A survey asked students whether they would like a
drama club, a step team, both clubs, or neither club.
The results are below:
• 34 students would like a drama club.
• 27 students would like a step team.
• 14 students would like both.
• 13 students would like neither.
How many students were surveyed?

Answer:

Step-by-step explanation:

Think of it as a triangle.

They give you the length of the bottom side and the location of the tops of the buildings.

You need to find the hypotenuse ( the longest side or the length of the rope)

Use the pythagorean theorem

\(a^{2} + b^{2} = c^{2}\)

10 ^2 + 4^2= c^2

100 + 16 = c^2

116 = c^2

c is about 10.77

The length of the rope is 10.77 m

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the length of the rope be = H

Let the distance between the two buildings be L = 10 m

Let the height of the first building be A = 8 m

Let the height of the second building B = 4 m

Now ,

The expressions form a right angled triangle with the base of the triangle has a length of 10 m and the height of the triangle is 4m

Height of the triangle = A / 2 = 4m

So , the hypotenuse of the triangle will be the length of the rope

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , H² = ( A / 2 )² + L²

Substituting the values , we get

H² = 4² + 10²

H² = 16 + 100

H² = 116

Taking square roots on both sides , we get

H = √116

H ≈ 10.77 m

Therefore , the value of H is 10.77 m

Hence , The length of the rope is 10.77 m

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The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

If A and B are dependent events, then the probability of both events occurring simultaneously is given by:

\(P(A \cap B)=P(B) \cdot P(A \mid B)\)

The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:

\(P(A \cap B)=P(A) \cdot P(B)\)

Multiplication Theorem of Probability:

The multiplication guidelines that we use in probability have already been taught to us, including;

\(\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}\)

Therefore, the relationship between two events is explained by the probability multiplication rule.

Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.

Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.

Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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lower control threshold for the data is LCL = -0.007

The lower control limit on a control chart is the value below which any particular data point would be deemed to be out of statistical control owing to specific cause variation. It is represented by a line below the centerline.

The lower control limit formula: LCL = Pbar - \(3 \sqrt{p bar (1- p bar)/n}\)

To date,

Size of sample = n

Sample size is 12 samples.

Televisions with defects = X

We have a sample defect = p

p chart week with n = 200

x = 4, 7, 5, 6, 8, 3, 12, 4, 4, 5, 6, 2.

P = x/n

p = 4/200 = 0.02

p = 7/200 = 0.035

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 8/200 = 0.04

p = 3/200 = 0.015

p = 12/200 = 0.06

p = 4/200 = 0.02

p = 4/200 = 0.02

p = 5/200 = 0.025

p = 6/200 = 0.03

p = 2/200 = 0.01

total will be 0.33

p bar = 0.33/12

p bar = 0.0275

The lower control limit formula: LCL = Pbar - \(3 \sqrt{p bar (1- p bar)/n}\)

LCL =  0.0275 - 3\(\sqrt{ 0.0275 (1- 0.0275/200}\)

LCL = -0.007

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Answer:

sadfasdaf

Step-by-step explanation:

ok, this should be easyyyyyyyy

Answer:

The answer is:

\(Q' = (-3, 3)\\\\R' = (-5, -3)\\\\S' = (-2, -2)\\\\T' = (0, 1)\\\\\)

Step-by-step explanation:

All vertices of its quadrilateral were co-ordinated;  

\(T(-2, 1), \ Q(1, 3), \ S(0, -2), \ R(3, -3)\) Therefore, we first undertake the operation correct: \(T(2, 0) \ QRST\), there;

\(T(2, 0) \ QRST\) \(\to T(-2 + 2, 1), \ Q(1 + 2, 3), \ S(0 + 2, -2), \ R(3 + 2, -3)\)

\(T(2, 0) \ QRST\)\(\to T(0, 1), \ Q(3, 3), \ S(2, -2), \ R(5, -3)\)

A preimage (x, y) will be the image in the next phase R-y-axis reflecting mostly on the y-axis (-x, y)  and we've got it;  

R y-axis \((T(0, 1), \ Q(3, 3), \ S(2, -2), \ R(5, -3)) = \ T'(0, 1), \ Q'(-3, 3), \ S'(-2, -2), \ R'(-5, -3)\)From which we get \((Ry-axis \ T(2, 0)) \ (QRST = T'(0, 1), \ Q'(-3, 3), \ S'(-2, -2),\ R'(-5,-3).\)

The statement 'the effect size for a regression analysis will be equal to the coefficient of determination' is True

In this question we have been given a statement 'the effect size for a regression analysis will be equal to the coefficient of determination'

We need to state whether the given statement is true or false.

We know that the effect size measures the strength of the relationship between two variables on a numeric scale.

And the coefficient of determination(R²) measures how well a statistical model predicts an outcome. It is a number between 0 and 1.

R² is a measure of effect size

Therefore, 'the effect size for a regression analysis will be equal to the coefficient of determination' is True.

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The minimum sample size needed is 93.

Given:

A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.

here

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

\(n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }\)

On submitting and solving using calculator

n = 93

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Answer:

Quadrant IV

Step-by-step explanation:

An angle whose measure is _302° is in standard position the terminal side of the angle fall in Quadrant IV

Answer:

113.04 (i used 3.14 for pi)

Step-by-step explanation:

area of circle formula = pi r^2

radius = 6

6^2 = 36

3.14 x 36 = 113.04

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

 1,616.60

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

substitute in the formula above  

Step-by-step explanation:

All three statements describe characteristics of a probability distribution.

The probability of an outcome is between 0 and 1: This means that the probability of an event occurring must be greater than or equal to zero and less than or equal to one.

The outcomes are mutually exclusive events: This means that if one event occurs, then the other event cannot occur at the same time.

The sum of the probabilities of all possible outcomes is one: This means that the probability of all possible events occurring must equal one, which is the total probability space.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

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Answer:

y = 35x - 517.

Step-by-step explanation:

y=35x−7

This line has a slope of 35so we can write a line parallel to it as

y - y1 = 35(x - x1) where (x1, y1) is a point on the line.

We are given this point (15, 8), so:

y - 8 = 35(x - 15)

y = 35x - 525 + 8

y = 35x - 517  is the required equation.

Answer:

x=6?

Step-by-step explanation:

it is 90 degresses

Answer:

my answer is D.)3 m + 2 = -10

Step-by-step explanation:

Answer:

Step-by-step explanation:

A rectangular carpet measures 8 m by 6 m​Part of the carpet is covered by a square rug of length 2 m

Answer:

$2.50

Step-by-step explanation:

1+2=3

1+5=6

2+5

The fraction that represents a thirty-seven-degree angle out of a full rotation is 37/360, which signifies that the angle occupies 37 out of the 360 equal parts that make up a complete circle.

In a full rotation, there are 360 degrees, so each degree is a fraction of that complete circle. To determine the fraction that represents a specific angle, we divide the measure of the angle (in degrees) by the total degrees in a full rotation.

In this case, we have a thirty-seven degree angle. Dividing 37 by 360 gives us the fraction 37/360. This means that the angle occupies 37 out of the 360 equal parts that make up a full rotation.

The fraction 37/360 can be simplified, if needed, by finding any common factors in the numerator and denominator. However, in this case, 37/360 is already in its simplest form.

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Answer:

6x - 3 + 4x = 13

10x - 3 = 13

10x = 16

x = 1.6

Any equation whose solution is    x=1.6   has the same solution as this one has.

Step-by-step explanation:

Answer:

25 cm

Step-by-step explanation:

If the string is 25 cm and it goes perfectly around the edge of a plate. The plate, is 25 cm.

Answer:

Angles in the same segment of a circle are equal

Step-by-step explanation:

if a line join two points subtends equal angles at two other points on the same side of that line segment,then the four points are concyclic

The percentage of actual yield to theoretical yield of SO3 + H2O → H2SO4

is B. 86.9%

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500g but the theoretical yield is 575g.

Therefore, The percentage of actual yield to theoretical yield is,

= (500/575)×100%.

= 0.8695×100%.

= 86.95%.

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Answer:

See attached graph

Graph is not continuous

Step-by-step explanation:

The function is not continuous as you can see from the break in the graph

It is discontinuous at x = -2

Answer:

See attachment for graph.

The function is not continuous.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

\(f(x)=\begin{cases} x-3 \;\;\;\;\: \text{if}\;\;\;x \leq -2\\4x+5 \;\;\; \text{if}\;\; \;x > -2 \end{cases}\)

Therefore, the function has two definitions:

When graphing piecewise functions:

First piece of the function

Substitute x = -2 into the first function:

\(\implies f(-2)=-2-3=-5\)

As the interval for the first equation is x ≤ -2, it includes the value of x = -2.  Therefore, place a closed circle at point (-2, -5).

To help graph the line, find another point on the line by inputting another value of x that is less than -2 into the same function:

\(\implies f(-5)=-5-3=-8\)

Plot point (-5, -8) and draw a straight line from the closed circle at (-2, -5) through (-5, -8).  Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of the function

Substitute x = -2 into the second function:

\(\implies f(-2)=4(-2)+5=-3\)

As the interval for the second equation is x > -2, it does not include the value of x = -2.  Therefore, place an open circle at point (-2, -3).

To help graph the line, find another point on the line by inputting another value of x that is more than -2 into the same function:

\(\implies f(1)=4(1)+5=9\)

Plot point (1, 9) and draw a straight line from the open circle at (-2, -3) through (1, 9).  Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attachment for the graph.

\(\boxed{\begin{minipage}{8cm}\underline{Determining if a function is continuous at $x=a$}\\\\Condition 1: $f(a)$ exists\\\\Condition 2: $\displaystyle \lim_{x \to a}f(x)$ exists at $x=a$\\\\Condition 3: $\displaystyle \lim_{x \to a}f(x)=f(a)$\\\end{minipage}}\)

If all three conditions are satisfied, the function is continuous at x = a.

If any one of the conditions is not satisfied, the function is not continuous at x = a.

To determine whether or not the given piecewise function is continuous, find if the function is continuous at x = -2.

Condition 1

Does f(-2) exist?  Yes → f(-2) = -5

Condition 2

\(\textsf{Does}\;\;\displaystyle \lim_{x \to -2} f(x)\;\; \sf exist\;at\;\;x=-2?\)

To the left of  x =- 2, f(x) = x - 3

To the right of  x = -2 , f(x) = 4x + 5

Evaluate the left and right limits as x approaches -2:

\(\displaystyle \lim_{x \to -2^-}f(x)=\lim_{x \to -2^-} -2-3=-5\)

\(\displaystyle \lim_{x \to -2^+}f(x)=\lim_{x \to -2^+} 4(-2)+5=-3\)

\(\textsf{As}\;\;\displaystyle \lim_{x \to -2^-} f(x) \neq \lim_{x \to -2^+} f(x), \;\; \lim_{x \to -2} f(x)\;\; \textsf{does not exist}.\)

As condition 2 fails, there is no need to proceed to condition 3.

Therefore, the function is not continuous.

This experiment is neither the subject nor the researcher because knows which treatment group each subject is in.

A scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact.

A group of doctors are conducting an experiment to test a new nutritional supplement they randomly selected 600 subjects, assigning 300 subjects to receive the supplement and 300 subjects to receive a placebo.

The doctors are unaware of which subjects are assigned to each treatment group. this experiment is neither the subject nor the researcher because know which treatment group each subject is in.

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You have to write an expression that involves exponents to represent the shaded area in square inches of the diagram. Use your expression to calculate the shaded area in square inches.

A data analyst should focus on sample size during the data collection process for several reasons like sample size plays a critical role in determining the accuracy and reliability of the data.

A small sample size may not provide a representative picture of the population being studied, leading to biased or skewed results.

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