less than 20 as given. Since 7 and 15 have no common factor, the only explanation of the requirements is a = 15 and d = 7. So the progression is

then, 15, 22, 29, 36, ...

The problem says to find the number of terms n for which the sum is 960:

putting value in the formula

[tex]30n+7n^{2}-7n=1920\\7n^{2}+23n-1920=0[/tex]

solving quadratic will give n = 15

thus, the correct answer is 15.

Answer:

P

Step-by-step explanation:

Since we are looking at an f(x) graph where x is time and y is distance. Any time a graph is sloping we are either moving closer or further from the school. When there is a horizontal line, this means that there is no change in distance, thus Liam is waiting/standing still.

Answer:

a. P

Step-by-step explanation:

i took the test :)

Answer: (f-g)(x) = - 5^x + 3x - 2

Step-by-step explanation:

if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)

(f-g)(x) = -5^x - 4 - (-3x - 2)

(f-g)(x) = -5^x - 4 + 3x + 2

(f-g)(x) = - 5^x + 3x - 2

Answer:

A sample of 17 must be selected.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation from a previous study is 4 hours.

This means that [tex]\sigma = 4[/tex]

How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?

A sample of n is required.

n is found for M = 2. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = 2.054\frac{4}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 2.054*4[/tex]

Simplifying both sides by 2:

[tex]\sqrt{n} = 2.054*2[/tex]

[tex](\sqrt{n})^2 = (2.054*2)^2[/tex]

[tex]n = 16.88[/tex]

Rounding up:

A sample of 17 must be selected.

Answer:

(10, 10 )

Step-by-step explanation:

Given the 2 equations

2x - y = 10 → (1)

y = [tex]\frac{1}{2}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)

2x - ([tex]\frac{1}{2}[/tex] x + 5) = 10 ← distribute parenthesis on left side by - 1

2x - [tex]\frac{1}{2}[/tex] x - 5 = 10

[tex]\frac{3}{2}[/tex] x - 5 = 10 ( add 5 to both sides )

[tex]\frac{3}{2}[/tex] x = 15 ( multiply both sides by 2 to clear the fraction )

3x = 30 ( divide both sides by 3 )

x = 10

Substitute x = 10 into (2) and evaluate for y

y = [tex]\frac{1}{2}[/tex] (10) + 5 = 5 + 5 = 10

solution is (10, 10 )

Answer:

Step-by-step explanation:

Since, CD is an altitude, ∠CDB will be a right angle.

m∠CDB = m∠CDA = 90°

By applying triangle sum theorem in ΔABC,

m∠CAB + m∠CBA + m∠ACB = 180°

20° + m∠CBA + 90° = 180°

m∠CBA = 180° - 110°

             = 70°

Therefore, m∠CBD = 70°

By applying triangle sum theorem in ΔBCD,

m∠BCD + m∠CDB + m∠DBC = 180°

m∠BCD + 90° + 70° = 180°

m∠BCD + 160° = 180°

m∠BCD = 20°

m∠CAD = m∠A = 20°

m∠ACD = 90° - m∠BCD

             = 90° - 20°

m∠ACD = 70°

Answer:

b. mutually exclusive.

Step-by-step explanation:

The given description is an illustration of mutually exclusive events.

Take for instance, when you roll a die;

It is impossible to have an outcome of 2 and 6 at the same time; these means that 2 and 6 are mutually exclusive.

In a nutshell, when two or more sates of events/states of nature can not happen at the same time; such events/states of nature are mutually exclusive.

Answer:

$7.13

Step-by-step explanation:

Given data

Cost of halibut per pound= $19

Let us convert pound to ounces first

1 pound = 16 ounces

Hence 16 ounces will cost $19

           6 ounces will cost x

cross multiply we have

x= 19*6/16

x=114/16

x=$7.13

Hence 6 ounces will cost $7.13

Answer:

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Step-by-step explanation:

The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385

At the null hypothesis, we test if the mean is of $39,385, that is:

[tex]H_0: \mu = 39385[/tex]

At the alternative hypothesis, we test if the mean differs from this, that is:

[tex]H_1: \mu \neq 39385[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

39385 is tested at the null hypothesis:

This means that [tex]\mu = 39385[/tex]

A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.

This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]

[tex]z = 2.72[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.

Looking at the z-table, Z = -2.72 has a p-value of 0.0033

2*0.0033 = 0.0066

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Answer:

The numerical values of the circumference and area of the circle are equal.

Answer:

9x

Step-by-step explanation:

Quick maths, I dont really have an explaination pls give me brainliest ;-;.

Answer:

The standard error of your estimate of the average height in the city is 0.5 inches.

Step-by-step explanation:

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.

You begin by collecting the heights of a random sample of 196 people from the city.

This means that [tex]n = 196[/tex]

The standard deviation of the heights in your sample is 7 inches.

This means that [tex]\sigma = 7[/tex]

The standard error of your estimate of the average height in the city is

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5[/tex]

The standard error of your estimate of the average height in the city is 0.5 inches.

Answer:

36/55

Step-by-step explanation:

Total 55 persons, total females 36.

The probability that the selected person is a female from the given table is gotten as; 0.65

From the given table we see that;

Males under 35 years = 8

Females under 35 years = 18

Males 35 years and older = 11

Females 35 years and older = 18

Thus;

Total number of people = 8 + 18 + 11 + 18

Total people = 55

Thus, probability that the selected person is a female is;

P(female) = (18 + 18)/55

P(female) = 36/55

P(female) = 0.65

Read more about Probability at; https://brainly.com/question/251701