Solve the following system of equations graphically on the set of axes below. y=−x+5 and y=2x−1

Answer:

50%

Step-by-step explanation:

Answer:

[tex] {(x - 1)}^{2} + {y}^{2} = {5}^{2} [/tex]

[tex] {(x - 1)}^{2} + {y}^{2} = 25[/tex]

The correct option is B, the 90% confidence interval estimate of the population mean speed is approximately 80 ± 1.1862 mph.

standard error = [tex]\frac{standard \:deviation}\sqrt{(sample \;size)}}[/tex]

Plugging in the values given, we have:

sample mean = 80 mph

standard deviation = 5 mph

sample size = 50

level of confidence = 90%

First, we need to find the critical value z from the standard normal distribution using a table or calculator. For a 90% confidence interval, the critical value is approximately 1.645.

Next, we can calculate the standard error:

standard error = [tex]5 / \sqrt{(50)[/tex]= 0.707

Finally, we can construct the confidence interval:

Confidence interval = 80 ± 1.645*(0.707)

Confidence interval = 80 ± 1.1862

Standard deviation is a measure of the variability or spread of a dataset from its mean or average. It is calculated by finding the square root of the variance, which is the average of the squared differences of each data point from the mean. A high standard deviation indicates that the data points are spread out over a wider range from the mean, while a low standard deviation indicates that the data points are closer to the mean.

Standard deviation is an important statistical tool in many fields, including finance, science, and engineering. It is commonly used in the analysis of data to describe the distribution of a set of values and to compare different sets of data. In finance, for example, standard deviation is used to measure the risk associated with an investment, while in science, it is used to quantify the variability of experimental data.

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Complete Question:-

Suppose we want to estimate the mean speed of trucks travelling on a particular highway. A simple random sample of 50 trucks visiting this highway is selected and their velocities are recorded. The sample provided a mean of 80 mph and a standard deviation of 5 mph. Assume the population of truck speeds is approximately normal. An 90% confidence interval estimate of the population mean speed is:

A. 80 ± 0.188

B. 80 ± 1.186

C. 80 ± 1.115

D. cannot be determined

Step-by-step explanation:

Perimeter =  l + l + w + w  = 20

                      2 l  + 2w = 20

                         l + w = 10    ======> l = 10-w  

Area = l * w = 24            sub in the definition of l (above)

    24 = (10-w)  * w

             -w^2 + 10w - 24  = 0      Use quadratic formula (or factoring)

                                   to find   l  and  w =   4 and 6  ft

Answer:

It looks like the angle between C and D are the same as between D and E, so the correct answer would be:

E. ∠CFD and ∠DFE

Brainliest? ;)

It helps a lot!

Answer:

A, C, E.

Step-by-step explanation:

Hope it helps. :)

Answer:

5605

Step-by-step explanation:

59*95

we can think 95 as 90+5

so we get :

59*(90+5)

5310+295

5605

Answer: The table that could be the data the student collected is table D.

Step-by-step explanation: What is an electromagnet?

An electromagnet is described as a type of magnet in which the magnetic field is produced by an electric current and usually consist of wire wound into a coil.

If student builds an electromagnet using a variable power source and 40 turns of wire. We have it that the student changes the voltage and counts the number of paper clips that are picked up. The table described below could perfectly described the scenario.

This is Table D

Voltage (V)

3

6

9

12

Number of paper clips

9

18

27

36

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The original piece of sheet metal was a square with side length 21 cm.

Let's denote the side length of the square piece of sheet metal as x. When we remove a square of side 6 cm from each corner, the length of each side of the remaining square becomes x-2(6) = x-12. Thus, the base of the box has dimensions (x-12) by (x-12) and the height of the box is 6 cm.

The volume of the box is given by

Volume = Base area x height

Volume = (x-12)² × 6

We are given that the volume is 486 cubic centimeters, so we can set up the equation

486 = (x-12)² × 6

Simplifying and solving for x, we get

81 = (x-12)²

9 = x-12

x = 21 cm

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If the body slides under action of its weight only , then the acceleration is (a) g - U.

Assuming that the question is asking for the acceleration of the body down the inclined plane:

The force of gravity acting on the body is given by F = mg, where m is the mass of the body and g is the acceleration due to gravity (9.8 m/s^2).

The force of friction acting on the body is given by Ff = Umg cos(0), where U is the coefficient of kinetic friction and cos(0) = 1 (since the angle between the plane and the horizontal is 0 degrees).

Since the body is sliding down the plane, the force of gravity is greater than the force of friction, and there is a net force acting on the body in the direction of motion. Using Newton's second law, F = ma, we can set up an equation relating the net force to the acceleration:

mg - Umg cos(0) = ma

Simplifying and solving for a, we get:

a = g - Ug cos(0)

Substituting cos(0) = 1, we get:

a = g - Ug

Therefore, the acceleration of the body down the inclined plane is (a) g - U.

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Answer:

$480.00

Step-by-step explanation:

The area of the counter is:

1 meter * 2 meters = 2 square meters

To calculate the cost of the granite countertop, we need to multiply the area of the counter by the cost per square meter:

2 square meters * $240.00/square meter = $480.00

Therefore, the granite countertop would cost $480.00.

Answer:

(x-h)2 +(y-k)2=r2

Step-by-step explanation:

If the circle has a centre at (0, 5) and radius 3 the above equation becomes:

x2 +(y-5)2=32

We want to know the point where this circle intersects the line y=x+5 in the first quadrant. In order to do that, we substitute y=x+5 into the equation for the circle or:

x2 +(x+5-5)2=32

x2 +x2 =9

2x2 =9

x = 3 sqrt(2)/2 =2.1213

Substituting to this value into the second equation for y, we find:

y = 2.1213 + 5 = 7.1213

Consequently, the line intersects the circle at (2.1213, 7.1213)

Hope this helps :)

The probability that calls last between 4.0 and 4.6 minutes is around 0.4332. 

To unravel this issue, we got to standardize the values and utilize the standard typical dispersion table or calculator.

To begin with, we discover the z-scores for 4.0 and 4.6 minutes:

z1 = (4.0 - 4.0) / 0.40 =0

z2 = (4.6 - 4.0) / 0.40 = 1.5

Employing a standard ordinary conveyance table or calculator, we are able to discover the likelihood of the calls enduring between 4.0 and 4.6 minutes:

P(0 ≤ Z ≤ 1.5) = 0.4332

Subsequently, the likelihood that calls final between 4.0 and 4.6 minutes is 0.4332, or around 0.4332. 

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The given demand and supply of the function has ,

Equilibrium price is Rs. 14 and the equilibrium quantity is equal to 40 units.

The consumer surplus for the given function is Rs. 1,080.

The producer's surplus for the given function is Rs. 40.

Demand of the function 'Qd' = -2P + 68

Supply  of the function 'Qs' = 2P + 12

The equilibrium price and quantity by setting the demand equal to the supply.

⇒ Qd =  Qs

Setting Qd equal to Qs, we get,

⇒-2P + 68 = 2P + 12

Solving for P, we get,

⇒4P = 56

⇒P = 14

Substituting P back into either the demand or supply equation, we get,

⇒Qd = -2(14) + 68

        = 40

⇒Qs = 2(14) + 12

        = 40

So the equilibrium price is Rs. 14 and the equilibrium quantity is 40 units.

The consumer's surplus,

= The area below the demand curve and above the equilibrium price.

⇒ Consumer's surplus

= (1/2) x (Equilibrium quantity) x (Difference between maximum price and equilibrium price)

⇒ Consumer's surplus = (1/2) x (40) x (68 - 14)

⇒ Consumer's surplus = Rs. 1,080

The consumer's surplus is Rs. 1,080.

The producer's surplus

= The area above the supply curve and below the equilibrium price.

⇒ Producer's surplus

= (1/2) x (Equilibrium quantity) x (Difference between equilibrium price and minimum price)

⇒ Producer's surplus = (1/2) x (40) x (14 - 12)

⇒ Producer's surplus = Rs. 40

The producer's surplus is Rs. 40.

Therefore, for the given demand and supply function we have,

Equilibrium price and the equilibrium quantity is equal to Rs. 14 and 40units.

Consumer’s Surplus  is Rs. 1,080.

Producer's surplus is Rs. 40.

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The above question is incomplete , the complete question is:

Given the demand = −2P + 68 and the supply function = 2P + 12. Calculate

The equilibrium price and the equilibrium quantity

(a) the consumer’s surplus

(b) the producer’s surplus assuming pure competition

The speed of snow traveling at 40 feet per hour is equivalent to 20.41 centimeters per minute.

To convert the speed of snow from feet per hour to centimeters per minute, we need to use the appropriate conversion factors.

We convert 40 feet per hour to feet per minute by dividing it by 60, since there are 60 minutes in an hour. 40 feet per hour / 60 = 0.67 feet per minute

We convert feet to centimeters by multiplying by the conversion factor of 30.48, since there are 30.48 centimeters in a foot. 0.67 feet per minute * 30.48 = 20.41 centimeters per minute.

It's important to pay attention to units when making conversions, as it can significantly affect the accuracy of calculations. In this case, we made sure to use the appropriate conversion factors to convert between feet per hour and centimeters per minute.

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A) The theoretical probability of drawing a red card is 1/2.

B) The theoretical probability of the intersection of the events "The first draw is a club" and "The second draw is a club" is 13/208

C) The theoretical probability of drawing a spade given that the card drawn is black is 1/2

D) The events "The card drawn is a spade" and "The card drawn is black" are not independent.

A) The theoretical probability of drawing a red card is:

P(Red card) = Number of red cards / Total number of cards

= 26/52

= 1/2

B) The probability of drawing a club on the first draw and a club on the second draw is the product of the probabilities of each event:

P(First draw is a club ∩ Second draw is a club) = P(First draw is a club) * P(Second draw is a club)

= (13/52) * (13/52)

= 169/2704

= 13/208

C) The probability of drawing a spade given that the card drawn is black is:

P(Spade | Black card) = P(Spade ∩ Black card) / P(Black card)

= 26/52

= 1/2

D) To determine if the events "The card drawn is a spade" and "The card drawn is black" are independent, we need to check if the probability of drawing a spade is affected by the knowledge that the card drawn is black. From Part C, we know that:

P(Spade | Black card) = 1/2

The probability of drawing a spade without any additional information is:

13/52 = 1/4.

Since P(Spade | Black card) ≠ P(Spade), the events are dependent, and not independent.

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The probability that the disc is either blue or white is 11/59

Given that

number of blue discs : number of white discs = 6:5

number of blue discs : number of green discs = 1:8

So, we have

Blue : White = 6 : 5

Blue : Green = 1 : 8

This can be expressed as

Blue : Green = 6 : 48

So, we have

Blue : White : Green = 6 : 5 : 48

So, we have

Blue or White : Green = 11 : 48

So, the probability is

P = 11/(48 + 11)

Evaluate

P = 11/59

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The correct option is :

Because the P-value is less than Alpha = 0.05, the student should reject H0.

H0:p = 0.30,Ha:p < 0.30

We have the information:

It was stated that the proportion of blue beads in the container is 0.30. Here, the interpretation of this value is :

The null hypotheses is 0.30

and, Alternative hypotheses is : 0.045

Therefore, Assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the sample proportion would be 0.20 by chance alone.

So, Because the P-value is less than Alpha = 0.05, the student should reject H0.

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If your p-value is 0.11 and the significance level is 0.05, you would conclude that there is insufficient evidence to reject the null hypothesis. In other words, you cannot establish a statistically significant relationship between the variables you are studying.

To explain this further, the p-value (0.11) represents the probability of observing the data, assuming that the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis. The significance level (0.05) serves as a threshold to determine whether the p-value is small enough to reject the null hypothesis.

If the p-value is less than or equal to the significance level, you would reject the null hypothesis and conclude that there is a statistically significant relationship between the variables. However, in this case, the p-value (0.11) is greater than the significance level (0.05), which means that the probability of observing the data is not low enough to reject the null hypothesis.

Therefore, you cannot establish a statistically significant relationship between the variables, and the observed results could be due to chance or random variation.

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Answer:

Step-by-step explanation:

First of all , we know that mean simply means average . The formula for calculating average / mean is :

Sum of all entities ÷ by number of entities.

So , lets start with Sadie.

41+ 44 +46+ 46 +48=225

225 ÷5 =53

Therefore the mean of Sadie's mean was 53.

Now for Penelope.

We will use the same formula.

44+44+47+48+50=233

233÷5=46.6

Therefore Penelope's mean was 46.6.

We can see that Sophie had the highest mean .To find the difference just subtract the means.

Answer:

2((5)(4) + (5)(3) + (4)(3)) = 2(20 + 15 + 12)

= 2(47) = 94

Answer:

To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.

\text{Volume of rectangular prism}=Volume of rectangular prism=start text, V, o, l, u, m, e, space, o, f, space, r, e, c, t, a, n, g, u, l, a, r, space, p, r, i, s, m, end text, equals \text{length}\times\text{width}\times\text{height}length×width×heightstart text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text

Want to learn more about finding volume of rectangular prisms?

Volume=length×width×heightstart text, V, o, l, u, m, e, end text, equals, start text, l, e, n, g, t, h, end text, times, start text, w, i, d, t, h, end text, times, start text, h, e, i, g, h, t, end text

\phantom{\text{Volume}}=3\times2\times3Volume=3×2×3empty space, equals, 3, times, 2, times, 3

\phantom{\text{Volume}}=18\text{ cubic units}Volume=18 cubic units

If the height of a rectangular prism is not given, divide the prism's volume by it's width and also divide it by it's length in order to find the height of the prism. For example:

Volume=30

Length=5

Width=3

Height=?

30/5=6, 6/3=2 so 2 equals your height.

Hope that helps.

From the given stem and leaf plot, the mode of the given data is 57.

A stem and leaf plot also called a stem and leaf diagram is a way of organizing data into a form that makes it easy to observe the frequency of different types of values.

We know that, mode is value appearing the most times.

From the given graph, we can 57 is repeated thrice.

Therefore, option B is the correct answer.

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The donation to the chi-square test statistic for men who named business networking as the most important factor is 4.29.

To calculate the donation to the chi-square test statistic for men who named business networking as the most important factor, we need to calculate the anticipated frequency and the donation for that cell.

The anticipated frequency for a cell is calculated as

anticipated frequency) = ( row aggregate) *( column aggregate)/( grand aggregate)

The row aggregate for the" business networking" row is 105, the column aggregate for the men is 1000, and the grand aggregate is 2000. thus, the anticipated frequency for the cell corresponding to men who named business networking is

anticipated frequency) = ( 105) *( 1000)/( 2000) = 52.5

To calculate the donation, we use the formula

donation) = (( observed frequency- anticipated frequency) 2)( anticipated frequency)

For men who named business networking, the observed frequency is 45. Plugging in the values, we get

donations = (( 45-52.5) 2)(52.5) = 4.29

thus, the donation to the chi-square test statistic for men who named business networking as the most important factor is 4.29

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Answer:

Step-by-step explanation:

Hi!!! Remember (SOHCAHTOA)

Sin= opposite/hypotenuse

Cosine= Adjacent/ hypotenuse

Tan= opposite/adjacent

SO, use the letter of the angle- and match this phrase.

answer 11= 5/12

answer 12= 7/25

answer 13= 4/5

answer 14= 5/12

Answer:

Step-by-step explanation:

In a parallelogram, opposite angles are equal. So we can set the two opposite angles equal to each other and solve for x:

17x + 3 = 19x - 5

Simplifying the equation, we get:

-2x = -8

Dividing both sides by -2, we get:

x = 4

Therefore, for ABCD to be a parallelogram, x must be equal to 4.

The probability that a patient shows improvement if it is known that the patient was given the drug is 0.7 or 70%.

Based on the information given in the table, the probability that a patient shows improvement if it is known that the patient was given the drug can be calculated as:

p(improvement | drug) = number of patients who improved and were given the drug / total number of patients who were given the drug

= 56 / (56 + 24)

= 0.7

Therefore, the probability that a patient shows improvement if it is known that the patient was given the drug is 0.7 or 70%. This suggests that the drug has a relatively high chance of leading to improvement in symptoms for patients with the particular condition being studied.

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Complete Question:

a study has been done to determine whether or not a certain drug leads to improvement in symptoms for patients with a particular condition. the results are shown in the table. based on this information, what is the probability that a patient shows improvement if it is known that the patient was given the drug? p(improvement | drug)

Any ordered pair of the form (x, 16x) would represent a weight in pounds and its equivalent weight in ounces according to the given equation

The given equation y = 16x represents the relationship between x, the number of pounds, and y, the number of ounces. In other words, for a given weight in pounds, we can calculate the corresponding weight in ounces using the equation y = 16x.

To find the ordered pairs that represent the number of pounds and the number of ounces, we can plug in different values of x and solve for y.

For example, if x = 1, then y = 16(1) = 16. This means that 1 pound is equivalent to 16 ounces. Therefore, one ordered pair that represents the number of pounds and the number of ounces is (1, 16).

Similarly, if x = 2, then y = 16(2) = 32. This means that 2 pounds is equivalent to 32 ounces. Therefore, another ordered pair that represents the number of pounds and the number of ounces is (2, 32).

We can continue this process for different values of x to get more ordered pairs that represent the relationship between the number of pounds and the number of ounces.

In general, any ordered pair of the form (x, 16x) would represent a weight in pounds and its equivalent weight in ounces according to the given equation.

Therefore, all ordered pairs of this form would be valid solutions. For example, (3, 48), (4, 64), and (5, 80) are all ordered pairs that represent the relationship between pounds and ounces in the given equation.

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Complete question is:

The equation y=16x represents the relationship between x the number of pounds and y the number of ounces, which order pairs expression represent the number of pounds and the number of ounces in the given equation?

Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

[tex]\frac{tan(59)}{1} = \frac{h}{45}[/tex]

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.