A cellular service provider is expanding the number of cell towers it has in Wayne County. Ona map of the towers, there are two that are 8 centimeters apart. The map uses a scale of 2centimeters = 1 kilometer. What is the actual distance between the two cell towers?kilometers

The equation is written as

Aisha has 15 points

Let's use the given information to set up an equation to represent the relationship between the points each friend has.

Let x be the number of points Aisha has.

Then, according to the problem statement, we know that:

Carter has 7 1/2 more points than Aisha, so he has

x + 7 1/2 points.

Jamila has 4 - 1/2 more points than Carter, so she has

x + 7 1/2 + 4 - 1/2 points,

which simplifies to x + 11 points.

Jamila has 26 points, so we can set x + 11 equal to 26 and solve for x:

x + 11 = 26

x = 26 - 11

x = 15

Therefore, Aisha has 15 points.

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Answer:

Step-by-step explanation:

Solution

Solve with the quadratic formula 

3k2+k−3=0    :    k=(−1+√376)/6 , k=(−1−√376 )/6   (Decimal:    k=0.84712…, k=−1.18046…)- Answer

Steps

3k2+k−3=0

Solve with the quadratic formula

For a quadratic equation of the form ax^2+bx+c=0,

the solutions are x1, 2=(−b±√b^2−4ac)/2a  where    a=3, b=1, c=−3 

Substituting we have

k1, 2= [(−1±√1^2−4· 3(−3)]/2· 3 

Apply rule 1^a=1 , therefore 1^2=1

=√1+4· 3· 3=√1+36

√1^2−4· 3(−3)=√37

Therefore,

k1, 2=(−1±√37)/2· 3 

k1, 2=(−1±√37)/6 

Separate the solutions

k1=(−1+√37)/6 

k2=(−1−√37)/6 

The solutions to the quadratic equation are:

k=(−1+√37)/6 , k=(−1−√37)/6 

k1=0.84712        k2=−1.18046

Difference quotient for f(x) = √x at (16,4) is  √16+h - 4 / h

Difference quotient is mathematical operation used to solve derivation of function by using following formula :

difference quotient = \(\frac{f(x+ h) - f(x) }{h}\)

For the function f(x) =  √x at point (16,4)

f(x +h) = \(\sqrt{x+h}\)  

putting value in formula

difference quotient =  \(\frac{\sqrt{x+h} -\sqrt{x} }{h}\)

now , putting x = 16 ,

difference quotient = √16+h - √16 / h

taking square root of 16 ,

= √16+h - 4 / h

So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h

option (d) is correct

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Answer:

sorry needed points so sorry

Step-by-step explanation:

Answer:

116

Step-by-step explanation:

we do pemdas so start with parenthesis

6+4=10

10 squared =100

then we divide before adding so

10/2 = 5+11= 16

100+16= 116

The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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Answer:

$468.75

Step-by-step explanation:

52 packages = $195

125 packages = ?

125 x (195/52)

= 125 x 3.75

= 468.75

Answer:

16.86 ft/s

Step-by-step explanation:

Given that,

Angular speed of a carousel, \(\omega=14\ rev/min\)

The diameter of the carousel, d = 23 feet

We need to find the speed of the carousel and jump on.

\(\omega=14\ rev/min=1.46\ rad/s\)

Radius, r = 11.5 feet

Let v is the velocity. So,

\(v=r\omega\\\\=11.5\times 1.46\\\\=16.79\ ft/s\)

Hernce, the correct option is (d) "16.86 ft/s"

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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The measure of the side MN is 19.1.

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The different trigonometric identities are expressed as:

From the information given, we have that:

Using the tangent identity:

\(\text{tan} \ \theta = \dfrac{\text{opposite}}{\text{adjacent}}\)

Substitute the values

\(\text{tan}(60) =\dfrac{\text{MN}}{11}\)

Cross multiply the values, we have:

\(\text{MN} = \sf 1.73(11)\)

\(\text{MN} = 19. 05 \thickapprox\bold{\underline{19.1 \ ft}}\)

Hence, the measure of the side MN is 19.1.

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Answer:

0.04

Step-by-step explanation:

1. 9/10 = 0.9 and 13/15 = 0.86

2. Subtract 0.9 and 0.86

3. You should end up with 0.04

Remember when a number goes like 0.86666666666 to use 0.86 or if it has 0.86666666667 to use 0.87 because you would be simplifying it.

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

like my answer and brainliest

Answer:8

Step-by-step explanation:

(16---->1,2,4,(8),16

24----->1,2,3,4,6,(8),12,24

40----->1,2,4,5,(8),10,20,40

Because 8 is the largest common divisor

SRS stands for Simple Random Sample. It consists of selecting a subgroup (of 5 students for this case), while each member of the whole population (80 students for this case) has the same probability of being selected.

That could be done by assigning each individual of the population a number, and then randomly generate a set of numbers to select the subgroup.

In this case, we can assign each of the 80 students a number, and generate 5 random numbers. Those 5 random numbers have to be two-digit numbers since we have more than 10 students.

We can assign numbers from 01 to 80 to each student, and select the first 5 pairs of numbers of the randomly generated set of digits found: 05166 29305 77482.

Let's separate the digits in pairs:

05 16 62 93 05 77 48 2.

We can discard the 2 at the end because it has only one digit:

05 16 62 93 05 77 48

The first five students would be the ones labelled with:

05, 16, 62, 93 and 05.

We have 05 twice, so we can delete it and replace it with the sixth pair of numbers (77):

05 16 62 93 77.

One of the selected numbers is 93, which is outside the range. The selected numbers should be lower than 80. Then, we can discard the 93, and replace it with the seventh pair of the randomly generated digits:

05 16 62 77 48.

Now we have the numbers of the 5 selected students after using the given digits to perform a Simple Random Sample.

The numbers of the selected students are 05, 16, 62, 77 and 48.

This is a fair selection since from the set of randomly generated digits, the probability of obtaining a pair of digits forming a number from 01 to 80 is the same for each of the 80 numbers.

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Answer:

The correct answer is C. Alternate Interior Angles Theorem.

Step-by-step explanation:

The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the alternate interior angles are congruent. In the proof, we are given that l∥m and t is a transversal that cuts l and m. We are also given that ∠1≅∠3. By the Alternate Interior Angles Theorem, we can conclude that ∠2≅∠4.

The other three options are not valid reasons for the third line of the proof. The Consecutive Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary. The Consecutive Interior Angles Converse states that if two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel. The Alternate Interior Angles Converse states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

The valid reason for the third line of the proof is the Alternate Interior Angles Theorem.

According to the Alternate Interior Angles Theorem, if a transversal overlaps two parallel lines, the alternate interior angles are congruent. Line an is parallel to line b in the given proof, while line c is parallel to line d. Line 13 is the transversal. Angles 213 and 132 are congruent because they are alternate internal angles. As a result, 213 = 132.

The other possibilities are not valid justifications for the proof's third line. According to the successive Interior Angles Theorem, if a transversal overlaps two lines, the successive interior angles are additional. Angles 213 and 132, on the other hand, are not successive internal angles.

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Answer:

Step-by-step explanation:

8/12=22/(12+6x-3)

8/12=22/(6x+9)

48x+72=264

48x=192

x=4

Answer:

\(P(X = 0) = 0.03125\)

\(P(X = 1) = 0.15625\)

\(P(X = 2) = 0.3125\)

\(P(X = 3) = 0.3125\)

\(P(X = 4) = 0.15625\)

\(P(X = 5) = 0.03125\)

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so \(p = 0.5\)

5 tosses:

This means that \(n = 5\)

Probability distribution:

Probability of each outcome, so:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125\)

\(P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625\)

\(P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125\)

\(P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125\)

\(P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625\)

\(P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125\)

Answer:

25

Step-by-step explanation:

x^2 – 10x = 7

Take the coefficient of x

-10

Divide by 2

-10/2 = 5

Square it

5^2 = 25

Add this to both sides

x^2 – 10x+25 = 7+25

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Net operating profit = (22 million - 19 million)*(1 - 0.36)

                                = $1.92  million

EVA = net operating profit after taxes - invested capital*WACC

       = 1.92 million - 15 million*0.10

       = $0.42 million

Therefore, The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million.

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Answer:

Step-by-step explanation:

280ora

To find the equation, we use the standard form

So, we replace the center and the given point to find the radius r

Now, we solve for r

Hence, the equation of the circle is

Answer:

I would say that the answer is D

Step-by-step explanation:

Hope this helps you:)

The required GCF for the expression is 5y

Since we are not given the expression to get the GCF. Using the function

5x²y + 25y²

From both terms, find the common factor

From both factors, we can see that 5 and y are common to both

GCF = 5 × y

GCF = 5y

Hence the required GCF for the expression is 5y

NB: Same process is application to any other expressions

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Step-by-step explanation:

1.23

hdhdjdjdhdhdhjdjdjdjd

Answer:35652846437467

Step-by-step explanation:simple math

Answer:

Step-by-step explanation:

its is 14

The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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