At the city Museum child omission is $5.70 and adult admission is $9.80. On Tuesday 124 tickets were sold for a total sales of $936. How many child tickets were sold that day

Answer:

B.

Step-by-step explanation:

Find the total profit.

P=7300-5500

P=1800

Since each shovel makes up 50 of the profit.

50N=1800

N=1800%2F50

N=36

36 shovels were sold.

Answer:

Therefore,

[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]\cot B =\dfrac{1}{2}[/tex]

[tex]\csc B = \dfrac{\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given:

Right △ABC has its right angle at C,

BC=4 , and AC=8 .

To Find:

Cos A = ?

Cot B = ?

Csc B = ?

Solution:

Right △ABC has its right angle at C, Then by Pythagoras theorem we have

[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]

Substituting the values we get

[tex](AB)^{2}=4^{2}+8^{2}=80\\AB=\sqrt{80}\\AB=4\sqrt{5}[/tex]

Now by Cosine identity

[tex]\cos A = \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}\\[/tex]

Substituting the values we get

[tex]\cos A = \dfrac{AC}{AB}=\dfrac{8}{4\sqrt{5}}=\dfrac{2}{\sqrt{5}}\\\\Ratinalizing\\\cos A=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]

Now by Cot identity

[tex]\cot B = \dfrac{\textrm{side adjacent to angle B}}{\textrm{side opposite to angle B}}[/tex]

Substituting the values we get

[tex]\cot B = \dfrac{BC}{AC}=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

Now by Cosec identity

[tex]\csc B = \dfrac{Hypotenuse}{\textrm{side opposite to angle B}}\\[/tex]

Substituting the values we get

[tex]\csc B = \dfrac{AB}{AC}=\dfrac{4\sqrt{5}}{8}=\dfrac{\sqrt{5}}{2}[/tex]

Therefore,

[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]\cot B =\dfrac{1}{2}[/tex]

[tex]\csc B = \dfrac{\sqrt{5}}{2}[/tex]

Question is Incomplete; Complete question is given below;

Roger is having a picnic for 78 guests. He plans to  serve each guest at least one hot dog. If each  package, p, contains eight hot dogs, which  inequality could be used to determine how many  packages of hot dogs Roger will need to buy?

1) [tex]p \geq 78[/tex]

2) [tex]8p \geq 78[/tex]

3) [tex]8 +p \geq 78[/tex]

4) [tex]78 + p \geq 8[/tex]

Answer:

2) [tex]8p \geq 78[/tex]

Step-by-step explanation:

Given:

Number of guest in the picnic = 78 guest

Number of hot dog each guest will have = 1

Number of hot dogs in each package = 8 hot dogs.

We need to write the In equality used to determine the number of packages of hot dogs roger must buy

Solution:

Let the number of packages be 'p'.

First we will find the total number of hot dogs required.

so we can say that;

total number of hot dogs required is equal Number of guest in the picnic multiplied by Number of hot dog each guest will have.

framing in equation form we get;

total number of hot dogs required = [tex]78\times 1 =78[/tex]

Now we can say that;

Number of hot dogs in each package multiplied by number of packages should be greater than or equal to total number of hot dogs required.

framing in equation form we get;

[tex]8p\geq 78[/tex]

Hence The In equality used to determine the number of packages of hot dogs roger must buy is [tex]8p\geq 78[/tex].

Answer:

a) [tex]P(\bar X >4)=P(Z>\frac{4-3}{\frac{3}{\sqrt{50}}}=2.357)[/tex]

[tex]P(Z>2.357)=1-P(Z<2.357) =1-0.9908=0.0092[/tex]

b) [tex]P(\bar X <2.5)=P(Z>\frac{2.5-3}{\frac{3}{\sqrt{50}}}=-1.179)[/tex]

[tex]P(Z<-1.179)=0.1192[/tex]

c)  

[tex] P(2.5 < \bar X< 3.5) = P(\frac{2.5-3}{\frac{3}{\sqrt{50}}} <Z<\frac{3.5-3}{\frac{3}{\sqrt{50}}})[/tex]

[tex]P(-1.179<Z<1.179)=P(Z<1.179)-P(Z<-1.179)=0.8808-0.1192=0.7616 [/tex]Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the number of people of a population, and for this case we know that:

Where [tex]\mu=3[/tex] and [tex]\sigma=\sqrt{9}=3[/tex]

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we want to find this probability:

[tex] P(\bar X >4)= P(z> \frac{4-3}{\frac{3}{\sqrt{50}}})[/tex]

And using a calculator, excel or the normal standard table we have that:

[tex]P(Z>2.357)=1-P(Z<2.357) =1-0.9908=0.0092[/tex]

Part b

[tex] P(\bar X <2.5)= P(z> \frac{2.5-3}{\frac{3}{\sqrt{50}}})[/tex]

And using a calculator, excel or the normal standard table we have that:

[tex]P(Z<-1.179)=0.1192[/tex]

Part c

For this case we want this probability:

[tex] P(2.5 < \bar X< 3.5) = P(\frac{2.5-3}{\frac{3}{\sqrt{50}}} <Z<\frac{3.5-3}{\frac{3}{\sqrt{50}}})[/tex]

And using a calculator, excel or the normal standard table we have that:

[tex]P(-1.179<Z<1.179)=P(Z<1.179)-P(Z<-1.179)=0.8808-0.1192=0.7616 [/tex]

Answer: This is an reduction.

Step-by-step explanation:

Given : A street is drawn by dilating segment [tex]\overline{FG}[/tex] about center A with a scale factor greater than 0 but less than 1.

Then by using (2.) , we can say that this is an reduction.

The maximum weight of boxes that can be placed into the elevator is:

[tex]\to 2000 - 200 = 1800 \ lbs[/tex]  

It should be noted that Y must be an even integer for the equivalence to hold, whereas X might be odd or even because 40X is always even.

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Answer:

a.

Option 1

Option 2

b. Sample statistics

Step-by-step explanation:

a.

The set that includes the list of all possible individual in the interested area of study is termed as population while the portion or a part of population is termed as sample. The given scenario indicates that population is all elderly people from which 949 elderly people are selected for study and so, 949 elderly people are included in sample. So, option 1 and option 2 are correct for indicated scenario.

b.

The percentages 22% and 17% are calculated from 949 elderly people that are indicated as sample. Hence, the percentages 22% and 17% are the measure of sample and so, they represents sample statistics.

Final answer:

The relevant population is all elderly people, and the sample consists of 949 elderly people. The numbers 22% and 17% represent sample statistics.

Explanation:

a. The relevant population is all elderly people, so options 2 and 3 are correct. The sample consists of 949 elderly people, so option 1 is also correct.

b. The numbers 22% and 17% represent sample statistics. The sample statistics are calculated from the data collected in the sample, which in this case is the proportion of elderly persons with depression who went on to develop dementia.

The answer is

[tex]f(x) = \begin{cases}x-2 \text{ if }x \ge -2 \\ -x-6 \text{ if }x < -2\end{cases}[/tex]

========================================================

Here's how I got that answer:

Start with the piecewise definition for y = |x|.

[tex]g(x) = \begin{cases}x \text{ if }x \ge 0 \\ -x \text{ if }x < 0\end{cases}[/tex]

Everywhere you see an 'x', replace it with x+2

[tex]g(x+2) = \begin{cases}x+2  \text{ if }x+2 \ge 0 \\ -(x+2) \text{ if }x+2 < 0\end{cases}[/tex]

[tex]g(x+2) = \begin{cases}x+2  \text{ if }x \ge -2 \\ -x-2 \text{ if }x < -2\end{cases}[/tex]

Now tack on "-4" at the end of each piece so that we shift the function down 4 units

[tex]g(x+2)-4 = \begin{cases}x+2-4  \text{ if }x \ge -2 \\ -x-2-4 \text{ if }x < -2\end{cases}[/tex]

[tex]g(x+2)-4 = \begin{cases}x-2  \text{ if }x \ge -2 \\ -x-6 \text{ if }x < -2\end{cases}[/tex]

[tex]f(x) = \begin{cases}x-2  \text{ if }x \ge -2 \\ -x-6 \text{ if }x < -2\end{cases}[/tex]

Check out the attached images below. In figure 1, I graph y = x-2 and y = -x-6 as separate equations on the same xy coordinate system. Then in figure 2, I combine them to form the familiar V shape you see with any absolute value graph.

Answer:

[tex]a\approx 31[/tex]

[tex]b\approx 72[/tex]

Step-by-step explanation:

Please find the attachment.

We have been given that in triangle ABC, A=25, C=55 and AB=60. We are asked to find the approximate measures of the remaining side lengths of the triangle.

We will use Law of Sines to solve for side lengths of given triangle.

[tex]\frac{\text{sin}(A)}{a}=\frac{\text{sin}(B)}{b}=\frac{\text{sin}(C)}{c}[/tex], where a, b and c are opposite sides corresponding to angles A, b and C respectively.

Upon substituting our given values, we will get:

[tex]\frac{\text{sin}(25)}{a}=\frac{\text{sin}(55)}{60}[/tex]

[tex]a=\frac{60\text{sin}(25)}{\text{sin}(55)}[/tex]

[tex]a=\frac{60*0.422618261741}{0.819152044289}[/tex]

[tex]a=\frac{25.35709570446}{0.819152044289}[/tex]

[tex]a=30.9552980807967304[/tex]

[tex]a\approx 31[/tex]

Therefore, the measure of side 'a' is approximately 31 units.

We can find measure of angle B using angle sum property as:

[tex]m\angle A+m\angle B+m\angle C=180[/tex]

[tex]25+m\angle B+55=180[/tex]

[tex]m\angle B+80=180[/tex]

[tex]m\angle B=100[/tex]

[tex]\frac{\text{sin}(100)}{b}=\frac{\text{sin}(55)}{60}[/tex]

[tex]b=\frac{60\text{sin}(100)}{\text{sin}(55)}[/tex]

[tex]b=\frac{60*0.984807753012}{0.819152044289}[/tex]

[tex]b=\frac{59.08846518072}{0.819152044289}[/tex]

[tex]b=72.1336967815383509[/tex]

[tex]b\approx 72[/tex]

Therefore, the measure of side 'b' is approximately 72 units.

Answer:

No because if the Rays meet at a point other than Q the angles will change

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation used to represent the height of the ball, h in feet after t seconds is expressed as

h = -16t^2 + 48t + 4

A) The height of the ball after 2 seconds would be

h = - 16 × 2² + 48 × 2 + 4

h = - 64 + 96 + 4

h = 36 feet

B)The equation is a quadratic equation. The plot of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the rocket.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = -16

b = 48

Vertex = - - 48/32= 1.5

So the ball will attain maximum height at 1.5 seconds.

C) The maximum height of the ball would be

h = -16 × 1.5² + 48 × 1.5 + 4

h = - 36 + 72 + 4

h = 40 feet

Final answer:

The ball will be at a height of 64 feet after 2 seconds. It will reach its maximum height of 58 feet after 1.5 seconds.

Explanation:

To solve the problem, we need to use the given quadratic equation for the ball's height h(t) = -16t2 + 48t + 4. This equation models the motion of the ball thrown into the air with an initial upward velocity.

A: Height After 2 Seconds

To find the height of the ball after 2 seconds, we substitute t = 2 into the equation:

h(2) = -16(2)2 + 48(2) + 4

h(2) = -16(4) + 96 + 4 = 64 feet

B: Time to Reach Maximum Height

To determine when the ball reaches its maximum height, we need to find the vertex of the parabola, which occurs at t = -b/(2a) where a=-16 and b=48. So t = -48/(2(-16)) = 1.5 seconds.

C: Ball's Maximum Height

To find the ball's maximum height, we substitute t = 1.5 into the height equation:

h(1.5) = -16(1.5)2 + 48(1.5) + 4

h(1.5) = -16(2.25) + 72 + 4 = 58 feet

The asymptotes are found using the rational function ax^n/ bx^m where n is the degree of the numerator and m is the degree of the denominator.

In the given equation the numerator isn’t raised to any power so n is considered equal to 1. The Demi actor has x raised to the 2nd power so m equals 2.

If n < m then the c axis, y= 0 is the horizontal asymptote.

Also because n is less than m there are no vertical asymptote.

The domain is any real number so the domain would be (-infinity, infinity)

Answer:

k = ln (6/5)

Step-by-step explanation:

for

f(x)=A*exp(kx)+B

since f(0)=1, f(1)=2

f(0)= A*exp(k*0)+B = A+B = 1

f(1) = A*exp(k*1)+B =  A*e^k + B = 2

assuming k>0 , the horizontal asymptote H of f(x) is

H= limit f(x) , when x→ (-∞)

when x→ (-∞) , limit f(x) =  limit (A*exp(kx)+B) = A* limit [exp(kx)]+B* limit = A*0 + B = B

since

H= B = (-4)

then

A+B = 1 → A=1-B = 1 -(-4) = 5

then

A*e^k + B = 2

5*e^k + (-4) = 2

k = ln (6/5)    ,

then our assumption is right and k = ln (6/5)  

The value of k is [tex]k=ln(\frac{6}{5} )[/tex].

Given function is,

                           [tex]f(x)=Ae^{kx} +B[/tex]

Substitute [tex]f(0)=1,f(1)=2[/tex] in above equation.

We get,

                       [tex]A+B=1\\\\Ae^{k}+B=2[/tex]

Given that horizontal asymptote of f is -4.

               [tex]\lim_{x \to -\infty} Ae^{kx}+B=-4\\ \\ B=-4[/tex]

So,  [tex]A=1-B=1-(-4)=5[/tex]

Substitute value of A and B.

                [tex]5e^{k}-4=2\\ \\e^{k} =\frac{6}{5}\\ \\k=ln(\frac{6}{5} )[/tex]

Hence, the value of k is [tex]k=ln(\frac{6}{5} )[/tex].

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Answer:option 1 and option 2 represents a direct variation.

Step-by-step explanation:

A direct variation is one in which, as one variable increases in value, the other variable increases in value. Also as one variable decreases in value, the other variable decreases in value.

Looking at the options,

1) y = 2х

When x = 2, y = 2×2 = 4

When x = 3, y = 2×3 = 6

Therefore, y = 2x is a direct variation.

2) y=x+4

When x = 2, y = 2 + 4 = 6

When x = 3, y = 3 + 4 = 7

Therefore, y = x + 4 is a direct variation.

3) y= 1/2x

When x = 2, y = 1/2×2 = 1/4 = 0.25

When x = 3, y = 1/2×3 = 1/6 = 0.17

Therefore, y = 1/2x is not a direct variation.

4) y = 3/x

When x = 2, y = 3/2 = 1.5

When x = 3, y = 3/3 = 1

Therefore, y = 3/x is not a direct variation.

Answer:

The perimeter of Roxanne's right triangular garden is 79 feet.

Step-by-step explanation:

Given,

Length of 1 side = 19 feet

Hypotenuse = 33 feet

We have to find out the perimeter of the triangular garden.

Solution,

Since the garden is in shape of right triangle.

So we apply the Pythagoras theorem to find the third side.

"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides".

So framing in equation form, we get;

[tex]33^2=19^2+(third\ side)^2\\\\1089=361+(third\ side)^2\\\\(third\ side)^2=1089-361\\\\(third\ side)^2=728[/tex]

Now taking square root on both side, we get;

[tex]\sqrt{(third\ side)^2} =\sqrt{728} \\\\third\ side=26.98\approx27\ ft[/tex]

Now we know that the perimeter is equal to sum of all the three side of a triangle.

Perimeter = [tex]19+27+33=79\ ft[/tex]

Hence The perimeter of Roxanne's right triangular garden is 79 feet.

The variable is the average miles per gallon (mpg), which is a quantitative measure. The implied population is all new cars.

(a) The variable in this situation is the average miles per gallon (mpg) for all new cars.

(b) The variable is quantitative, as it deals with a numerical measure, i.e., the number of miles a car can travel per a gallon of fuel.

(c) The implied population would be all new cars in general - though it's specified that this is based on a sample from Consumer Reports, which may not cover every single new car in existence.

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Answer:

Step-by-step explanation:

Check the attachment the solution of the work is given there

Answer: 0.74

Step-by-step explanation:

Let h = rhombus' height

Looking at the attachment, we see that the circle has an area of [tex]\pi *(\frac{h}{2}) ^{2}[/tex]

The rhombus has an area of [tex]\frac{h^2}{sin(70°)}[/tex]

because the base is [tex]\frac{b}{sin(90)} = \frac{h}{sin(70)}[/tex]

due to the law of sines

Thus, Area Circle / Area Rhombus is

[tex]\frac{(\pi(\frac{h}{2})^2)}{(\frac{h^2}{sin(70)}) } = 0.74[/tex]

The drag force can be mathematically expressed as Fd = 0.5 × ρ × v^2 × A × Cd, where Fd is the drag force, ρ is the density of the fluid, v is the velocity of the object, A is the reference area, and Cd is the drag coefficient.

The drag force can be mathematically expressed as:

Fd = 0.5 × ρ × v2 × A × Cd

Where:

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Answer:

True

Step-by-step explanation:

First statement

[a b c | d][x]

[a b c]x=d

ax+bx+cx=d

Second statement

Ax=d

Given that A = [a b c]

[a b c]x=d

ax+bx+cx=d

ax+bx+cx=d

Then, they are going to have the same solutions

The statement is false. The solution sets for the augmented matrix [a, b, c, d] and the matrix equation Ax = d (where A = [a, b, c]) are not the same unless 'd' is consistently a column vector with 'a', 'b', 'c'.

The statement presented in the question is false. When we talk about a linear system, an augmented matrix generally pairs a coefficient matrix with an answer matrix. This would look like [A|d], where 'A' would be a matrix, and 'd' is the constants column vector.

Conversely, Ax = d is a matrix equation where 'A' is again the coefficient matrix, 'x' is the variable matrix, and 'd' is the constants column vector.

In your provided augmented matrix, [a b c d], unless 'd' is a consistent column vector with the other column vectors, it can't be virtually the same as the matrix system Ax = d where A = [a b c] because the augmented matrix [a b c d] would mean that A = [a b c] and d = [d].

Unless 'd' is mathematically consistent with the column vectors 'a', 'b', and 'c', the solution sets would not be the same.

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Answer: Zoey needs 168 square feet if carpet squares.

Step-by-step explanation:

Zoey wants to cover her bedroom floor with carpet squares. Each square has an area of 1 square foot.

The formula for determining the area of a rectangle is expressed as

Area = length × width

Her bedroom measures 12 feet by 14 feet. Therefore, the area of her bedroom would be

12 × 14 = 168 square feet.

Therefore, the number of carpet squares that Zoey needs would be

168/1 = 168 square feet

Answer:

  168 squares

Step-by-step explanation:

Each square is 1 foot on a side, so along the 14-foot wall, Zoey will need 14 squares. Altogether, Zoey will need 12 rows of 14 squares, so 12×14 = 168 squares.

Answer: 5 seconds

Step-by-step explanation:

Given : A ball is thrown into the air from the top of a building.

The height, h(t), of the ball above the ground t seconds after it is thrown can be modeled by [tex]h(t) = -16t^2 + 64t + 80[/tex] .

When ball reaches the ground , then its height from ground become zero.

i.e. [tex]h(t) = -16t^2 + 64t + 80=0[/tex]

Divide equation by 16 , we get

[tex]-t^2 + 4t + 5=0\\\\\Rightarrow\ t^2-4t-5=0\\\\\Rightarrow\ t^2+t-5t-5=0\\\\\Rightarrow\ t(t+1)-5(t+1)=0\\\\\RIghtarrow\ (t+1)(t-5)=0 \\\\\Rightarrow\ t= -1 , 5[/tex]

Since time cannot be negative , therefore t= 5

Hence, the ball will take 5 seconds ( after being thrown) to hit the ground.

The ball will hit the ground 5 seconds after being thrown.

Settingh(t) equal to zero gives us the equation:

[tex]\[ -16t^2 + 64t + 80 = 0 \][/tex]

 To solve this quadratic equation, we can factor out the common factor of -16:

[tex]\[ -16(t^2 - 4t - 5) = 0 \][/tex]

 Now we need to factor the quadratic expression inside the parentheses.

We are looking for two numbers that multiply to -5 and add up to -4. These numbers are -5 and +1. So we can write:

[tex]\[ -16(t - 5)(t + 1) = 0 \][/tex]

 Setting each factor equal to zero gives us two possible solutions for t

[tex]\[ t - 5 = 0 \quad \text{or} \quad t + 1 = 0 \][/tex]

 Solving these, we get:

[tex]\[ t = 5 \quad \text{or} \quad t = -1 \][/tex]

Since time cannot be negative, we discard the solution  t = -1

Therefore, the ball will hit the ground 5 seconds after being thrown."

Answer: The other dimension can be expressed as

(50 - 2L)/2

Step-by-step explanation: First and foremost, we would let the other dimension be represented by B. Then, the perimeter of a rectangle is measured as L+L+B+B or better put;

Perimeter = 2L + 2B

Where L is the measurement of the longer side and B is the measurement of the shorter side.

In this case the perimeter of the rectangle measures 50m, and this can now be written as

50 = 2L + 2B

Subtract 2L from both sides of the equation

50 - 2L = 2L - 2L + 2B

50 -2L = 2B

Divide both sides of the equation by 2

(50 - 2L)/2 = B

Answer:

  25-L

Step-by-step explanation:

Let W represent the other side length. The perimeter (P) of the rectangle is ...

  P = 2(W+L)

Solving for W, we get ...

  P/2 = W+L

  P/2 -L = W

Filling in the given value for P, we find ...

  W = 50/2 -L = 25 -L

The other dimension is (25-L) meters.

Answer:

Estimated Average Requirement (EAR)

Step-by-step explanation:

The Estimated Average Requirement (EAR) is the average amount of daily intake value which is estimated to meet the needs of 50% of the healthy individuals.

The EAR is estimated on the basis of specific conditions of adequacy, and are derived from a careful study of the literature.

The major parameters which is selected for the criterion are reduction of disease risk.

Answer:

Step-by-step explanation:

The absolute value of z is the distance between the point graphed from the complex number and the origin on a complex plane.  In a complex plane, the x axis is replaced by R, real numbers, and the y axis is replaced by i, the complex part of the complex number.  Our real number is positive 3 and the complex number is -5, so we go to the right 3 and then down 5 and make a point.  Connect that point to the origin and then connect the point to the x axis at 3 to construct a right triangle that has a base of 3 and a length of -5.  To find the distance of the point to the origin is to find the length of the hypotenuse of that right triangle using Pythagorean's Theorem.  Therefore:

[tex]|z|=\sqrt{(3)^2+(-5)^2}[/tex] and

[tex]|z|=\sqrt{9+25}[/tex] and

[tex]|z|=\sqrt{34}[/tex]

Answer:

Therefore, we conclude that  R is an equivalence relation.

Step-by-step explanation:

We know that  a relation on a set  is called an equivalence relation if it is reflexive, symmetric, and transitive.

R is refleksive because we have that   a+b = a+b.

R is symmetric because we have that a+d =b+c equivalent with   b+c =a+d.

R is transitive because we have that:

((a, b), (c, d)) ∈ R ; ((c, d), (e, f)) ∈ R

a+d =b+c ⇒ a-b=c-d

c+f =d+e ⇒ c-d =e-f

we get

a-b=e-f ⇒  a+f=b+e ⇒((a, b), (e, f)) ∈ R.

Therefore, we conclude that  R is an equivalence relation.

The survey question 'Do you eat at least five servings a day of fruits and vegetables?' is designed to collect categorical data, as it classifies respondents into groups based on their affirmative or negative answer, rather than providing a numerical value.

The question "Do you eat at least five servings a day of fruits and vegetables?" is designed to collect categorical data. This is because the answers to the question will classify respondents into different categories, specifically those who do eat at least five servings of fruits and vegetables per day and those who do not. As such, the data obtained will be qualitative in nature, allowing us to compare and organize individuals based on their dietary habits.

For a more comprehensive understanding, let's compare data types. In contrast to categorical data, a quantitative variable is numeric and can be measured or counted. It can further be subdivided into discrete or continuous data. Quantitative discrete data involve counts of items or occurrences (e.g., the number of classes you take per school year), while quantitative continuous data involve measurements that can take on any value within a given range (e.g., the weights of soups measured in ounces).

Returning to the student's survey question about fruit and vegetable consumption, it is evident that the data collected does not involve counting or measuring numerical values, but rather involves placing respondents into categories based on their dietary habits. Therefore, the variable in question is indeed categorical.

Answer:

24.2%  students received grades with z-scores between 0.15 and 0.85

Step-by-step explanation:

We are given the following in the question:

The grades of a benchmark test for North High School were normally distributed.

WE have to find the percentage of students that  received grades with z-scores between 0.15 and 0.85.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(score between 0.15 < z < 0.85)

[tex]P(0.15 \leq z \leq 0.85)\\\\= P(z \leq 0.85) - P(z \leq 0.15)\\\\\text{Calculating the value from standard normal z-table}\\\\= 0.802 - 0.560 = 0.242 = 24.2\%[/tex]

24.2%  students received grades with z-scores between 0.15 and 0.85

Answer:

After factorizing the given expression we get the value as [tex]x(3x-1)[/tex].

Step-by-step explanation:

Given:

[tex]3x^2-x[/tex]

We need to factorize the given expression using GCF.

Solution:

[tex]3x^2-x[/tex]

Now GCF means Greatest common factor.

From the given 2 numbers we need to find the greatest common factor.

[tex]3\times x\times x- 1 \times x[/tex]

In the given expression GCF is 'x'.

Hence we can say that;

[tex]x(3x-1)[/tex]

Hence After factorizing the given expression we get the value as [tex]x(3x-1)[/tex].

Answer:

Option 3)  Closer to 0      

Step-by-step explanation:

Correlation:

Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship.

Values between 0 and -0.3 tells about a weak negative linear relationship, values between -0.3 and -0.7 shows a moderate negative correlation and a correlation value of of -0.7 and -1.0 states a strong negative linear relationship.

Thus, for the given situation, if there is no relationship between two quantitative variables then the value of the correlation coefficient, r, is close to 0

Final answer:

To solve for q in the equation 3(q + 4/3) = 23, we distribute the 3, subtract 4 from both sides, and then divide by 3 to find that q is approximately 6.33.

Explanation:

To solve for q in the equation 3(q + \dfrac{4}{3}) = 23, we need to apply some basic algebra principles. First, we distribute the 3 into the parentheses.

3q + 3 \times \dfrac{4}{3} = 23

3q + 4 = 23

Now, subtract 4 from both sides to get 3q alone on one side.

3q = 23 - 4

3q = 19

Last, divide both sides by 3 to solve for q.

q = \dfrac{19}{3}

q = 6.333...

Thus, q is approximately equal to 6.33 when rounded to two decimal places.

The value of q is q= 19 / 3.

Let's solve for q in the equation:

3(q+ 3 / 4)=23

We can solve the equation by distributing the terms, adding/subtracting to both sides, dividing both sides by the same factor, and simplifying.

Steps to solve:

1. Distribute the terms:

3q+4=23

2. Add/subtract to both sides:

3q+4−4=23−4

3q=19

3. Divide both sides by the same factor:

3q / 3 = 19 / 3

4. Simplify:

q= 19 / 3

Therefore, the value of q is q= 19 / 3.