Help would be greatly appreciated.

Help Would Be Greatly Appreciated.

Answers

Answer 1

The description of the ensembles would be: 1. Students who attend both recitals, 2. Students who attend one of the two recitals, 3. students who attend both recitals, 4.The difference between the set P and U, that is, 3 students.

How to graph the information?

To graph the information in a Venn diagram we must take into account the information in the statement. In this case we must place 6 students outside the circles because there are 6 who do not attend any activity.

So, there would be 34 remaining students, of which 20 go to the piano recital and 23 to the voice recital. So, we can establish that 20 go to both recitals, 3 go to the voice recital, and 1 go to the piano recital.

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Help Would Be Greatly Appreciated.

Related Questions

Solve the system of equations x + y = 8; y = x ^ 2 - 4

Answers

The solution to the system of equations is (x, y) = (-4, 12) or (3, 5).

What are systems of equations?

simultaneous equations, or system of equations Two or more equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a distinct solution. Even then, a solution is not assured.

According to the given information:

We can solve this system of equations by substitution or elimination. Here, we will use substitution:

Substitute y in the first equation with its expression from the second equation:

x + (x^2 - 4) = 8

Now, we have a quadratic equation in x:

x^2 + x - 12 = 0

Factor the quadratic equation:

(x + 4)(x - 3) = 0

So, either x + 4 = 0 or x - 3 = 0:

x = -4 or x = 3

Substitute each value of x into either equation to find the corresponding value of y:

If x = -4, then y = (-4)^2 - 4 = 12

If x = 3, then y = 3^2 - 4 = 5

Therefore, the solution to the system of equations is (x, y) = (-4, 12) or (3, 5).

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Question 19 (2 points)

According to research conducted by the Department of Education, 80% of college
students took a mathematics course as part of their general education requirements.
If ten college students are selected at random, what is the probability at least one of
the ten has not taken a mathematics course?

0.0800
0.1073
0.7927
0.8000

Answers

Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.

what is probability?

Probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability that a college student has taken a mathematics course is 0.80. Therefore, the probability that a student has not taken a mathematics course is

1 - 0.80 = 0.20.

The probability that at least one of ten college students has not taken a mathematics course can be found using the complement rule. That is, the probability that at least one student has not taken a mathematics course is equal to one minus the probability that all ten students have taken a mathematics course.

The probability that all ten students have taken a mathematics course is:

0.80¹⁰ = 0.1074

Therefore, the probability that at least one student has not taken a mathematics course is:

1 - 0.1074 = 0.8926

Therefore, Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.

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construct shear and bending diagrams for the following beams. show your equations used to create the plots. p p p p l/2 l/4 l/4 p p p l/3 l/3 l/3

Answers

The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.

To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:

Leftmost section (0 ≤ x ≤ L/4)

Second section (L/4 < x ≤ L/2)

Third section (L/2 < x ≤ 5L/12)

Fourth section (5L/12 < x ≤ 7L/12)

Rightmost section (7L/12 < x ≤ L)

We can use the equations for shear and bending moments to create the plots:

For section 1: 0 ≤ x ≤ L/4

The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.

For section 2: L/4 < x ≤ L/2

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.

For section 3: L/2 < x ≤ 5L/12

The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.

For section 4: 5L/12 < x ≤ 7L/12

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.

For section 5: 7L/12 < x ≤ L

The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.

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Last night, Roberto spent 90 minutes doing homework, two-thirds of an hour reading, and 540 seconds making his lunch for the next day. How many more minutes did Roberto spend doing homework than he did reading and making his lunch?

Answers

The answer is 41 minutes.

explaination:

540 secs = 9 minutes

2/3 of 60 mins= 40 mins

(to find a fraction of a number you divide it by the denominator and times it after by the numerator)

9+40= 49

homework: 90 mins

reading and making lunch: 49 minutes

we want the difference so:

90-49= 41

Roberto spent 41 more minutes doing his homework than reading and making lunch.

I will mark you brainiest!

SSS is used to prove two triangles are congruent.
A) False
B) True

Answers

Answer:

A

Step-by-step explanation:

because___________________________________

Answer:

B) True

Step-by-step explanation:

SSS or Side-Side-Side is used to prove two triangles are congruent.

of the following values, which is least important to today's college students according to the yearly values survey?

Answers

The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.

The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.

This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.

It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.

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The complete question is:

Which of the following values, which is least important to today's college students according to the yearly values survey?

A. Career success

B. Political involvement

C. Healthy lifestyle

D. Social media presence

find all real numbers k for which there exists a nonzero 2 dimensional vector bold v such that begin bmatrix 2

Answers

Answer:

We can write the given system of equations as a matrix equation:

$\begin{bmatrix} 2 & 4 \ 4 & k \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 0 \ 0 \end{bmatrix}$

To find nontrivial solutions (i.e., $x$ and $y$ not both equal to zero), the coefficient matrix must be singular, which means its determinant must be zero:

$\det\begin{bmatrix} 2 & 4 \ 4 & k \end{bmatrix} = 2k - 16 = 2(k - 8) = 0$

Thus, $k = 8$ is the only value for which there exists a nonzero 2-dimensional vector $\boldsymbol{v} = \begin{bmatrix} x \ y \end{bmatrix}$ satisfying the given system of equations. For $k \neq 8$, the only solution is the trivial one, $\boldsymbol{v} = \boldsymbol{0}$.


I hope this us helpful

Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2

Answers

The function g(t) is defined as:

g(t) = 1/√(16-t^2)

The function is continuous for all values of t that satisfy the following conditions:

The denominator is non-zero:

The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].

There are no vertical asymptotes:

The function does not have any vertical asymptotes, because the denominator is always positive.

Thus, the function g(t) is continuous on the interval [-4,4].

question 1 write an inequality and a word sentence that represent the graph. let x represent the unknown number.

Answers

The inequality is X > 0 and a word sentence represent the graph is  X  the graph of a number line with an open circle on zero and an arrow pointing to the right.

The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.

In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."

This means that X must be a positive number, and it can be any value that is greater than zero.

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Solve the equation.
Cos 9= sin 56.3

Answers

According to the problem the answer is cos 9 = sin 56.3.

What is cos?

Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc. Cos is typically used in conjunction with sin and tan to measure angles and distances in a triangle. Cos can also be used to calculate wave lengths in physics and to determine the magnitude of a vector in vector calculus. Cos is an important concept in mathematics and is used in many areas of science, engineering, and technology.

Use the identity sin(90°-x) = cos x:

sin 56.3 = cos (90° - 56.3)

cos 9 = cos (90° - 56.3)

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For cos 9°, angle lies between 0° and 90° (First Quadrant). Since cosine function is positive and in the first quadrant, thus cos 9° value = 0.9876883. Also Cos 9 = √(1-sin²(9°)).

What is cos?

Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc.

The value of cos 9 degrees in decimal is 0.987688340, since Cos 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707)

Using degree to radian conversion, θ in radians is:

= θ in degrees × (pi/180°)

⇒ 9 degrees

= 9° × (π/180°) rad

= π/20 or 0.1570

∴ cos 9° = cos(0.1570)

= 0.9876883

Since the cosine is the periodic function, we can represent cos 9° as,

So, cos 9 degrees = cos(9° + n × 360°).

⇒ cos 9°

= cos 369°

= cos 729°, and so on.

Cos 9 = √(1-sin²(9°))

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PLEASE HELP 30 POINTS!

Answers

Answer:

57

57

123

123

57

57

123

that's all.

Answer:

m<1 = 57°

m<2 = m<1 = 57°

m<3 = x = 123°

m<4 = x = 123°

m<5 = m<1 = 57°

m<6 = m<5 = 57°

m<7 = m<4 = 123°

Step-by-step explanation:

[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]

a relation r is called circular if arb and brc imply that cra. if r is an equivalence relation, then would r be circular?

Answers

If a relation R is an equivalence relation, then R will be circular.

If a relation R is an equivalence relation, then it must satisfy three properties: reflexivity, symmetry, and transitivity.

(i) Reflexivity: For any element "a" in the set, "aRa" must be true.

(ii) Symmetry: For any elements "a" and "b" in the set, if "aRb" then "bRa" must be true.

(iii) Transitivity: For any elements "a", "b", and "c" in the set, if aRb and bRc then "aRc" must be true.

A Circular relation is where "aRb" and "bRc" imply "cRa".

This is a stronger condition than the transitivity property of an equivalence relation, which only requires that "aRb" and "bRc" together imply "aRc".

Therefore, a relation that is an equivalence-relation have to be circular.

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The given question is incomplete, the complete question is

A relation R is called circular if "aRb" and "bRc" imply that "cRa". if R is an equivalence relation, then would R be circular?

what is the ordered pair to this question using substitution? y = −2x − 7
2y − x = 1

Answers

Answer: (-3, -1)

Step-by-step explanation:

First, we can use the first equation to solve for one variable in terms of the other.

y = -2x - 7

Next, we can substitute this expression for y into the second equation:

2y - x = 1

2(-2x - 7) - x = 1

Simplifying:

-4x - 14 - x = 1

-5x - 14 = 1

-5x = 15

x = -3

Now that we have the value of x, we can substitute it back into either of the original equations to find y. Using the first equation:

y = -2(-3) - 7

y = 6 - 7

y = -1

Therefore, the ordered pair that satisfies both equations is (-3, -1).

Answer: (-3,-1)

Explanation Step By Step

point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.

Answers

The measurement of angle PCD in equilateral triangle  is 67.38°.

Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.

Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.

Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.

Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.

Using the Pythagorean theorem in triangle $OCE$, we have

CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]

Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,

∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°

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HELP MY TEST IS DUE TONIGHT
find the area of the trapezoid
Show work:

Answers

Answer:

A = 32

Step-by-step explanation:

A= (a+b divided by 2) mulitiplied by height

a = 6

b = 2+6+2 = 10

h = 4

a+b = 6 + 10= 16

16 divided by 2 = 8

8 x 4 = 32

Therefore, the area is 32.

PLEASE HELPP DUE TODAY!!!!!

Calculate the value of c in the triangle below.

Answers

Answer:

82

Step-by-step explanation:

jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country

Answers

I will multiply 1040 by .30 and get 312
therefore, country songs consists of 312

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

Step-by-step explanation:

my previous answer assumed we need a kind of average change rate.

but it seems you need the immediate change rate ?

or what ? the question does not specify.

I would appreciate if you would leave a comment, when you find that my answer is seemingly not matching some expected answers.

so, let's try now the immediate change rate (as I have no information to go - I have also no information about what you are currently learning in your class, and if you do already derivatives or not, so, this might be now above your learning level ...) :

again, the area between the inner circle and the outer square is

A = As - Ac = s² - pi×r²

where s is the square's side length, and r is the radius of the circle.

the immediate change rate of that area is the sum of first derivatives of A based on both used variables multiplied by their individual change rates :

dA/dt = dAs/ds × ds/dt - dAc/dr × dr/dt

and this is then calculated for the given data point (s = 16, r = 3) and the individual change rates of the variables (ds/dt = 2 meters/minute, dr/dt = 1 meter/minute).

so, we have

dA/dt = 2s × 2 - 2×pi×r × 1

as (s²)' = 2s, (pi×r²)' = 2×pi×r

dA(16, 3)/dt = 2×16×2 - 2×pi×3×1 = 64 - 6pi =

= 45.15044408... meters²/minute ≈

≈ 45.15 meters²/minute

so, you see, for a curved function (not a line) there has to be a difference between the average change rate between 2 points and the immediate change rate directly at a point.

I hope this works now for you.

and here now the original answer for an average change rate :

right now the radius is 3 m, and the square side lengths are 16 m.

1 minute ago the radius was 2 m, and the square side lengths were 14 m.

the area between the circle and the square is always the area of the square minus the area of the circle.

these areas are right now

circle : pi×3² = 9pi m²

square : 16² = 256 m²

area between = 256 - 9pi = 227.7256661... m²

these areas were one minute ago

circle : pi×2² = 4pi m²

square : 14² = 196 m²

area between = 196 - 4pi = 183.4336294... m²

the change rate of the area between the circle and the square is

227.7256661... - 183.4336294... = 44.29203673... m² per minute

What is the meaning of "invertible n x n matrices"?

Answers

Answer: A matrix A of dimension n x n is called invertible if and only if there exists another matrix B of the same dimension, such that AB = BA = I, where I is the identity matrix of the same order.

Step-by-step explanation:

hope it helped! <3

c. The expression ax² + 11x + 3 can be factorised. List the possible values of a given that a is a positive integer.​

Answers

Step-by-step explanation:

If the polynomial 3x^3+ax^2-11x+3 is exactly divisible by (x – 1), then find the value of a. Hence, factorize the polynomial. can anyone help

A human head can be approximated as a sphere with a circumference of 60
centimeters. What is the approximate volume of a human head, rounded to the nearest 1,000
cubic centimeters?(GEOMETRY HELP)

Answers

The approximate volume of a human head is 4000 cubic centimeter.

What is the approximate volume of a human head?

A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

The circumference of a sphere is given by the formula:

C = 2πr

Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:

60 cm = 2πr

Solve for r

r = 60/2π

r = 30/π

The volume of a sphere is given by the formula:

V = (4/3)πr³.

Substituting the value we found for r, we get:

V = (4/3) × π × ( 30/π )³

V = (4/3) × π × ( 30/π )³

V = 3647.566 cm³

V = 4000 cm³

Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.

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PLS Answer help i will give 10 brainly points if you help

Answers

The two in the middle column and the one in the bottom right corner

Answer:

12×2, 3×8, 4×6

Step-by-step explanation:

To find the area of a parallelogram, the formula is A = bh.

1. Height: 6 ft

Base: 2 ft

6 × 2 = 12 ft

So it does not work.

2. Height: 12 ft

Base: 2 ft

12 × 2 = 24 ft

So it does work.

3. Height: 10 ft

Base: 14 ft

14 × 10 = 140 ft

So it does not work.

4. Height: 3 ft

Base: 4 ft

3 × 4 = 12 ft

So it does not work.

5. Height: 3 ft

Base: 8 ft

3 × 8 = 24 ft

So it does work.

6. Height: 4 ft

Base: 6 ft

4 × 6 = 24 ft

So it does work.

The volume, V , of a sphere in terms of its radius, r , is given by V(r)=4/3πr^3 . Express r as a function of V , and find the radius of a sphere with volume of 100 cubic feet.
Round your answer for the radius to two decimal places.
A sphere with volume 100 cubic feet has radius ??

Answers

So the radius of the sphere is approximately 2.88 feet (rounded to two decimal places).

What is volume?

Volume is the amount of space occupied by a three-dimensional object as measured in cubic units. It is the measure of the amount of material or substance that a container, object, or shape can hold.

Here,

To express r as a function of V, we can rearrange the equation V = 4/3πr³ to solve for r:

V = 4/3πr³

V / (4/3π) = r³

r = ³√(V / (4/3π))

r = ³√(3V / 4π)

To find the radius of a sphere with volume 100 cubic feet, we can substitute V = 100 into the equation:

r = ³√(3V / 4π)

= ³√(3(100) / (4π))

≈ 2.88 units

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The star Bellatrix is 1.4 × 1015 miles from Earth. Barnard’s star is 35,000,000,000,000 miles from Earth. Part A How far is Barnard’s star from Earth, in scientific notation? 3.5 × 1013 35 × 1013 3.5 × 1015 35 × 1015

Answers

In scientific notation the distance of the Barnard’s star from Earth, is given as 3.5 × 10^13

What is scientific notation?

Scientific notation is a way of writing very large or very small numbers in a more compact form using powers of 10. In scientific notation, a number is expressed as a product of a coefficient and 10 raised to a power. The coefficient must be greater than or equal to 1 but less than 10. The power of 10 indicates the number of places the decimal point is moved to obtain the original number.

For 35,000,000,000,000

you have to start counting the digits from the right. The decimal point would occur just before the first digit (that is the number 3)

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An inlet pipe on a swimming pool can be used to fill the pool in 16
hours. The drain pipe can be used to empty the pool in 24
hours. If the pool is 13
filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answers

Answer:

Step-by-step explanation:

19
The diagram shows a sector OBC of a circle with centre O and radius (6 + x) cm.
B
A
es 50°
6 cm
DX
find the value of x.
Give your answer correct to 3 significant figures.
x cm
A is the point on OB and D is the point on OC such that OA = OD = 6 cm
Angle BOC= 50°
Given that
Diagram N
accurately
the perimeter of sector OBC= 2 x the perimeter of triangle OAD

Answers

The value of the variable, x, obtained using the formula for the perimeter of a sector of a circle is; x = 6 cm

What is a sector of a circle?

A sector of a circle is the region of the circle that has two radii of the circle and the arc between the two radii as the boundary of the region.

The perimeter of a sector of a circle can be obtained using the formula;

Perimeter = 2·r + (θ/360°) × (2·π·r)

The radius of sector OAD, r = 6 cm

Therefore;

The perimeter of sector OAD = 2 × 6 + (50/360) × 2 × π × 6 = 12 + 5·π/3

The perimeter of sector OBC = 2 × The perimeter of sector OAD

Therefore;

The perimeter of sector OBC = 2 × (12 + 5·π/3) = 24 + 10·π/3

Which indicates;

The perimeter of sector OBC = 2  × (6 + x) + (50/360) × 2 × π  × (6 + x)

2  × (6 + x) + (50/360) × 2 × π  × (6 + x) = (5·π·x + 30·π + 36·x + 216)/18

24 + 10·π/3 = (5·π·x + 30·π + 36·x + 216)/18

432 + 60·π = 5·π·x + 30·π + 36·x + 216

432 - 216 + 60·π - 30·π  = x·(5·π + 36)

216 + 30·π = x·(5·π + 36)

6 × (5·π + 36 ) = x·(5·π + 36)

x·(5·π + 36) = 6 × (5·π + 36 )

x = 6 × (5·π + 36 )/(5·π + 36 ) = 6

x = 6 cm

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Which expression represents the distance
between point G and point H?
|-12|16| |-12|+|-9|
1-9|-|-6|
|-12|+|6|
-15
H(-9,6)
G(-9,-12)
15+y
0
-15-
15

Answers

Answer:

Step-by-step explanation:

2

The mean weight of 4 parcels is 8.5kg. Three of them weighed 7.7 kg, 7.6 kg and 8.2 kg.
What is the weight of the fourth parce1?

Answers

Answer:

Weight of the fourth parcel will be 10.5 kg

Step-by-step explanation:

Weight of first parcal = 7.7 kg Weight of second parcel = 7.6 kgWeight of third parcel = 8.2 kg Mean Weight = 8.5 kg

Let weight of fourth parcel be x

Mean = Sum of all values/total number of values.

8.5 = 7.7 + 7.6 + 8.2 + x/4

8.5 = 23.5 + x/4

8.5 × 4 = 23.5 + x

34 = 23.5 + x

34 - 23.5 = x

10.5 = x

Therefore, weight of the fourth parcel will be 10.5 kg

What is the end behavior of the polynomial function?

Answers

Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 92 people are called to jury duty and only 11 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection process? Again run a test using the PHANTOMS method to complete all parts of your problem.

Answers

Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.

To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.

First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.

The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.

We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).

Plugging in the values, we get

z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39

Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.

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