Two weather stations are aware of a thunderstorm located at point c. The weather stations A and B are 34 miles apart. How far is weather station A from the storm?

There is only one solution for this equation. v = 31/4 is the only solution to this equation.

To solve for v in the equation (3)/(4v)+(7)/(v)=1, we need to get a common denominator and then solve for v.

Step 1: Get a common denominator. The common denominator for 4v and v is 4v. So, we will multiply the second fraction by 4/4 to get a common denominator:
(3)/(4v)+(7*4)/(v*4)=1

Step 2: Simplify the fractions:
(3)/(4v)+(28)/(4v)=1

Step 3: Combine the fractions:
(3+28)/(4v)=1

Step 4: Simplify the numerator:
(31)/(4v)=1

Step 5: Cross-multiply to solve for v:
31=4v

Step 6: Divide both sides by 4 to get v:
v=31/4

The solution is v=31/4.

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If you are solving for z:

-8=z/14

multiply by 14 on both sides:

z = -112

1. (a)  Using a z-table, we can find the probability corresponding to this z-score, which is 0.758. Therefore, the probability that a student's mark is less than 52 is 0.758. (b) To find the number of students whose marks are between 45 and 55, we need to calculate the z-scores for 45 and 55 . The z-score for 45 is (45 - 45) / 10 = 0, and the z-score for 55 is (55 - 45) / 10 = 1.  (c)  The probability corresponding to this z-score is 0.3085. Therefore, the percentage of students whose marks exceed 40 is 1 - 0.3085 = 0.6915, or 69.15%. 2. (a)  So, the probability that a student only has regular study time is 750/1000 - 550/1000 = 200/1000 = 0.2. (b) The probability that a student either has a regular study time or uses reference books is 750/1000 + 550/1000 - 550/1000 = 750/1000 = 0.75. (c) The probability that a student neither studies regularly nor uses reference books is 1 - 0.75 = 0.25.

Therefore, the probability that a student's mark is between 45 and 55 is 0.8413 - 0.3413 = 0.5. Since there are 220 students in the college, the number of students whose marks are between 45 and 55 is 0.5 * 220 = 110.

To find the probability that a student's mark is less than 52, we need to calculate the z-score for 52 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. So, z = (52 - 45) / 10 = 0.7.

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Answer:

B

Step-by-step explanation:

2 is hundred = 2x100

0 is tens =0x10

4 is unit =4 x 1

All numbers after the decimal point to the right are fractions

0 is tenth = 0/10 =0

1 is hundredth =1/100

7 is thousandth 7/1000

Now you can choose the right answer

No, the set of vectors x, x + 3x², x³, x² does not span P[x].

To span P[x], a set of vectors must be able to generate any polynomial in P[x] through a linear combination of the vectors in the set. However, the set given only includes polynomials of degree 1, 2, and 3. This means that it cannot generate polynomials of degree 0 (constants) or polynomials of degree 4 or higher.

For example, the polynomial 5 cannot be generated from a linear combination of the vectors in the set, as there are no constants in the set. Similarly, the polynomial x⁴ cannot be generated, as there are no vectors of degree 4 or higher in the set.

Therefore, the set of vectors x, x + 3x², x³, x² does not span P[x].

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Answer: 89 miles

Step-by-step explanation:

Well, if the construction crew added one mile every day for 38 days, then the formula would look like this.

L = 51 + (38)

51 + 38 = 89

L = 89 miles

Answer:

To calculate the ending balance, we can use the following formula:

Ending Balance = Principal x (1 + Interest Rate x Time)

Given:

Principal = $7,900

Interest Rate = 1.9%

Time = 2 3/4 years

Therefore,

Ending Balance = $7,900 x (1 + 0.019 x 2.75) = $8,084.60

Answer: 8319.66994

Step-by-step explanation:

your initial x your interest all raised to your time interval.

7,900(1+.019)^2.75

The equation of the line is y = 780x + 150, r² value  is 0.186, the r value is 0.431, and the predicted population in year 12 is 9450.

To find a linear regression that fits this data, we need to use the following formula:
y = mx + b
where y is the population, x is the number of years, m is the slope, and b is the y-intercept.

We can use the data given to find the slope (m) and the y-intercept (b). The slope can be found by calculating the difference in the population between two consecutive years and dividing it by the difference in the number of years. The y-intercept can be found by plugging in the values of x and y into the equation and solving for b.

Using the data given, we can find the slope and y-intercept as follows:

m = (1950 - 1170) / (3 - 2) = 780
b = 150 - (0)(780) = 150

Therefore, the equation of the line is:
y = 780x + 150

To find the r² value, we can use the formula:
r² = 1 - (SSres / SStot)

where SSres is the sum of squares of residuals and SStot is the total sum of squares.

SSres = (150 - 150)² + (620 - 930)² + (1170 - 1710)² + (1950 - 2490)² = 2,484,400
SStot = (150 - 1222.5)² + (620 - 1222.5)² + (1170 - 1222.5)² + (1950 - 1222.5)² = 3,051,875

r² = 1 - (2,484,400 / 3,051,875) = 0.186

The r value can be found by taking the square root of the r²value:
r = √0.186 = 0.431

To predict the population in year 12, we can plug in the value of x into the equation of the line:
y = 780(12) + 150 = 9450

Therefore, the predicted population in year 12 is 9450.

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Benito and his family will save $1,315 by the move to Oakland.

Savings in house = $1200 - $565

                               = $635

Savings in food = $655 - $545

                          = $110

Saving in health care = $495 - $245

                                   = $250

Saving in taxes  = $625 - $450

                          = $175

Saving in necessities = $495 - $350

                                   = $145

Total saving = $635 + $110 + $250 + $175 + $145

                    = $1,315.

Hence, Benito and his family will save $1,315 by the move to Oakland.

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Your question is incomplete, the complete question is:

Benito's family is thinking of relocating from Los Angeles to Oakland to save money. They set up a budget comparing the cost of living for both cities.

Oakland     Los Angeles  

Cost Housing       $565        $1200

Food                     $545        $655

Health Care         $245        $495

Taxes                    $450         $625

Other Necessities $350        $495

How much money will they save monthly by the move to Oakland? $1315, $1560, $1665, or $1765?

The experimental probability of choosing a nickel based on the 13 trials is 4/13.

What is probability ?

Probability can be defined as ratio number of favourable outcomes, total number of outcomes.

Based on the experimental probabilities shown in the table, we can calculate the probability of choosing a nickel on the 13th trial using the following steps:

Calculate the total number of trials: 12 + 1 = 13

Calculate the total number of times a nickel was chosen in the 12 trials: 12 * 1/4 = 3

Add 1 to the total number of times a nickel was chosen to account for the 13th trial: 3 + 1 = 4

Calculate the experimental probability of choosing a nickel based on the 13 trials: 4/13

Therefore, the experimental probability of choosing a nickel based on the 13 trials is 4/13.

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The chemist must use 12 ml of the 11% acid solution and 42 ml of the 20% acid solution to make a solution of quantity 54 ml of 18% concentration acid solution.

It is already given that the chemist wishes to make a solution of 54 milliliters of 18 percent concentration using two different solutions of concentration 11% and 20% each.

Now let us consider that the quantity of acid to be present in the final solution is (18/100)×54 = 9.72 ml

If we consider that x ml of 11% solution and y ml of 20% solution are added, then following relations can be obtained:

Total volume of x and y in the final solution = x + y = 54 ...(1)

Considering the concentration of acid and its volume, the following equation is formed:

0.11x + 0.2y = 9.72 ...(2)

Solving the equations (1) and (2) for the value of x and y, we get:

x = 54 - y

∴ 0.11(54 - y) + 0.2y = 9.72

⇒ 5.94 - 0.11y + 0.2y = 9.72

⇒ 0.09y = 3.78

⇒ y = 42 ml

Putting the value of y in equation (1), we get

x = 54 - y

x = 54 - 42 = 12 ml

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The Height of the pool should be 1.6 m.

Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.

Given:

length of pool= 12.5 m

width of pool = 5.7 m

and, Maximum volume of pool = 114 m³

So, Volume= l w h

114 = 12.5 x 5.7 x h

114 = 71.25 h

h = 114/ 71.25

h = 1.6 m

Thus, the height can be 1.6 m.

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Answer:

22

Step-by-step explanation:

10+11=21

.05+.05=1

1+21=22

The total distance of 2 and 1/7 laps of the race track is given as follows:

[tex]3\frac{39}{42}[/tex]

The total distance is obtained applying the proportions in the context of the problem.

The length of one lap, as a fraction, is given as follows:

1 and 5/6 km = (6 + 5)/6 = 11/6 km.

The number of laps is given as follows:

2 and (1/7) = (14 + 1)/7 = 15/7 laps.

Hence the total distance is given as follows:

11/6 x 15/7 = 165/42.

165 divided by 42 has a quotient of 3 with a remainder of 39, hence the mixed number representing the number of laps is given as follows:

[tex]3\frac{39}{42}[/tex]

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The degree 4 polynomial with the given zeroes is P(x) = x^4-(94/5)x^3-(24/5)x^2.

A degree 4 polynomial with the given zeroes can be represented as:


P(x) = (x-4)(x+(6)/(5))(x-0)^2


Simplifying the polynomial gives:


P(x) = (x-4)(x+(6)/(5))(x^2)


P(x) = (5x-20)(x+(6)/(5))(x^2)


P(x) = (5x^2-20x+(6x)/(5)-24/(5))(x^2)


P(x) = (25x^2-100x+6x-24)/(5)(x^2)


P(x) = (25x^2-94x-24)/(5)(x^2)


P(x) = (5x^4-94x^3-24x^2)/(5)


P(x) = x^4-(94/5)x^3-(24/5)x^2


So the degree 4 polynomial with the given zeroes is P(x) = x^4-(94/5)x^3-(24/5)x^2.

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Answer:

x=6

My best attempt

Step-by-step explanation:

The ratio is 4:5.6 from top to bottom.

We have a ratio of x:8.4

We will make an equation.

4:5.6=x:8.4

Cross multiply:

5.6x=4x8.4

5.6x=33.6

Divide both sides by 5.6:

x=6

a) The regression prediction for a classroom with 22 students is 651.24.

b) The predicted change in the classroom's average test score for a change from 19 to 23 students is 23.28.

c) The sample average of the test scores across the 100 classrooms is approximately 639.88.

d) The R-squared (R²) measure is 0.08, which indicates a relatively small amount of variation in test scores is explained by variation in class size.

e) The magnitude of the coefficient of correlation (r) is 0.283, indicating a weak positive linear association between class size and test scores.

f) The sample standard deviation of test scores across the 100 classrooms is approximately 11.28.

a) If a classroom has 22 students, then the regression prediction for that classroom's average test score would be:

S = 520.4 + 5.82(22) = 651.24

b) If last year a classroom had 19 students and this year it has 23 students, then the predicted change in the classroom's average test score would be:

ΔS = 5.82(23-19) = 23.28

Note that this calculation assumes that the other factors affecting test scores remain the same, which may not be realistic.

c) The sample average class size across 100 classrooms is 21.4. To find the sample average of the test scores across the 100 classrooms, we simply plug in the average class size into the regression equation:

S = 520.4 + 5.82(21.4) = 639.88

Therefore, the sample average of the test scores across the 100 classrooms is approximately 639.88.

d) The R-squared (R²) measure in this model is 0.08. This is a relatively small value, which means that only 8% of the variation in test scores can be explained by variation in class size. The remaining 92% of the variation is due to other factors that are not captured by the regression model.

e) The magnitude of the coefficient of correlation (r) in this model can be found by taking the square root of R²:

r = √0.08 = 0.283

The interpretation of r is that there is a weak positive linear association between class size and test scores. This means that as class size increases, test scores tend to increase slightly, but the relationship is not very strong.

The difference between R² and r is that R² measures the proportion of variance in the dependent variable (test scores) that is explained by the independent variable (class size) and any other variables in the model, while r measures the strength and direction of the linear association between the two variables.

f) The standard error of the regression (SER) is given as 11.5. This represents the average amount of variation in test scores that is not explained by the regression model. The sample standard deviation of test scores can be estimated by multiplying SER by the square root of (1 - R²) and dividing by the square root of the number of observations:

s = SER × √(1 - R²) / √n

= 11.5 × √(1 - 0.08) / √100

= 11.28

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The length of the arc AB is 44.7 mm

A sector is a part of a given circle which is bounded by two radii and an arc. The length of an arc is simply the path of the incomplete circle.

The length of an arc can be determined by:

length of an arc = θ/ 360 2πr

Where is the measure of the central angle, and r is the radius of the circle.

From the diagram given,

The length of arc AB =  θ/ 360 2πr

                                   = 61/ 360*2*22/7*42

                                   = 44.7333

The length of arc AB is 44.7 mm.

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So, by resolving the given, we obtain the result: As a result, the range of standard deviation timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.

A statistic called standard deviation may be used to represent the variability or variation of a collection of statistics. A low standard deviation means that the values often tend to be closer to the set mean, whereas a large standard deviation shows that the values are widely spread. The standard deviation is an indicator of how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is small, and are more scattered when it is big. Standard deviation is the average degree of variability in the data collection. It displays each score's standard deviation from the mean.  

We can thus get the z-scores that correspond to the bottom and upper bounds of this range using the z-score calculation formula:

Lower bound: z = (x - )/z = (x - 80)/z = 2.5 z = -3

The maximum value is z = (x - ) / z = (x - 80) / 2.5 z = 3.

The area under the curve between z = -3 and z = 3 can be calculated using a calculator or a conventional normal distribution table.

The minimum value is z = -3 (x - 80) / 2.5 = -3 x - 80 = -7.5 x = 72.5.

z = 3 (x - 80) / 2.5 = 3 x - 80 = 7.5 x = 87.5 is the upper limit.

As a result, the range of timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.

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the friends receive one eighteenth each

The price for adults to visit the mammoth cave is $16 and the price for students is $9.

The first step is to form a system of equations that represent the information in the question.

2a + 5s = 77 equation 1

2a + 7s = 95 equation 2

Where:

a = price of one adult

s = price of one student

The elimination method would be used to solve the equations.

Subtract equation 1 from equation 2:

2s = 18

Divide both sides of the equation by 2

s = 18/2

s = $9

Substitute for s in equation 1:

2a + 5(9) = 77

2a + 45 = 77

2a = 77 - 45

2a = 32

a = 32 / 2

a = 16

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The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.

A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.

The area of the rectangle is given as:

A = (l)(w)

A = 10(8)

A = 80 sq. units

The area of the triangle is:

A = 1/2(b)(h)

In the figure:

b = 16 - 10 = 6 and h = 8.

A = 1/2(6)(8)

A = 24 sq. units

The total area of the figure is:

Area = area of rectangle + area of triangle

Area = 80 + 24

Area = 104 sq. units

Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

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Answer: (a) From the graph, we can see that the function f is increasing on the interval [-5, -1), (-2, 2), and (3, 5]. Therefore, we can write the increasing intervals in interval notation as:

[-5, -1) ∪ (-2, 2) ∪ (3, 5]

(b) From the graph, we can see that the function f is decreasing on the interval (-1, 1) and (2, 3]. Therefore, we can write the decreasing intervals in interval notation as:

(-1, 1) ∪ (2, 3]

(c) From the graph, we can see that the function f is constant on the interval [-4, -3]. Therefore, we can write the constant interval in interval notation as:

[-4, -3]

Step-by-step explanation:

Answer: 10134.2425

Step-by-step explanation:

Your initial number, 8900, is multiplied by 1+.033 because your percent and your adding money. It all is then raised to the power of 4. Your equation will be 8900(1+.033)^4 Your percentage is always moved two decimal points to the left all multiplied by the amount of years.

Answer:

12

Step-by-step explanation:

g(-4)=2(-4)^2+4(-4)-8

g(-4)=8

f(8)=2(8)-4

f(8)=12