Solve using substitution.
y = –7x − 8
y = 2x + 10

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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Speed the top of the ladder is sliding down = 1.6ft/sec  when it is 12 feet away from the wall

15-foot ladder is leaning against a wall.

the top of the ladder is sliding down the wall at a rate of 2 ft/sec.

how fast is the bottom of the ladder moving when it is 12 feet away

Using equivalent proportion

15 ft -------------------2ft/sec

12 ft-------------------X ft/sec

Hence X = (12 x 2) ÷ 15 =1.6 ft/sec

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The equation of the line passing through these points i.e (7,3 ) and (14,6) is

y = (3/7) x or 3x - 7y = 0 ,

Which is linear equation of two variables.

A linear equation is an algebraic equation of the form y = mx + b , with only one constant and one first-order (linear) term, m is the slope and b is the y-intercept.

We have given that,

the ratio of y and x is y : x = 3 : 7

So the ratio of x and y can be expressed as ,

x : y = 7 : 3 ( reverse order)

So let's consider two points as

(x₁, y₁)=(7 , 3) and (x₂, y₂) = (14 , 6)

The equation of the line passing through these points will be,

( y - y₁ )/ (y₂ - y₁) = (x - x₁)/(x₂ - x₁)

=> (y - 3)/(6-3) = (x - 7)/(14 - 7)

=> (y - 3)/3 = (x - 7)/7

=> 7(y - 3) = 3( x - 7)

=> 7y - 21 = 3x - 21

=> 7y = 3x

=> y = (3/7) x

Hence, y = (3/7) x is required equation of line.

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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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Answer:

Winning jump = 5.474

Her best jump = 4.76

Step-by-step explanation:

4.25×1.12=4.76

4.76×1.15=5.474

The error of type I is Despite the fact that the median age is 34, we get to the conclusion that it is not. The appropriate response to this question is option C.

A Type I error is rejecting the null hypothesis when it is actually true. It involves making inferences from statistically significant outcomes even though they might have happened by chance or for other reasons.

The probability of error will depend on the significance level (alpha or) that you choose. In order to determine the statistical likelihood of receiving your results, you established that number at the outset of your investigation (p-value).

The usual level of significance is 0.05 or 5%. The likelihood that the null hypothesis is true is only

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Answer: none of them

Step-by-step explanation:

they are not equal and dont look right i dont think im sorry if i get it wrong

golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. The value of this golden ratio = 1/2 (1 + √5) = 1.618

Ratio:

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.

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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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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

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

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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The trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

cos(-x) =cosx= 3/4

and tanx=

We need to find sin(-x)

tank is ratio of sinx and cosx

We know that tanx=sinx/cosx

√7/3=sinx/3/4

Apply cross multiplication

sinx=√7/3.3/4

sinx=√7/4

sin(-x)=-sinx=-√7/4

Hence, Trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3

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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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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.

When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.

Here,

The length of side=10 inch

The length of diagonal= 12 inch

Let the length of diagonal be x.

6²+(x/2)²=10²

(x/2)²=64

x/2=8

x=16 inch

The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.

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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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⇒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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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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I think its 30!

Please let me know if its right!

If there is a 0.41% chance that an American citizen will die from falling, then the probability  that you will not die from a fall is 99.59%

The chances of an American citizen will die from falling = 0.41%

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The equation will be

The probability = Number of favorable outcomes / Total number of outcomes

The probability  that you will not die from a fall = 1 -  The chances of an American citizen will die from falling

Substitute the values in the equation

The probability  that you will not die from a fall = 1 - 0.41

= 99.59%

Therefore, the probability  that you will not die from a fall is 99.59%

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the Degree of freedom is 9.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

We have given,

Sample size =n=10

Degree of freedom =n-1=10-1=9

Hence the Degree of freedom is 9

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Answer:

Okapi weighs 290, and llama weighs 160.

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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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:

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

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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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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