An instructor of a biology class believes the average final exam score for his biology class was more than 75. Suppose a sample of 25 was taken and the sample mean he observed was 78.48 and a standard deviation of 5 points. What is the value of the test statistic?Report your answer to 2 decimal places.

Answer:

88

Step-by-step explanation:

Mean of five test = 85

Sum of five tests = 85*5 = 425

Mean of first three test =83

Sum of first three test = 83 * 3 = 249

Sum of 4th and 5th test scores = 425 - 249

                                                   = 176

Mean of his 4th and 5th test = 176/2 = 88

The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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Answer:

The mean would be 45. But since that's not a option it might be C. The value of the mean would remain the same at about 46.

Step-by-step explanation:

Answer:

  (c)  The value of the mean would remain the same at about 46.

Step-by-step explanation:

You want to know how the mean of the given list would change if a value of 45 were added to the list.

The mean is the sum, divided by the number of items being summed. The calculator shows the mean of the given numbers is about 46 1/6.

This means the sum is (46 1/6)·12 = 554.

Adding 45 to the list would make the sum be 599, and the mean would change to ...

  599/13 ≈ 46.08

The value of the mean remains the same at about 46.

__

Additional comment

The added value is 46 1/6 -45 = 1 1/6 below the mean. Adding this value changes the mean by (-1 1/6)/13 = -7/78 ≈ -0.0897, so the nearest integer to the mean does not change.

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

84%

Step-by-step explanation:

84 out of 100 = 84%

Answer:

i am so sorry if its wrong

Each of the triangles making up the sides and base have a base of 8 cm and a height of 6.9 cm. Then the area of the pyramid is that of 4 such triangles.

 A = 4×(1/2)×b×h

 A = 2×(8 cm)×(6.9 cm)

 A = 110.4 cm²Step-by-step explanation:

Answer:

B. For every dollar the admission price increases, 50 fewer people will attend.

Explanation:

The given equation is:

The slope of the equation = -50.

Thus, the slope of this equation means that for every dollar the admission price increases, 50 fewer people will attend.

Hello!

Answer:

\(\huge\boxed{\frac{12}{20}}\)

To find the numerator and denominator, we can set up a proportion where:

x = denominator

x -8 = numerator

\(\frac{3}{5} = \frac{x-8}{x}\)

Cross multiply:

\(3(x) = 5(x - 8)\)

\(3x = 5x - 40\)

Simplify:

\(3x - 5x = -40\\\\-2x = -40\\\\x = 20\)

Substitute in this value of x to find the numerator and denominator:

\(\frac{(20) - 8}{(20)} = \frac{12}{20}\)

Hope this helped you! :)

\( \LARGE{ \boxed{ \rm{ \orange{ Solution:}}}}\)

Let the numerator be x

It is given that,

Then,

⇛ Denominator- 8 = x

⇛ Denominator = x + 8

According to condition -2)

⇛ Fraction = 3/5

⇛ x/x + 8 = 3/5

Cross multiplying,

⇛ 3(x + 8) = 5x

⇛ 3x + 24 = 5x

⇛ 24 = 5x - 3x

⇛ 24 = 24

Flipping it out,

⇛ 2x = 24

⇛ x = 24/2 = 12

Then,

⇛ x + 8 = 12 + 8 = 20

\( \large{ \therefore{ \boxed{ \rm{ \pink{Then, \: the \: fraction = \dfrac{12}{20} }}}}}\)

━━━━━━━━━━━━━━━━━━━━

The following information about the mean and standard deviation has been provided:

ц=25, б=3,n=20

We need to compute Pr(X⁻≥26.3).

The corresponding z-value needed to be computed is:

\(Z=\frac{X-u}{o/\sqrt{n} } =\frac{26.3-25}{3/\sqrt{20} }=1.9379\)

Therefor, we get that

\(Pr(X\geq 26.3)=Pr(Z\geq \frac{26.3-25}{3/\sqrt{20} } )=Pr(Z\geq 1.9379)\\=1-0.9737=0.026\)

Answer:

1/6 or 6/36

Step-by-step explanation:

Given the qualifications, there are six qualifying combinations out of the 36 combinations, which simplified, is 1 out of 6.

Answer:

you need more than one point to find the slope of a line?

Step-by-step explanation:

The distance between fours points are calculated with a function 'distance'.

Given four real numbers representing cartesian coordinates: (x1,y1),(x2,y2). write a function distance(x1, y1, x2, y2) to compute the distance between the points (x1,y1) and (x2,y2).

Read four real numbers and print the resulting distance calculated by the function

import math

def calculateDistance(x1,y1,x2,y2):

    dist = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)

    return dist

distance = calculateDistance(2,4,6,8)

print distance

Therefore, the above program is used to calculate the distance between points and print the result.

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Answer:

B

Step-by-step explanation:

Using a minor key within a song is usually to make it more sad or negative in emotion, though with this question the fast tempo should already rule out A because it is quite the opposite to laziness.

Answer: NO

Step-by-step explanation:

This is not a function, since there are multiple outputs for ONE input.

Answer:

no

Step-by-step explanation:

to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.

Answer:

yes its true

Step-by-step explanation:

hope i help have a fant

Answer:

\(\sin(2u)=-\dfrac{24}{25}\)

\(\cos(2u)=\dfrac{7}{25}\)

\(\tan(2u)=-\dfrac{24}{7}\)

Step-by-step explanation:

Given sin(u) = -3/5, use the trigonometric identity sin²θ + cos²θ = 1 to find cos(u):

\(\begin{aligned}\sin^2(u)+\cos^2(u)&=1\\\\\left(-\dfrac{3}{5}\right)^2+\cos^2(u)&=1\\\\\dfrac{9}{25}+\cos^2(u)&=1\\\\\cos^2(u)&=1-\dfrac{9}{25}\\\\\cos^2(u)&=\dfrac{16}{25}\\\\\cos(u)&=\dfrac{4}{5}\end{aligned}\)

As u is in the interval 3π/2 < u < 2π, the angle is in quadrant IV of the unit circle. In quadrant IV, cos is positive and sin is negative. Therefore:

\(\sin(u)=-\dfrac{3}{5} \qquad \cos(u)=\dfrac{4}{5}\)

Calculate tan(u) by using the identity tanθ = sinθ/cosθ:

\(\tan(u)=\dfrac{-\frac{3}{5}}{\frac{4}{5}}=-\dfrac{3}{4}\)

\(\boxed{\begin{minipage}{5 cm}\underline{Double Angle Identities}\\\\$\sin (2\theta)=2\sin \theta \cos \theta $\\\\$\cos (2\theta)=\cos^2\theta-\sin^2\theta$\\\\$\tan (2\theta)=\dfrac{2\tan\theta}{1 -\tan^2\theta}$\\\end{minipage}}\)

Use the double angle identities to find sin(2u), cos(2u) and tan(2u).

\(\hrulefill\)

\(\begin{aligned}\sin (2u)&=2\sin u \cos u\\\\&=2\left(-\dfrac{3}{5}\right) \left(\dfrac{4}{5}\right)\\\\&=-\dfrac{24}{25}\end{aligned}\)

\(\hrulefill\)

\(\begin{aligned}\cos (2u)&=\cos^2u - \sin^2u\\\\&=\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2\\\\&=\dfrac{16}{25}-\dfrac{9}{25}\\\\&=\dfrac{7}{25}\end{aligned}\)

\(\hrulefill\)

\(\begin{aligned}\tan (2u)&=\dfrac{2\tan(u)}{1 -\tan^2(u)}\\\\&=\dfrac{2\left(-\frac{3}{4}\right)}{1 -\left(-\frac{3}{4}\right)^2}\\\\&=\dfrac{-\frac{3}{2}}{1 -\frac{9}{16}}\\\\&=\dfrac{-\frac{3}{2}}{\frac{7}{16}}\\\\&=-\dfrac{3}{2} \cdot \dfrac{16}{7}\\\\&=-\dfrac{48}{14}\\\\&=-\dfrac{48\div2}{14\div2}\\\\&=-\dfrac{24}{7}\end{aligned}\)

Answer:

\(x = 7\)

Step-by-step explanation:

Given

The attached figure

Required

Find x

Since both shapes are similar, then:

\(LM : KN = RV : SP\)

This gives:

\(4x + 4 : 7x - 9 = 48 : 60\)

As fraction:

\(\frac{4x + 4 }{ 7x - 9} = \frac{48 }{ 60}\)

Simplify:

\(\frac{4x + 4 }{ 7x - 9} = \frac{4 }{ 5}\)

Cross Multiply:

\(5(4x + 4) = 4(7x - 9)\)

\(20x + 20 = 28x - 36\)

Collect Like Terms

\(28x - 20x = 20 + 36\)

\(8x = 56\)

\(x = 7\)

The statement(B)The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI is true .

The slope of  a line passing through two points A(x₁,y₁) and B(x₂,y₂) is calculated using the formula

slope = (y₂-y₁)/(x₂-x₁)

In  the question ,

given that ΔDEF and ΔGHI are similar ,

and hypotnuse of ΔDEF is DF and hypotnuse of ΔGHI is GI ,

we can see that the coordinates of D = (-9,6) , F = (-6,4) and

coordinates of G = (-3,2) and I = (6,-4)

Using slope formula for line DF

we get ,

slope = (4-6)/(-6 - (-9))

= -2/(-6+9)

= -2/3        ...(i)

Using slope formula for line GI

we get ,

slope = (-4-2)/(6 - (-3))

= -6/(6+3)

= -6/9

In simpler form

= -2/3         ...(ii)

From equation (i) and equation (ii) , we can see that slope of hypotnuse of both the triangles are equal .

Therefore , only statement(B)The slope of the hypotenuse of triangle DEF is equal to the slope of the hypotenuse of triangle GHI ,  is true .

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Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:

a-) -√2 / 2.

Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.

In this problem, the function is:

xcos(y) = 2.

The derivative is relative to t, applying the product rule, as follows:

\(\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0\)

\(\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}\)

Since dx/dt=−2, we have that:

\(\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}\)

When y = π/4, x is given by:

xcos(y) = 2.

\(x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}\)

Hence:

\(\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}\)

\(\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}\)

Since cot(pi/4) = 1, we have that:

\(\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}\)

Which means that option a is correct.

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Answer:

y = x -6

Step-by-step explanation:

First find the slope

m= ( y2-y1)/(x2-x1)

   = (0- -6)/(6-0)

   =( 0+6)/(6-0)

   = 6/6

   = 1

The slope is 1 and the y intercept is -6

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = x -6

Answer:

the answer is C

Step-by-step explanation:

y = x -6

Respuesta: Es más probable sacar un mango.

Explicación:

La probabilidad se refiere a la posibilidad de que un evento occura y no otro. En el caso que se describe, la probabilidad de sacar cada fruta puede ser calculada dividiendo el total de cada fruta en el número de frutas totales:

Probabilidad de sacar un mango:

\(\frac{cantidad de mangos}{cantidad de frutas en la canasta}\) =  \(\frac{30}{50}\)  =\(0.6\)

Probabilidad de sacar una piña:

\(\frac{cantidad de pinas}{cantidad de frutas en la canasta} = \frac{20}{50}\) \(= 0.4\)

De acuerdo a lo anterior la probabilidad de sacar un mango es de 0.6 o de 60% (multiplica la probabilidad por 100 para saber su equivalente en porcentaje), mientras que la probabilidad de sacar un mango es de 0.4 o 40% lo cual es mucho más bajo. Es decir que es más probable sacar un mango.

Therefore, the point (v, w) = (x, y) = (6, 15)

The diagram above has two graphs (ABC and DE) intercepting at a point, (v, w).

To find the interception point (v, w), we need to first find the equations of each graph, with ABC being a parabola and DE, a straight line.

Since ABC is a parabola and the vertex is given, the standard vertex form of a parabola is given by:

y = a(x – h)2 + k ----------- eqn(1)

where (h, k) is the vertex of the parabola (the vertex is the point where the parabola changes direction) and "a" is a constant that tells whether the parabola opens up or down (negative indicates downward and positive indicates upward).

Given vertex (4, 19), eqn(1) becomes:

y = a(x - 4)2 + 19 -------------- eqn(2)

Since the parabola passes through point (0, 3), that is, x = 0 and y = 3,

we substitute the value of x and y into eqn(2) to find the value of "a"

3 = a(0 - 4)2 + 19

3 = a(-4)2 + 19

3 = 16a + 19

16a = 3 - 19

16a = -16

a = -1

Thus, eqn(2) becomes:

y = -(x - 4)2 + 19 ------------- eqn(3)

Next, we find the equation of DE (straight line).

Since DE is a straight line and the general form of straight-line equation is given by:

y = mx + c ------------------ eqn(4)

where m is the slope and c is the point at which the graph intercepts the y-axis.

c = -9

m = (y2 - y1) / (x2 - x1)

At points (0, -9) and (2, -1)

x1 = 0

x2 = 2

y1 = -9

y2 = -1

m = (-1 - (-9)) / (2 - 0)

= (-1 + 9)/2

= 8/2

m = 4

Substitute the values of m and c into eqn(4)

y = 4x - 9 ---------------- eqn(5)

Since point (v, w) is the point where both graphs meet,

eqn(3) = eqn(5)

-(x - 4)2 + 19 = 4x - 9

-[(x - 4)(x - 4)] + 19 = 4x - 9

-(x2 - 8x + 16) + 19 = 4x - 9

-x2 + 8x - 16 + 19 = 4x - 9

-x2 + 8x - 4x - 16 + 19 + 9 = 0

-x2 + 4x + 12 = 0

multiply through with -1

x2 - 4x - 12 = 0 ----------- eqn(6)

The above is a quadratic equation and can be simplified either by factorization, completing the square, or quadratic formula method.

Using the factorization method,

product of roots = -12

sum of roots = -4

Next, find two numbers whose sum is equal to the sum of roots (-4) and whose product is equal to the product of roots (-12)

Let the two numbers be 2 and -6

Replace the sum of roots (-4) in eqn(6) with the two numbers

x2 - 6x + 2x - 12 = 0

Group into two terms

(x2 - 6x) + (2x - 12) = 0

factorize each term

x(x - 6) + 2(x - 6) = 0

Pick and group the two values outside each bracket and inside one of the brackets

(x + 2) (x - 6) = 0

x + 2 = 0 and x - 6 = 0

x = -2 and x = 6

Since the point, (v, w) is on the right side of the y-axis, it follows that x cannot be –2. Therefore, x = 6.

substitute the value of x into eqn(5)

y = 4(6) - 9

y = 24 - 9

y = 15

Therefore, the point (v, w) = (x, y) = (6, 15)

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Answer:

PRT/100.

200*8*5/100

2*8*5

$80

Answer:

\(\sqrt{269}\) is ≈ 14.01

Step-by-step explanation:

If the table top is a square, to find the area, you would multiply one side times itself.

If you are given the area, and need to find the sides, you will take the square root of the area to find the side length.

Your question doesn't say to round, but 269 is not a perfect square.

\(\sqrt{269}\) is ≈ 14.01

If the area of the base was 169, that is a perfect square. \(\sqrt{169}\) = 13

Step-by-step explanation:

8 ÷ 0.5 = 16

Quotient = 16

Convert them all into decimals. Percent is just 0.--, and the fraction you can calculate out which gives: 0.625=5/8,0.64=64%

5/8

64%

0.65

9514 1404 393

Answer:

  A = 2

Step-by-step explanation:

Using 0 for p, we have ...

  F(0) = (2·0 +4)/(0 -A) = 4/-A

We want this to be -2, so ...

  -2 = 4/-A

  A = 4/(-(-2)) = 2 . . . . multiply by A/-2

  A = 2