Find the product in simplest form. (3√2) ( √10) 3 √10 3 √20 6 √5 6 √10

Answer:

24.83 degrees.

Step-by-step explanation:

In the diagram, Bugs Bunny was initially at point A 42 meters below ground and dug diagonally 100 meters to point B.

We are to determine the angle of elevation, [tex]\angle BAX[/tex] of his climb.

Now, [tex]\angle BAX=\angle ABC$ (Alternate Angles)[/tex]

Using Trigonometric ratios

[tex]\sin B=\dfrac{AC}{AB} \\\sin B= \dfrac{42}{100}\\\\B=\arcsin \dfrac{42}{100}\\\\B=24.83^\circ[/tex]

The angle of elevation of Bugs Bunny's climb is 24.83 degrees. (correct to 2 decimal places).

Answer:

3(20 - y - 3)

Explanation:

If you expand it:

3 · 20 = 30

3 · -y = -3y

3 · -3 = -9

Combine them altogether to get:

30 - 3y - 9

exact form

5/2

decimal form

2.5

mixed number form

2 1/2

[tex]answers \\ a. \: \: 0 \\ b. \: \: \frac{ - 63}{8} \\ c. \: \: {c}^{3} - {5c}^{2} \\ d. \: \: {t}^{3} + 25t + {10t}^{2} \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

The mean absolute deviation (MAD) of the dataset is 33.333.

Step-by-step explanation:

The mean absolute deviation (MAD) of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

These are the steps to calculate the mean absolute deviation.

Step 1: Calculate the mean.

[tex]Mean = \frac{20+90+25+100+85+30}{6} =\frac{175}{3}\approx58.333[/tex]

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

[tex]|20-\frac{175}{3} |=\frac{115}{3}\\\\|90-\frac{175}{3} |=\frac{95}{3}\\\\|25-\frac{175}{3} |=\frac{100}{3}\\\\|100-\frac{175}{3} |=\frac{125}{3}\\\\|85-\frac{175}{3} |=\frac{80}{3}\\\\|30-\frac{175}{3} |=\frac{85}{3}[/tex]

Step 3: Add those deviations together.

[tex]\frac{115}{3}+\frac{95}{3}+\frac{100}{3}+\frac{125}{3}+\frac{80}{3}+\frac{85}{3}=\frac{600}{3}=200[/tex]

Step 4: Divide the sum by the number of data points.

[tex]MAD=\frac{200}{6} =33.333[/tex]

Answer: 231.6

Step-by-step explanation:

Answer:

231.6 ft³

Step-by-step explanation:

volume of sphere:

V=[tex]\frac{4}{3} \pi r^{3}[/tex]

radius=4.8

plug in:

[tex]\frac{4}{3} \pi (4.8)^{3}[/tex]

463.246686328

Volume of Hemisphere HALF of Volume of Sphere:

[tex]\frac{463.246686328}{2}[/tex] =231.623343164

≈231.6 ft³

Answer:

p(x)=19x+15

Step-by-step explanation:

Distribution property

- you should end up with p(x)=(25x-6x+15)(x)

- 25x minus 6x equals 19x

- form there you distribute the (x) and it will square 19x and multiply with 15

- end answer should be p(x)=19x²+15x

- simply by factoring the ² and 15x and you should get 19x+15

Answer:

A. p(x) = 19x - 15

Step-by-step explanation:

→Set it up, like so:

[tex](25x)-(6x+15)[/tex]

[tex]25x - 6x-15[/tex]

→Add like terms (25x and -6x):

[tex]19x - 15[/tex]

Answer:

3

Step-by-step explanation:

2*1+1

2+1

3

how this helps :)

Answer:

Scores of students:

Mean: 34.3

Mode: no mode

No. of students:

Mean: 8.3

Mode: no mode

Step-by-step explanation:

(for scores of students)

6, 30, 35, 40, 45, 50

Mean: 6 + 30 + 35 + 40 + 45 + 50 = 206/6 = 34.3

Mode: there are no mode in the set of data.

(for No. of students)

4, 5, 6, 8, 12, 15

Mean: 4 + 5 + 6 + 8 + 12 + 15 = 50/6 = 8.3

Mode: no mode

Answer:

Step-by-step explanation:

When we propose an hypothesis, it is either true or false. The same goes for a proposition.

The required objective here is to determine the truth value in the following proposition.

(a) The integer 24 is prime.

(b) Is the integer 3​15​ even?

(c) The sum of 3 and 4 is 12.

(d) -4 ∈ Ζ

From the first option:

(a) The integer 24 is prime.

The sentence is a proposition but the truth value is FALSE because a prime number is a number that can only be divide by 1 and itself but in the case of 24, Its factors include  1,2,3,4,6,8,12 and 24 which make 24 to falsify the proposition of being  a prime number.

(b) Is the integer 3​15​ even?

This option is not a proposition but rather a question since it has a question mark, however, 315 is an odd number since it is not divisible by 2.

( c)  The sum of 3 and 4 is 12.

This is a proposition and the truth value is FALSE

The sum of 3+4 = 7  ; Hence; 7 ≠ 12

(d)   -4 ∈ Ζ

This is a proposition and the truth value is TRUE.

-4 ∈ Ζ  is read as ( minus four is an integer  (∈)  of Z )

Yes, this is a proposition and its Truth value is TRUE , since  minus four is an integer  (∈)  of Z

Answer:

x=2 or x=-2

Step-by-step explanation:

x2−4=0

Step 1: Add 4 to both sides.

x2−4+4=0+4

x2=4

Step 2: Take square root.

x=±√4

x=2 or x=−2

Answer:

The value that will create an equation with no solutions is 5x.

Step-by-step explanation:

No solution would mean that there is no answer to the equation. It is impossible for the equation to be  true no matter what value we assign to the variable.

To create a no solution equation, we can need to create a mathematical statement that is always false.  To do this, we need the variables on both sides of the equation to cancel each other out and have the remaining  values to not be equal.

Use distributive property on the left side first.

[tex]3(x - 4) = [blank] - 2x +7\\\\3x-12=5x - 2x +7\\\\3x-12=3x+7\\\\3x-12+12=3x+7+12\\\\3x=3x+19\\\\3x-3x=3x+19-3x\\\\0=19[/tex]

Notice that we combined like terms first and then eliminated the variable from one side. When that  happened, the variable on the other side was eliminated as well, giving us a false result.

Since zero does not equal nineteen, we know we have an equation with no solution.

Answer:

y=7/3

Step-by-step explanation:

Answer:

7/3 = y

Step-by-step explanation:

-5+8=-3y+10

3 = -3y + 10

Subtract 10  from each side

3- 10 = -3y +10-10

-7 = -3y

Divide each side by -3

-7/-3 = -3y/-3

7/3 = y

Answer:

it depends on how many red marbles are there

Step-by-step explanation:

is there any green or orange or yellow?

Answer:1 over 3

Step-by-step explanation:

Answer:

  104 inches

Step-by-step explanation:

No window dimensions are given. We might assume that the shape of the window can be defined by these coordinates:

   (18,64), (28,40), (18,16), (8,40)

A graph of the points reveals the window to be a rhombus, so we can figure the length of one side to determine the lengths of all sides.

On edge of the window will have a length determined by the distance formula:

  d = √((x2 -x1)^2 +(y2 -y1)^2)

For (x1, y1) and (x2, y2) as (8, 40) and (18, 64), the edge length is ...

  d = √((18 -8)^2 +(64 -40)^2) = √(10^2 +24^2) = √676

  d = 26 . . . . . the length of one of the four edges

The total length of the four window edges is ...

  4 × 26 = 104

104 inches of tape are needed.

Answer:

does NOT have right angles at the corners

Step-by-step explanation:

we are given that the sides of a table are 27" and 36" long.

If we assume the table to be rectangular, then by Pythagorean formula, we can find the diagonal and compare it to the 40" that we are given.

(refer to attached)

diagonal² = 27² + 36²

diagonal² = 27² + 36²

diagonal² = 2025

diagonal = √2025

diagonal = 45 inches

because the diagonal that we found is not the same as the 40" that was given, we can conclude that the table is not a rectangle (i.e does not have right angles at the corners)

Answer:

Thirty Residents Who Live Within a 2-Miles Radius Of Natasha’s School

Step-by-step explanation:

Answer:

The correct answer is "thirty residents who live within a 2-miles radius of Natasha’s school." or (D)

Step-by-step explanation:

teehee

Answer:

D

Step-by-step explanation:

You can plug in the given x and y values into the equations and see which one works for both of them.

D works for both of them:

5 = 5/4(4)

0 = 5/4(0)

Answer:

y=5/4x

Step-by-step explanation:

I just took the TSI2 and it says its correct

Answer: A.

The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

Explanation: a system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column. Since every column of the coefficient matrix is a pivot column, none of the leading coefficients are in the rightmost column of the augmented matrix. Therefore the rightmost column of the augmented matrix cannot be a pivot column and the system must be consistent.

Answer: C-13 = -2   C = 11

Step-by-step explanation:

difference means subtraction.

the wording "is" implies the answer to the equation = -2

let C be a variable

C - 13 = -2

C = -2 + 13      solve for C by getting C by itself

C = 11

The word sentence as an equation will be as C - 13 = -2, then the solution is 11.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have been given that  difference between a number c and 13 is −2.

Here the difference means subtraction.

Assume C be a variable;

C - 13 = -2

C = -2 + 13      

Now solve for C by getting C by itself;

C = 11

Therefore, the word sentence as an equation will be as C - 13 = -2, then the solution is 11.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Answer:

Hospital A is less likely to record an average birth weight of at least 3400 g.

Step-by-step explanation:

Applying the Central Limit Theorem and the normal probability distribution.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Applying the Central Limit Theorem to find the z-score.

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

Probability of an average birth weight of at least 3400 g?

This probability is 1 subtracted by the pvalue of Z when X = 3400.

Mean is 3100, so [tex]\mu = 3100[/tex]

Suppose s is the same for both.

Hospital A:

n = 50. So

[tex]Z = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

[tex]Z = \frac{3400 - 3100}{\frac{s}{\sqrt{50}}[/tex]

[tex]Z = \frac{300\sqrt{50}}{s}[/tex]

Hospital B:

n = 10. So

[tex]Z = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

[tex]Z = \frac{3400 - 3100}{\frac{s}{\sqrt{10}}[/tex]

[tex]Z = \frac{300\sqrt{10}}{s}[/tex]

Comparasion:

[tex]\frac{300\sqrt{50}}{s} > \frac{300\sqrt{10}}{s}[/tex]

This means that hospital A has the higher z-score.

The higher the z-score, the higher the pvalue.

So, for A, 1 subtracted by the pvalue of Z when give a lower value than the 1 subtracted by the pvalue of Z in b. This means that hospital A is less likely to record an average birth weight of at least 3400 g.

Answer: y=-4/3x+22/3

Step-by-step explanation:

the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line

y=-4/3x+b

if you put in the x and y values

18=-4/3*-8+b

18-32/3=b

b=22/3

y=-4/3x+22/3

Answer:

B 3(20-y-3)

Step-by-step explanation:

This is the answer u lookin for ✌

Answer: The clubs goal is to raise  $436.

Step-by-step explanation:

175%  * x  = 763     where x is the goal  

1.75 *x  = 763

1.75x = 763

x= 436

[tex]\$436[/tex]

A percentage is a number or ratio expressed as a fraction of [tex]\boldsymbol{100}[/tex]

Percentage of amount raised for charity [tex]=175\%[/tex]

Amount raised for charity [tex]=\$763[/tex]

Therefore,

[tex]175\%[/tex] of amount of goal [tex]=\$763[/tex]

    [tex]\frac{175}{100}\times [/tex] Amount of goal  [tex]=\$763[/tex]

Amount of goal [tex]=\frac{76300}{175} [/tex]

                          [tex]=\boldsymbol{\$436}[/tex]

For more information:

https://brainly.com/question/2724587?referrer=searchResults

Answer:

20

Step-by-step explanation:

When we use Pythagorean Theorem we get x² + 21² = 29² which means x = 20.

Answer:

B: 20

Step-by-step explanation:

By the pythagorean thereom, x^2+21^2=29^2. Solving gives X^2=29^2-21^2=400, so X=20.

Answer:

h=7.65

Step-by-step explanation:

h=k√p

k=h/√p

k=5.4/√1.44

k=4.5

h=4.5√p

when p=2.89

h=4.5√2.89

h=7.65

Answer:

H = 7.65

I hope it helps

[tex]h \: = \sqrt{p} \\ h \: = k \sqrt{p} .....(1) \\ when \: h \: = 5.4 \: p = 1.44 \\ 5.4 = k \: \sqrt{1.44} [/tex]

[tex]5.4 = 1.2k \\ divide \: both \: sides \: by \: 1.2 \\ k \: = 4.5[/tex]

[tex]h \: = 4.5 \sqrt{p} = \: formula \: connecting \: h \: and \: p \\ from \: equation \: .....(1) \\ when \: p \: = 2.89 \: h = \\ when \: p \: = 2.89 \: h \: = \\ h \: = 4.5 \sqrt{2.89} \\ h = [/tex]

[tex]h \: = 4.5 \sqrt{2.89} \\ h = 4.5 \times 1.7 \\ h \: = 7.65[/tex]

Answer:

the dimensions in the drawing are 16.25 inches by 6.375 inches

Step-by-step explanation:

The first thing is to use the same unit on the scale, that is, they tell us that the scale is 1:40 but that scale cannot be applied because they are different units of measurement.

The answer is preferable to give it in inches because it is more adapted to the measurements in a drawing, therefore we will pass the scale all in inches, knowing that 1 foot is 12 inches:

40 feet * 12 inches / 1 foot = 480 inches, therefore the scale is 1: 480

Now, if we pass the dimensions that give us inches, we are left with:

650 feet * 12 inches / 1 foot = 7800 inches

255 feet * 12 inches / 1 foot = 3060 inches

Now applying the scale:

7800/480 = 16.25

3060/480 = 6.375

It means that the dimensions in the drawing are 16.25 inches by 6.375 inches

Answer:

work is shown and pictured

Answer:

[tex]Area = 140[/tex]

Step-by-step explanation:

Given

R(6, 10)

Q(-9, 5)

S(2, -10)

Required

Area of triangle RQS

The are of RQS is calculated using the following formula;

[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]

Where x and y represent the axis of the given coordinates;

Given that R(6, 10);

[tex]R_x = 6 ; R_y = 10[/tex]

Given that Q(-9, 5);

[tex]Q_x = -9 ; Q_y = 5[/tex]

Given that S(2, -10);

[tex]S_x = 2 ; S_y = -10[/tex]

By Substituting these values in the given formula;

[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]

[tex]Area = \frac{1}{2} [6(-10 -5) + -9(10 - (-10)) + 2(5 - 10)][/tex]

[tex]Area = \frac{1}{2} [6(-15) + -9(10 + 10)) + 2(-5)][/tex]

[tex]Area = \frac{1}{2} [-90 + -9(20)) - 10][/tex]

[tex]Area = \frac{1}{2} [-90 -180 - 10][/tex]

[tex]Area = \frac{1}{2} [-280][/tex]

The expression |-280| means absolute value of -280 and the value is 280

[tex]Area = \frac{1}{2} [-280][/tex]

[tex]Area = \frac{1}{2}* 280[/tex]

[tex]Area = 140[/tex]

Hence, the area of the triangle is 140

Answer:

a) A sample size of 5615 is needed.

b) 0.012

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

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

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

99.5% confidence level

So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].

(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.

This is n for which M = 0.015.

We have that [tex]\pi = 0.2[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}[/tex]

[tex]0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}[/tex]

[tex]\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}[/tex]

[tex]n = 5615[/tex]

A sample size of 5615 is needed.

(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

Now [tex]\pi = 0.12, n = 5615[/tex].

We have to find M.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 2.81\sqrt{\frac{0.12*0.88}{5615}}[/tex]

[tex]M = 0.012[/tex]