Please help me with these math problems! I have had so much going on lately and haven't had time to do them
Will give lots of points and make brainliest please help

a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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The Perimeter of rectangle 3cm 5cm is 16 cm.

In geometry, a rectangle is a plane figure of four sides having four angles of 90 degree. A rectangle has different length and breadth.

Some important formulas for rectangle :

Perimeter is define as the distance around all the edges of a shape. In case of rectangle perimeter is the distance of all 4 edges i.e. 2 lengths and 2 breadth .

Thus , perimeter of rectangle = ( 2 × length ) + (2 × breadth)

                                                 = 2 ( length + breadth )

In the given question,

length of rectangle =  3cm

breadth of rectangle = 5cm

therefore, perimeter of rectangle = 2(3+5) = 16cm

Hence, The Perimeter of rectangle is 16 cm.

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Answer:

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

3/5 part of 60 CD's were gifts.

That makes:

Answer:

35.6

Step-by-step explanation:

By the Pythagorean Theorem:

\( {x}^{2} + {91.3}^{2} = {98}^{2} \)

\(x = \sqrt{ {98}^{2} - {91.3}^{2} } = 35.6\)

The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°.

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°.

Por la geometría Euclídea conocemos que un conjunto de ángulos cuando comparten entre cada par de ángulos vecinos comparten el mismo vértice y la misma semirrecta.

De acuerdo con el enunciado, tenemos las siguientes condiciones:

∠AOB + ∠BOC = 125°   (1)

∠BOC + ∠COD = 100°  (2)

Por (1) y (2) tenemos las siguiente identidad:

∠AOB - 25° = ∠COD

∠AOB - ∠COD = 25°

La diferencia entre los ángulos AOB y COD del sistema de tres ángulos consecutivos es igual a 25°. \(\blacksquare\)

En el segundo caso, tenemos el siguiente sistema:

∠AOB = ∠BOC + ∠COD     (3)

∠AOB + ∠BOC - ∠COD = 40°     (4)

Por (3) y (4) tenemos la siguiente identidad:

2 · ∠BOC = 40°

∠BOC = 20°

La medida del ángulo BOC pertenenciente al sistema de tres ángulos consecutivos es igual a 20°. \(\blacksquare\)

Para aprender más sobre ángulos, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/21209282

From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC

The two column proof to show that ∠BAC ≅ ∠DAC is as follows:

Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD

Reason 1: Given

Statement 2: AB ≅ AD

Reason 2:  Definition of isosceles Triangles

Statement 3: ∠1 and ∠2 are right angles

Reason 3: Definition of perpendicular

Statement 4: AC ≅ AC

Reason 4: Reflexive Property

Statement 5: ΔABC and ΔADC are right triangles

Reason 5: Definition of right triangle

Statement 6: ΔABC ≅ ΔADC

Reason 6: HL Congruency

Statement 7: ∠BAC ≅ ∠DAC

Reason 7: CPCTC

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Answer:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

Step-by-step explanation:

An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.

The horizontal asymptote is given as y = 33, so we have:

c = 33

The y-intercept is given as (0, 408), so we have:

b + c = 408

Substituting c = 33, we get:

b + 33 = 408

b = 375

So the function we're looking for is of the form:

\(\bold{f(x) = 375a^{-x}+ 33}\)

To find a, we use the fact that the function passes through P(2, 93):

93 = 375a^(-2) + 33

60 = 375a^(-2)

a^2 = 375/60

a^2 = 6.25

a = \(\sqrt{6.25 } =2.5\)

Therefore, the exponential function that satisfies the given conditions is:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

Given that x is equal to 1 and S is the centroid of the triangle NLQ, NS will have a length of 4 units.

The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition. The centroid of a triangle is the location where the triangle's three medians connect. It may alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.

Here,

We may infer from the centroid's features that it divides each median in a ratio of 2:1.

NS=2SR

7x-3=2(5x-3)

7x-3=10x-6

3x=3

x=1

NS=7x-3

=7*1-3

=4 units

The length of NS will be 4 units as the value of x is 1 and S is the centroid of triangle NLQ.

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Answer:

B

Step-by-step explanation:

y-y1=m(x-x1)

y-1=4(x-4)

Answer:

Point to Tangents on a Circle: Make a line that connects the point to the middle of the circle. Draw the perpendicular bisector for that line. Locate the compass on the centre, adjust its length to reach till the end-point, and then, make an arc through the circle.

Step-by-step explanation:

Answer:

Answer:

True

Step-by-step explanation:

Answer:

Isolate the variable and then use substitution to solve the system of equations.

Step-by-step explanation:

.

Answer:

C. The Texture of the Surface

Step-by-step explanation:

I know it's confusing because of A.. But if you think about what would happen if you were to bounce a ball with a lot of force onto the surface, it wouldn't cause a difference in the friction because it would still just bounce right back up. D. is also not applicable because the weight of the ramp wouldn't matter if the ball is rolling on top of it.

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

(D) I think

Step-by-step explanation:

Lets look at our answer choices; A.

The intervals are not comparable. The shorter bar spans more than 10 years. When it comes to a horizontal axis it doesn't matter how far it expands,just if it's expanded correctly.

B.The intervals are appropriately labeled. There not it goes from 25 to 50 in just in instant few climbs up.

C.The intervals are not comparable, but the data on the graph is not misleading. It is misleading the graphs are incorrectly labeled.

Which brings us to our answer D.The vertical axis does not have an appropriate scale. it goes from 0-25 25-50 and 50-75 then 75-100. that's a short distance for such numbers that are pretty far apart.

I hope I'm right and I hope this helps:)!

Answer: A: the intervals are not comparable. The shorter bar spans more than 10 years

Step-by-step explanation:

edge 2021

According to the information given, the equation of the elipse is:

\(\frac{(x - 1)^2}{25} + \frac{(y - 6)^2}{21} = 1\)

The equation of an elipse of center \((x_0, y_0)\) is given by:

\(\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 1\)

In this problem, the center is (1,6), hence \(x_0 = 1, y_0 = 6\).

There is a vertex at (6,6), hence \(a = 6 - 1 = 5\).

The focus at (-1,6) means that \(c = 1 - (-1) = 2\), hence:

\(c^2 = a^2 - b^2\)

\(b^2 = a^2 - c^2\)

\(b^2 = 5^2 - 2^2\)

\(b^2 = 21\)

The equation is:

\(\frac{(x - 1)^2}{25} + \frac{(y - 6)^2}{21} = 1\)

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Step-by-step explanation:

2^2 x 3 x 7

hope this helps. :))

Answer:

2*2*3*7

Step-by-step explanation:

84=2*2*3*7

thanks for.the points

Answer:

1. 73 degrees   2.  53 degrees

Step-by-step explanation:

1.  In this triangle, the opposite side has length 22, the hypotenuse has length 23.  The trigonometric ratio that uses opposite and hypotenuse is the sine.

The sine = (opposite) / (hypotenuse) so the sine of the angle is 22/23.

Use the inverse sine function to find the angle.

\(\sin^{-1} (22/23) \approx 73^\circ\)

2.  In this triangle, the adjacent side has length 3, the hypotenuse has length 5.  The cosine ratio uses these two sides.

The cosine = (adjacent) / (hypotenuse) so the cosine of the angle is 3/5.

Use the inverse cosine function to find the angle.

\(\cos^{-1}(3/5) \approx 53^\circ\)

The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

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Answer:

option c is the answer for your question

The cube root of -2i,

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

We can represent -2i in polar form as,

r(cosθ + i sinθ)

by computing its magnitude and angle.

The magnitude of -2i is 2

Since the absolute value of any imaginary number is equal to its magnitude.

To find the angle θ,

We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case,

The opposite side is -2 and the adjacent side is 0.

Therefore, we have tanθ = -2/0, which is undefined.

However,

We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.

So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).

Now, we need to find the value of θ/3. Since θ is undefined,

we will represent it as π/2 + 2πn,

where n is any integer.

So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.

Therefore, the cube root of -2i is equal to

⇒  ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]

Now put n = 0

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

This is the final form of the cube root of -2i in the required form.

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Answer:

The inverse represents the temperature F corresponding to a temperature C.

The domain of the inverse function is all real numbers.

194°F

Step-by-step explanation:

Let C= y

y= 5/9 (F - 32),

F= 9/5y + 32

But y= C, hence;

F= 9/5 C +32

The inverse represents the temperature F corresponding to a temperature C.

Given;

F= 9/5 C +32

The domain of the inverse function is all real numbers.

Given C= 90°

F= 9/5 C +32

F= 9/5 (90°) +32

F= 194°F

Answer:

Probability that the temperature below average = 20%

Step-by-step explanation:

Given:

Probability that tomorrow's temperature average = 55%.

Probability that the temperature above average = 25%

Find:

Probability that the temperature below average

Computation:

Probability that the temperature below average = 100% - Probability that tomorrow's temperature average - Probability that the temperature above average

Probability that the temperature below average = 100% - 55% - 25%

Probability that the temperature below average = 100% - 80%

Probability that the temperature below average = 20%

Answer:

See below

Step-by-step explanation:

1. The rule defining the function on the graph:

2. f(x) = |4x + 36|

3. See attachment for the graph

4. Item 4 is not included in the question

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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