A city currently has 139 streetlights. As part of a urban renewal program, the city council has decided to install 6 additional streetlights at the end of each week for the next 104 weeks. How many streetlights will the city have at the end of 48 weeks?

Answer:

The mean length of time is 27 minutes.

Step-by-step explanation:

To find the mean, we have to first calculate x and fx.

(0+12)/2=6

(12+24)/2=18

(36+48)/2=42

(48+60)/2=54

Now we have x, and f

Calculate fx by multiplying:

6×11=66

18×25=450

30×23=690

42×15=630

54×6=324

The mean is the sum of fx/sum of f

(66+450+690+630+324)/(11+25+23+15+6)=27

Hope this helps!

The diameter of the conductor with a cross-sectional area of 18,225 cmils is approximately 152.7 mils.

What is Diameter?

Diameter is a measurement of the size of a circle, defined as the distance between any two points on the circle passing through the center. It is the longest chord of a circle, and it bisects the circle into two equal halves.

To find the diameter in mils of a conductor with a cross-sectional area of 18,225 cmils, we can use the formula for the area of a circle:

A = π[tex]r^{2}[/tex]

where A is the cross-sectional area, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

Convert the cross-sectional area from cmils to square inches:

A = 18,225 cmils = 18,225/1,000,000 sq. in. ≈ 0.018225 sq. in.

Solve for the radius of the circle:

A = π[tex]r^{2}[/tex]

[tex]r^{2}[/tex] = A/π

r = sqrt(A/π) ≈ 0.07635 inches

Convert the radius from inches to mils:

r = 0.07635 inches * 1000 mils/inch ≈ 76.35 mils

Find the diameter by doubling the radius:

diameter = 2 * r ≈ 152.7 mils

Therefore, the diameter of the conductor with a cross-sectional area of 18,225 cmils is approximately 152.7 mils.

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Let X be the number of employees the company had last year.

According to the problem, the number of employees this year is 225% of the number last year, which can be written as:

135 = 2.25X

To solve for X, we can divide both sides by 2.25:

X = 135 / 2.25

X = 60

Therefore, the company had 60 employees last year.

Answer:

Diameter-3 inches

Circumference- 9.42 inches

Step-by-step explanation:

In order to get this, you must know that radius is 1/2 of diameter or diameter is 2 times the radius.

As such,

D-Diameter

R-Radius

R = 1.5

D = 2R--> FOR ANY CIRCLE

D = 2(1.5)

D = 3 inches

Now to find circumference you must understand the difference of formulas between the area of a circle and circumference of a circle.

Merely saying, the circumference of a circle is the perimeter of a circle and it is much different from finding the perimeter of other shapes.

The circumference formula is...

C - 2лr

As such,

C - 2(3.14)(1.5)

C - 9.42 inches

As such your answers are

Diameter - 3 inches

Circumference - 9.42 inches

Hope this helped!

Answer:

4 units²

Step-by-step explanation:

Calculate some vectors from the point (2,3).

Vector A = <1, 5>

Vector B = <-2, -2>

The area of the triangle is 1/2 * (the magnitude of the cross product of the vectors)

A × B = -2 + 10 = 8

the magnitude of 8 is 8.

Therefore 1/2 * 8 = 4

Answer:

4 units²

Step-by-step explanation:

The simplified expression is 3x³ -5x² -13x +10.

We have,

(x-2)(3x² + 4x-5)

Now, simplifying the expression as

(x-2)(3x² + 4x-5)

= x(3x²)+  x (4x) -5x -3(3x²) -2 (4x) +10

= 3x³ + 4x² -5x -9x² -8x +10

= 3x³ -5x² -13x +10

Thus, the simplified expression is 3x³ -5x² -13x +10.

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Answer:

Step-by-step explanation:

I looked at it like if I evened out the 2 shapes so that sat flush like in picture. I know all of the angles should =360 to go all the way around

So

120+120+2x+x=360

240+3x=360

3x=120

x=40

Answer:

point = ( -6, 2)

slope = -3

Step-by-step explanation:

point slope formula;

y - y1 = m ( x - x1) ,

where m= slope , (x1, y1) = the coordinates of a point

y - 2 = -3 ( x + 6)

a point the line passes through = (-6 , 2)

slope of the line = -3

Using the area formula for rectangle, we can find the height of the rectangle to be 8m.

The quantity of unit squares that can fit inside a rectangle is known as an area. The quantity of space occupied by a flat surface of a specific form is determined by its area. Each shape's area is specified as a "number of" square units and is based on the maximum number of unit squares that can fit inside it (square centimetres, square inches, square feet, etc.).

Area of the rectangle has been given = 52m².

Base of the rectangle has been given as = 6.5m.

Let height be = h

Area = b × h

⇒ 52 = 6.5 × h

⇒ h = 52/6.5

⇒ h = 8m.

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Answer: 21//2

Step-by-step explanation: 1 1/2 = 3/2

So it takes 3/2 hours to set up 1 comupter workstation.

If we want to find how many hours would it take to set up 7 computer workstation we would have to do 3/2 x 7 and get 21/2 or 20 1/2

The conditional statement is solved and the following argument is invalid

Given data ,

Let the first statement be A

Now , (∀x)(∃y)(p(x, y) ⇒ r(x)):

This statement asserts that for every x, there exists a y such that if x is a factor of y, then x is prime. This is a valid statement, as it essentially says that there exists a prime factor for every integer x

Let the second statement be B

Now , (∀x)(∀y)(∀z)(¬q(x, y, z)): This statement asserts that for all x, y, and z, z is not the greatest common factor (GCF) of x and y. This is a generic statement and does not provide any specific information about the values of x, y, and z. It is not relevant to the conclusion of the argument.

Let the third statement be C

Now , (∃x)(∀y)(p(x, y) ∨ r(x)): This statement asserts that there exists an x such that for all y, either x is a factor of y or x is prime. This is also a valid statement, as it states that there exists an integer x that is either a factor of y or prime for all y.

According to the conclusion, there must exist an x and a z such that z is the GCF of x and y for any y. However, the premises merely state that x is a factor of y or that x is prime; they make no direct mention of the largest common factor between x and y.

Hence , the conclusion (y)(z)(x)q(x, y, z) is not supported by the argument. A stronger case for this conclusion would require more evidence or premises

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Dish D has the density of clusters closest to 0.75 per square centimeter.

A substance's density is determined by how much mass there is per unit volume. It is typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

To find the density of clusters in each circular dish, we need to calculate the area of each dish and divide the number of clusters by that area.

The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, we are given the diameter of each circular dish, which is 8 cm. Therefore, the radius of each dish is 4 cm.

The area of each dish is:

A = πr² = π(4 cm)² ≈ 50.27 cm²

Now, we can calculate the density of clusters in each dish:

Density in A = 53 clusters / 50.27 cm² ≈ 1.05 clusters/cm²

Density in B = 13 clusters / 50.27 cm² ≈ 0.26 clusters/cm²

Density in C = 151 clusters / 50.27 cm² ≈ 3.00 clusters/cm²

Density in D = 38 clusters / 50.27 cm² ≈ 0.76 clusters/cm²

Therefore, dish D has the density of clusters closest to 0.75 per square centimeter.

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The total cost of stay at Oceanview Hotel would be:

Total Cost = $45 x

The total cost of stay at Beachside Hotel would be:

Total Cost = $115 x

What is cost?

Cost is a term used in economics and business to refer to the total monetary expense incurred by a company or an individual in the production or purchase of goods and services.

The two given statements are about the total costs for staying at two different hotels. Let's break down what each of the statements mean:

"Oceanview Hotel changes their fee to $45": This means that the daily rate for staying at Oceanview Hotel is now $45. To find the total cost of staying at this hotel, we simply multiply the daily rate by the number of days stayed. This gives us the equation:

Total Cost = $45 x

where x is the number of days of stay.

"Beachside Hotel changes their daily rate to $115": This means that the daily rate for staying at Beachside Hotel is now $115. Again, we can find the total cost of staying at this hotel by multiplying the daily rate by the number of days stayed. This gives us the equation:

Total Cost = $115 x

where x is the number of days of stay.

So, these two equations give us the total costs for staying at Oceanview Hotel and Beachside Hotel respectively, given the new changes in their rates.

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The triangles are similar by the sas similarity theorem.

The similarity theorem for tri angles states that if two triangles have the same shape, then their corresponding angles are equal and their corresponding sides are proportional.

More specifically, if we have two triangles, Triangle ABC and Triangle DEF, such that:

Angle A = Angle D

Angle B = Angle E

Angle C = Angle F

And also, their corresponding sides are proportional:

AB/DE = BC/EF = AC/DF

Then, we can say that Triangle ABC is similar to Triangle DEF. This means that these two triangles have the same shape and they are only different in size.

The similarity theorem is important in geometry, as it allows us to determine unknown side lengths or angle measures of similar triangles by using proportions. It is also useful in real-life situations where we need to determine the size of objects that are not directly measurable

To prove that two triangles are similar using the SAS (Side-Angle-Side) similarity theorem, you need to show that:

Two pairs of corresponding sides are proportional (have the same ratio).

The included angles (the angle between these two pairs of corresponding sides) are congruent.

So, for the SAS similarity theorem to apply, you need to have two triangles where two pairs of corresponding sides are proportional and the included angle between these sides is congruent. If these conditions are met, then the triangles are similar.

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The number of teenagers who gave data for the survey was 52 teenagers .

The number of teenagers who ate red meat at least once a week was 50 teenagers.

The percentage that ate red meat more than twice per week was 77 %.

The distribution can be described as normal.

The number of teenagers in the survey :

= ∑ ( Frequency of number of times meat eaten )

= 2 + 3 + 7 + 9 + 10 + 8 + 7 + 5 + 1

= 52 teenagers

Number of teenagers eating at least once a week :

= ( 52 total - 2 eating zero times )

= 50 teenagers

Percentage eating red meat more than twice :

= ( 52 total - 2 eating zero times - 3 eating once - 7 eating twice ) / 52 x 100 %

= 77 %

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Answer:

The answer to your problem is, radian measure of angle AOB is π /3 radian

Step-by-step explanation:

How to find the length of an arc:

Arc Length (L) = θ × r

θ being the radian measure of the angle and r is the radius of the circle

From what is give;

L = 2π/9 yards, r = 2 feet = 2/3 yard

Using the formula, L = θ x r

Then concluding to:

2π/9 = θ × 2/3

θ  = (2π × 3) / (9×2) 

θ  = π /3 radian

Thus the answer to your problem is, radian measure of angle AOB is π /3 radian

The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

To find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:

Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.

Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.

Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.

Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.

Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).

Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).

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The solutions to the linear function are;

1. The soccer team makes more money per car ($8) than the French club ($5).

2. The graph that demonstrates Arnold's journey is graph 3

3. The graph that demonstrates Francisco's journey is graph 1

4. The graph that demonstrates Celia's journey is graph 2

To determine which group makes the most money per car, we can calculate the slope of the linear function representing the amount earned per car washed for both the French club and the soccer team. The slope of a linear function is the change in the dependent variable (y) divided by the change in the independent variable (x).

Let's calculate the slope for the soccer team. We can choose any two points to calculate the slope. Let's use the points (3, 24) and (6, 48):

Slope (m) = (change in y) / (change in x) = (48 - 24) / (6 - 3) = 24 / 3 = 8

The soccer team earns $8 per car washed.

We can choose any two points to calculate the slope for the French club. Let's use the points (2, 10) and (4, 20):

(20 - 10) / (4 - 2) = 10 / 2 = 5

The French club earns $5 per car washed

The above answer is dependent on the questions below;

The french club and soccer team are washing cars to earn money. The amount earned, (y) dollars for washind (x) cars is a linear function.  Which group makes the most money per car? explain

                                      French club

Number of cars (x)                       Amount earned (y)

2                                                         10

4                                                          20

6                                                          30

8                                                         40

10                                                         50

Soccer team

Number of cars (x)                       Amount earned (y)

3                                                      24

6                                                       48

9                                                      72

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Answer:

33

Step-by-step explanation:

4×4=16

7×3=21

21+16= 37

2×2=4

37-4=33

The value of x in chords is 25.857 and this is a isosceles triangle.

In geometry, a chord is a line segment that connects two points on the circumference of a circle. A chord is the longest distance between two points on a circle, and it passes through the center of the circle. The endpoints of a chord are referred to as its "endpoints." A chord that passes through the center of a circle is called the "diameter" of the circle. The length of a chord can be calculated using the Pythagorean theorem, given the radius and the distance between the center and the chord. Chords are used in various geometric calculations involving circles, such as finding the area of a sector or segment of a circle.

The sum of the angles of a triangle is 180 degrees. In a circle, the angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference. Using these facts, we can set up the following equation to find x:

(1/2)(14x - 7) + (1/2)(12x + 4) + (1/2)(4x) = 180

Simplifying and solving for x, we get:

7x - 1 = 180

7x = 181

x = 25.857

Therefore, x is approximately equal to 25.857.

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Answer:

x = 20

Step-by-step explanation:

You have pointed out the angles are supplementary, so they add to 180.

Add both angles to equal 180.

7x + x + 20 = 180

Combine like terms.

8x + 20 = 180

Subtract 20 from both sides.

8x = 160

Divide out the 8 to get x.

x = 20

Answer:

15.58

Step-by-step explanation:

1. Arrange n number of data points in ascending order: x1, x2, x3, ... xn

2. Calculate the rank r for the percentile p you want to find: r = (p/100) * (n - 1) + 1

3. If r is an integer then the data value at location r, xr, is the percentile p: p = xr

4. If r is not an integer, p is interpolated using ri, the integer part of r, and rf, the fractional part of r:

p = xri + rf * (xri+1 - xri)

Answer: 1 just like my answer dawg

Step-by-step explanation:

To make r the subject from the equation v = br + y, first subtract y from both sides to get v - y = br. Then divide both sides by b, to get r = (v - y) / b.

The question requires us to rearrange the given formula

v = br + y

to make

r

the subject. To do this, we have to isolate

r

on one side of the equation. The first step is to subtract

y

from both sides of the equation, getting us

v - y = br

. The next step is to divide both sides of the equation by

b

to completely isolate

r

. Therefore, the formula with

r

as the subject is

r = (v - y) / b

.

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The largest area the farmer can enclose with 100 feet of fencing is a rectangle with sides that measure 25 feet by 40 feet. The area of this rectangle is 1000 square feet. The farmer can use this information to fence off the largest possible area for his farm with the 100 feet of fencing he has available.

Area is the measurement of a two-dimensional figure or space. It is represented by a numerical value and is typically measured in units of square meters, square centimeters, or square feet. Area is often used to measure the size of a piece of land, the area of a room, or the total surface of a 3D object. In mathematics, area is a fundamental concept and is used to calculate various other figures, such as the perimeter and volume.

The largest area the farmer can enclose with 100 feet of fencing is a rectangle with sides that measure 25 feet by 40 feet. This can be determined through the proper and complete calculation of the perimeter and area of the rectangle. To start, the perimeter of a rectangle is equal to the sum of its four sides, so the farmer needs to use all of the fencing to create a rectangle with a perimeter of 100 feet. This means that the two sides of the rectangle, x and y, have to add up to 100 feet when added together. This equation can be expressed as x + y = 100.

Next, the area of a rectangle is equal to the product of its two sides, so the farmer needs to find the two sides that will give the largest product when multiplied together. To do this, the farmer can use the equation from the perimeter, x + y = 100, to solve for x and y. This gives the equation x = 100 – y. Plugging this equation into the area equation gives the equation A = (100 – y)y. To find the maximum area, the farmer needs to take the derivative of this equation and set it to zero. This gives the equation y = 50, meaning that the two sides of the rectangle are both 50 feet.

Therefore, the largest area the farmer can enclose with 100 feet of fencing is a rectangle with sides that measure 25 feet by 40 feet. The area of this rectangle is 1000 square feet. The farmer can use this information to fence off the largest possible area for his farm with the 100 feet of fencing he has available.

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The null and alternative hypothesis for a physician who check your blood pressure are as follows:

When a physician checks a patient's blood pressure, they may use a diagnostic threshold of 90 mmHg to diagnose hypertension. In statistical terms, the null hypothesis (H0) would be that the patient's blood pressure is less than or equal to 90 mmHg. The alternative hypothesis (H1) would be that the patient's blood pressure is greater than 90 mmHg.

The physician would then use various statistical tests, such as a t-test or a z-test, to determine whether the patient's blood pressure is statistically significantly different from the threshold of 90 mmHg. Based on the results of the test, the physician would either reject the null hypothesis in favor of the alternative hypothesis, indicating that the patient has hypertension, or fail to reject the null hypothesis, indicating that the patient's blood pressure is within the normal range.

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Answer:

Step-by-step explanation:

Given a circle of radius 7 m with central angle AOB = 150°, you want the length of long arc AB and the area of the sector it bounds.

The length of an arc of a circle is ...

  s = rθ

where θ is the central angle in radians.

Here, the long arc in degrees is 360° -150° = 210°. In radians, that is ...

  210° = 210°×π/180° radians = 7π/6 radians

So, the arc length is ...

  s = (7 m)(7π/6) = 49π/6 m . . . . arc length

The area of the sector is half the product of the arc length and the radius; (You can think of it as a kind of triangle.)

  A = 1/2s·r

  A = 1/2(49π/6 m)(7 m) = 343π/12 m² . . . . area

Answer: 58

Step-by-step explanation:

3^2 + 7^2 = 9 + 49

= 58

[tex]X^2 = 7^2 + 3^2 = 49+ 9[/tex]

[tex]X^2 = 58[/tex]

[tex]X = \sqrt{(58)}[/tex]

Therefore, the hypotenuse is approximately 7.62.

The length of ML rounded to nearest tenth is 4.5.

From figure, KML is a right-angled triangle at M, with KM = 8 and KL = 9.2. Let ML = x be the length of the base.

Using Pythagorean theorem, we have:

KL² = KM² + ML²

Substituting the given values ML=x, KM = 8 and KL = 9.2, we have:

9.2² = 8² + x²

Simplifying the right-hand side, we get:

84.64 = 64 + x²

Subtracting 64 from both sides, we get:

20.64 = x²

Taking the square root of both sides, we get:

x ≈ 4.54

x=4.5 (rounded to nearest tenth)

Therefore, the length of ML is approximately 4.5.

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