a local zoo found that if the price of admission was $15$⁢15, the attendance was about 15501550 customers per day. when the price of admission was dropped to $9$⁢9, attendance increased to about 29002900 per day. write a linear equation for the attendance in terms of the price, p. ( a

By using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

So, draw a figure of the 2 buildings as follows:

(Refer to the  image attached below)

Now, we know that we can get the distance between the rooftops using the Pythagorean theorem.

Pythagorean theorem: c² = a² + b²

Now, insert the values and calculate as follows:

c² = a² + b²

c² = 12² + 16²

c² = 144 + 256

c² = 400

c = √400

c = 20ft

Therefore, by using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.

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The value of 'p' obtained by completing the square is √5 - 2.

The given equation in the question is-

p² + 4p = 1

4 divided by half is 2, but 2 squared is 4, therefore

p² + 4p + 4 = 1 + 4

Putting that part of "b" between parenthesis is the simplest method to describe it at this point.

(p + 2)² = 5

The result of multiplying (p + 2)(p + 2) is p² + 4p + 4.

A square root from both sides is now calculated.

p + 2 = √5

p = √5 - 2

Thus, the value of 'p' obtained by completing the square is √5 - 2.

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The correct question is-

Solve the equation p² + 4p = 1 by completing square.

The probability that the average length of a randomly selected bundle of steel rods is 155.8 then P = 0.174 cm

Given sample size 'n' = 30 steel rods

Mean of the Population = 155.1 cm

Standard deviation of the Population = 1.4 cm

Given x⁻ be the random variable of Normal distribution

Let x₁⁻ =  155.8cm

The probability that the average length of a randomly selected bundle of steel rods is  155.8-cm.

P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)

                      = P(Z <Z₂) - P(Z<Z₁)

                     = 0.5 +A(1.629) - (0.5 +A(0.7541)

                     = A(1.629) - A(0.7541)

                     = 0.4474 - 0.2734

                     = 0.1

The probability that the average length of a randomly selected bundle of steel rods is 155.8 cm = 0.174

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2648625 cubic feet of water that have flowed down the river in 5 minutes

Given that:

The flow of the water can be modeled mathematically with the

function, w(t) = 250t, where w(t) represents the volume of the water in cubic meters, at time t, in seconds.

In order to find the number of cubic feet of water that have flowed down the river in 5 minutes. We'll first convert the time t = 5 minutes into seconds and then substitute it into the function. That is:

t = 5 minutes = 5 × 60 = 300 seconds

w(t) = 250t

w(300) = 250 × 300

w(300) = 75000 cubic meters

To convert to cubic feet multiply by 35.315:

w(300) =  75000 × 35.315 = 2648625 cubic feet

Therefore, the number of cubic feet of water that have flowed down the river in 5 minutes is 2648625 cubic feet

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Based on the slope (-8) of the linear equation, the amount Austin pays each week, which is $8.

A linear equation can be defined as y = mx + b, which shows the relationship between variable x and variable y, where we have the following:

Slope value = m = change in y / change in x [this is also the unit rate]

Y-intercept of initial value = b.

Given that the table represents a linear equation, find the slope or unit rate of the linear equation, which represents the amount Austin pays every week.

Slope (m) = change in L / change in t

Using two pairs of values from the table, (2, 24) and (4, 8):

Slope (m) = change in L / change in t = (24 - 8) / (2 - 4) = 16/-2

Slope (m) = -8

This implies that, Austin pays $8 every week.

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Using test statistic z, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.

In the given question we have to estimate how much a typical parent would spend on their child's birthday gift using a 98% confidence level.

Given in the question

Number of sample (n) = 29

Sample mean (X) = 35.9

Sample standard deviation (S) = 9.5

We need to calculate 98% confidence interval which can be calculated as

CI = X± [tex]t_{\alpha/2}[/tex] * S/√n

Here confidence level CI = 0.98

Level of significance (\alpha) = 1-0.98=0.02

α/2 = 0.01

Degree of freedom (df) = n-1 = 29-1 = 28

from t table we found [tex]t_{\alpha/2}[/tex] = 2.821

So 98% confidence interval is

CI = 35.9 ± 2.821* 9.5/√29

CI = 35.9± 2.821* 9.5/5.39

CI = 35.9± 2.821*1.763

CI = 35.9± 4.973

CI = (35.9-4.973, 35.9+4.973)

CI = (30.927, 40.873)

30.927 < μ < 40.873

So, Typical parent would spend on their child's birthday gift is between $30.927 and $40.873.

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Answer:  The correct answer is C. y + 3 = 5(x − 1)

Step-by-step explanation:

Change the equation into slope-intercept form

y + 3 = 5(x − 1)

y = 5x - 8

Using the slope-intercept form of y = mx + b, m = slope, and b = the y-intercept.

Therefore, y = 5x - 8 has a slope of 5 and a y-intercept of -8

When we graph the slope from y = -8, it passes through (1, -3)

The length of the other leg of the triangle is 26.4 inches.

Here, we are given that one side of a right angled triangle has length 17 inches and the hypotenuse is 31.4 inches.

Now, the Pythagoras theorem states that, in a right angled triangle, the following equation holds-

[tex]hypotenuse^{2} =height^{2} +base^{2}[/tex]

we already know two of these values so we can calculate the 3rd one.

Let the length of the 3rd side be x inches.

then, substituting the values in the Pythagoras equation, we have-

[tex]31.4^{2}[/tex] = [tex]17^{2}+ x^{2}[/tex]

985.96 = 289 + [tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 985.96 - 289

[tex]x^{2}[/tex] = 696.96

x = 26.4

Thus, the length of the other leg of the triangle will be 26.4 inches.

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Noelia has 216 cards after buying part of the set with her friends.

Combining items and counting them as a single, large group is done through addition.

Given that, Noelia has 144 role-playing cards.

Now, she bought 72 cards more, therefore, the number of cards Noelia has is:

144 + 72

= 216

Hence, Noelia has 216 cards after buying part of the set with her friends.

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multiply 144 times 27 which is 3,888

3888

-     9                      

-----------

3,879     3,879

              -      72

           --------------

          3,807

An exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.

Population growth is seen to increase at an exponential rate. We use the following to model this growth.

y = A₀(1 + r)ⁿ

where

y = value at time

A₀ = original value

r = rate of growth

n = time elapsed

An exponential function that models the quail population is set up like:

y = 765(1+0.16)ⁿ

so that, for example, if we wanted to figure out the population at time (4 years), then we would set up the function as follows,

y = 765(1+0.16)⁴

y = 765(1.16)⁴

y = 765* 1.81

to get

y = 1384.65 quails after 4 year has elapsed.

Hence, an exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.

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Alyssa knows the mass of the rock is 16 grams.

Measurement is a method in which the property of an object are determined by comparing them to the standard quantity.

It is important metric to express any quantity of object , things.

Some basic type of measurement are:

According to the question

It is given that Alyssa finds the measurement of a rock sample to be 16 grams

Here, 18 grams is the mass of the rock

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⇒We can represent this phone lattice in two minimum number of ways and states to represent it.

What is phone lattice?

A state diagram, or directed network in which each node stands for a state of a system, is what is known as a phone lattice. Each edge of a phone lattice has exactly one letter. A word is represented by each route from the start node to the final/end node.

The minimum no. Of states in using a phone lattice to the given requirement is  two.

We can represent this phone lattice in two minimum number of ways and states to represent it.

A  dual lattice may be  defined as the  inclusion on the extents. We represent a lattice using a  Hasse diagram of the given partial ordering on all the  maximal rectangles, transitivity and reflexivity arcs that are omitted. Concepts in the given system are often known  as elements of this lattice.

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Answer: Nonlinear.

Step-by-step explanation:

The correct answer is Independent groups design.

Given that,

Participants in a study are randomly allocated to one of two groups; one group is run at night, while the other is run during the day. Then, each member of each group is measured twice under the red and blue conditions, respectively.

Independent groups design.

Independent measures style, conjointly called between groups is an experimental style wherever completely different participants are employed in every condition of the experimental variable. This suggests that every condition of the experiment includes a distinct cluster of participants.

Therefore, the correct answer is Independent groups design.

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3206 students are randomly chosen since there is no knowledge of the sample fraction.

The following can be used to represent the formula for calculating the margin of error for a single proportion:

ME = z√p(1 - p)/n

In order to be 91% certain that the sampling percentage seems to have an error margin of 1.5 percentage points, the number of randomly chosen students that must be surveyed is equal to;

0.015 = 1.6954×√0.5(1 - 0.5)/n

0.015/1.6954 = √0.5(0.5)/n

On further solving,

n = 3205.128

n ≈ 3206

As a result, 3206 students are randomly chosen since there is no knowledge of the sample fraction.

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The correct question is-

College officials want to estimate the percentage of students who carry a gun, knife, or other such weapons. How many randomly selected students must be surveyed in order to be 91% confident that the sample percentage has a margin of error of 1.5 percentage points?

a) Assume that there is no available information that could be used as an estimate of p.

Answer: x≥3

Step-by-step explanation:

Answer:

Okapi weighs 290, and llama weighs 160.

The graph of the change in Cmax is (see in attachments).

Cmax  Change in Cmax  predicted percentage

2.34                         29.5 22.96%

2.46                 40.7         20.62%

1.87                         5.3         32.14%

3.09                23.3          8.32%

5.59               -45.1     -40.47%

4.05                     -35.3        -10.42%

6.21                      -44.6        -52.58%

2.34                       29.5          22.96%

Graph:

A graph is a logical visual representation of any data in mathematics. The correlation between the variable values is depicted on the graph. A graph is used in graph theory to depict a group of items that are interconnected in some way. In essence, the vertices or nodes of the objects are mathematical notions, and the edges are representations of the connections between the nodes. In mathematics and statistics, many graph types are used to visually display data. The study of points and lines is the focus of the field of graph theory. It is a branch of mathematics with a focus on graph analysis. The mathematical truth is visually illustrated in this image. Relationships are studied using the graph theory.

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Answer:ralph got an 90 on his math test and a 80 on his history test

Step-by-step explanation:

so i divided 170 and that = to 85 so i took the two 5 from the two 80 and added it to the 80 for math

After finding the value of the angle CAE will be equal to 22°.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the information provided in the question,

 The perpendicular bisector of side AB of ABC intersects side AB at point D and BC at point E in the ABC equation. Also, m∠CAB = 82° and m∠C = 68°.

Join A and E.

In Δ ABC

∠A+∠B+∠C = 180° (Angle sum property of triangle.)

82°+∠B+68° = 180°

∠B = 180°-150°

∠B =30°

In Δ ADE and Δ BDE

AD=B D(DE shown is a perpendicular bisector.)

∠ADE =∠BDE = 90°

DE is common.

Δ ADE ≅ Δ EDB (By using the property SAS)

∠DEB=∠D A E [By using the property CPCT]     (1)

In Δ DBE

∠EDB + ∠DBE+∠BED = 180°

90° +30°+∠BED = 180°

∠BED = 180°-120°

∠BED = 60°

So, ∠BAE=∠BED=60° (By using equation 1)

∠CAE=∠CAB - ∠BAE

∠CAE = 82°-60°

∠CAE = 22°.

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Using the probabilities the variance of x represented by Var(x) is equal to var(X) = E(X²) – [E(X)]² , where E(x)  represents the expected value of x.

Given the probabilities of the random variable given by x₁ , x₂ , x₃ ,... has the probabilities of P₁ , P₂ , P₃ ...

We know that Variance is given by the formula:

[tex]Var(x) = \sigma^2=\sum_{i=1} ^n (x_i-\mu)^2px_i)\\\\=\sum_{i=1} ^n(x_i^2-2x_i+\mu^2)\\\\=E(x^2)-[E(x^2)][/tex]

We know that expected value is denoted by E(x) .

Hence the variance is denoted by var(X) = E(X²) – [E(X)]² .

In probability theory and statistics, variance is the predicted squared deviation of a random variable from its population mean or sample mean.

The scattering, or how far apart from the mean a bunch of data are from one another, is measured by variance. A few ideas that involve variance are descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.

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Option B. Because when you have quantitative data, but assumptions of normality are not met. This is because, unlike parametric tests, non-parametric tests do not make assumptions about the data's underlying distribution.

Non-parametric tests are often used when dealing with data that is not normally distributed, as they allow for a more accurate analysis of such data. They can also be used when a linearity of the data cannot be assumed and when dealing with ordinal data. Non-parametric tests are more powerful than parametric tests, which makes them a good choice when a more precise analysis is needed.

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I think its 30!

Please let me know if its right!

As per dr. Chidi Anagonye, self esteem and success on school project results in low distinctiveness.

The focus of attribution theory is on how people make sense of events and how this influences their perceptions and actions. Heider (1958) was the first to suggest a psychological theory of attribution, but Wener and his colleagues (e.g., Jones et al., 1972; Wener, 1974, 1986) created a theoretical framework that has grown to be a significant research paradigm in social psychology. Attribution theory assumes that people try to figure out why people do what they do, i.e., attribute causes to behavior. If someone is trying to figure out why someone else did something, they could assign one or many reasons to that action. An attribution is based on a three-stage process: (1) the person must notice or watch the activity, (2) the person must think that the behavior was done purposefully.

Education, legislation, clinical psychology, and the field of mental health have all seen extensive use of Wener's thesis. Achievement and one's self-concept are closely related. Causal attributions control how we feel about success and failure, according to Wener (1980). For example, one is unlikely to feel satisfaction in achievement or competence while obtaining a 'A' from a professor who only delivers that grade, or when defeating a tennis opponent who always loses... An 'A' from a teacher who gives few high grades, on the other hand, or a victory over a highly rated tennis player after a lot of practice has a big impact. Higher self-esteem students and students who perform well academically have a tendency to credit success to internal, stable, uncontrolled causes.

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I think it might be all them but the third one, if I'm wrong sorry.

The points after dilation will be A'(-2, -2), D'(0, 4), L'(6, 2) if the points are  A(-1,-1),D(0,2),I(3,1)

The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.

It is given that:

Dilate A(-1,-1),D(0,2),I(3,1) by scale factor of 2 from the origin

After dilation:

A (-1,-1) --> ( -1x2 , -1x2 ) --> (-2, -2)

D (0,2) --> ( 0x2 , 2x2 ) --> (0, 4)

L (3,1) --> ( 3x2 , 1x2 ) --> (6, 2)

Thus, the points after dilation will be A'(-2, -2), D'(0, 4), L'(6, 2) if the points are  A(-1,-1),D(0,2),I(3,1)

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Answer: x = 3

Step-by-step explanation: both expressions are equal to each other because the angles are opposite of each other, so you would set the expressions equal to each other and solve from there.

set equations = to each other: 6x - 7 = 4x - 1

add 7 to the other side: 6x = 4x + 6
subtract 4x to the other side: 2x = 6

divide both sides by 2: x = 3

Answer: 27.3 %

Step-by-step explanation:

There are 8 blue and 3 red marbles in the bad so total is 11 marbles

We just need to take 3 divided by 11, then timed 100 and will get the percent of 27.27, or I round up to 27.3%

Answer:

z = − 5 + 7i

Step-by-step explanation:

z + 14 - 5i = 9 + 2i
Subtract 14 from both sides.

z - 5i = 9 + 2i -14
Subtract 14 from 9 to get -5.

z - 5i = -5 +2i
Add 5i to both sides.

z = -5 + 2i + 5i
Combine real and imaginary parts.

z = -5 + (2+5)i
Add 2 to 5.

z = -5 + 7i

Hope this helps!

Answer:

7i - 5

Step-by-step explanation:

z + (14 - 5i) = 9 + 2i

=> z + 14 - 5i = 9 + 2i

=> z = 9 + 2i + 5i - 14

=> z = 7i - 5