The city manager made a scatter plot of the number of retail stores in a


city over many years. The trend line for the scatter plot has the equation y =


11x + 12, where y is the total number of stores and x is the number of years


after 1990. Predict how many retail stores there were in 1997.

Answer:

Step-by-step explanation:

1) The distance that Lauren drove to the coast is the same as the distance he drove back from the coast. It means that the total miles that Lauren drove in this round-trip is

75 + 75 = 150 miles

2) time = distance/speed

Time spent in driving to the coast is

75/75 = 1 hour

His return speed is 25 mph

Time spent in driving back from the coast is

75/25 = 3 hours

3) Average speed = total distance/total time

Total distance = 75 + 75 = 150 miles

Total time = 1 + 3 = 4 hours

Average speed = 150/4 = 37.5 mph

Answer:

Domain :  0 ≤ t ≤ 3

Range :   -4 ≤ d ≤ 0

Step-by-step explanation:

The graph attached models the depth of submarine as a function of time.

Points on x-axis represent the time and points on y-axis represent increase in height of the submarine.

Domain of a function is represented by the points on x-axis.

Therefore, Domain :  0 ≤ t ≤ 3

Range of function is represented by te points on y-axis.

Therefore, Range :   -4 ≤ d ≤ 0

Answer:

Step-by-step explanation:

h(x) = 2x + 3

f(2x+3)

2x+3 - 7

2x - 4

Answer:

[tex]P(X \leq 3) = 0.1738[/tex]

Step-by-step explanation:

Binomial probability distribution

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

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this question, we have that:

[tex]n = 8, p = 0.6[/tex]

P(3 or fewer)

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.6)^{0}.(0.4)^{8} = 0.0007[/tex]

[tex]P(X = 1) = C_{8,1}.(0.6)^{1}.(0.4)^{7} = 0.0079[/tex]

[tex]P(X = 2) = C_{8,2}.(0.6)^{2}.(0.4)^{6} = 0.0413[/tex]

[tex]P(X = 3) = C_{8,0}.(0.6)^{3}.(0.4)^{5} = 0.1239[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0007 + 0.0079 + 0.0413 + 0.1239 = 0.1738[/tex]

Answer:

Pythagoras theorem: hypotenuse² = opposite² + adjacent²

Step-by-step explanation:

To know if a triangle is a right angle, we need to have the length of each sides of the triangle. Then we would apply Pythagoras theorem to determine if it is truly a right angled triangle.

Pythagoras theorem is a theorem in the form of an equation which shows the relationship between the sides of a right angled triangle.

let the sides of the right angled triangle be:

opposite =a, adjacent = b and hypotenuse = c

Using Pythagoras theorem

hypotenuse² = opposite² + adjacent²

c² = a² + b²

If the left hand side of the equation = the right hand side of the equation, it is a right angled triangle.

Answer:

290

Step-by-step explanation:

(11*8)*2=176, (11*3)*2=66, (3*8)*2=48, 48+176+66= 290

Answer:

B

Step-by-step explanation:

Notice that

[tex](3.5-5)^2 + (4.5-3)^2 = 4.5[/tex]

Since 4.5 is less than 6.25, tower B transmits to that phone

Answer:

Towers B and C transmit to the phone.

Step-by-step explanation:

First, let see the location of the center for each tower:

Tower A

[tex]A (x,y) = (0,0)[/tex]

Tower B

[tex]B (x,y) = (5,3)[/tex]

Tower C

[tex]C(x,y) = (2,5)[/tex]

Now, the distance between the location of the phone and any of the towers by means of the Pythagorean equation. The phone is under the influence of a tower only if distance is less than transmission boundaries. Then:

Tower A

[tex]d_{A} = \sqrt{(3.5-0)^{2}+(4.5-0)^{2}}[/tex]

[tex]d_{A} \approx 5.701[/tex]

[tex]d_{A} > 3[/tex]

Tower B

[tex]d_{B} = \sqrt{(3.5-5)^{2}+(4.5-3)^{2}}[/tex]

[tex]d_{B} \approx 2.121[/tex]

[tex]d_{B} < 2.5[/tex]

Tower C

[tex]d_{C} = \sqrt{(3.5-2)^{2}+(4.5-5)^{2}}[/tex]

[tex]d_{C} \approx 1.581[/tex]

[tex]d_{C} < 2[/tex]

Towers B and C transmit to the phone.

Answer:

48+25=x

Step-by-step explanation:

Answer:

The answer is D :)

Thank me later.

Answer:

The variable y is eliminated.

Step-by-step explanation:

To add a system of equations, we add the common terms. x with x, y with y and values with values.

In this question:

5x + 6y = 32

5x – 6y = 8

Adding:

5x + 5x + 6y - 6y = 32 + 8

10x = 40

So the variable y is eliminated.

Answer:

10x 40

Step-by-step explanation:

Answer:

  -1/5

Step-by-step explanation:

Perpendicular lines have slopes that are the opposite reciprocal of one another.

The slope of line t is the opposite reciprocal of the slope of line s:

  slope of t = -1/(slope of s)

  slope of t = -1/5

Answer:

D) -7

Step-by-step explanation:

[tex] \because \: PQ + QR = PR \\ \therefore \: 2x + 17 + 12 = 22 + x \\ \therefore \: 2x + 29 = 22 + x \\ \therefore \: 2x - x = 22 - 29 \\ \therefore \: x = - 7 \\ [/tex]

Answer:

Absolute error = 2m

Step-by-step explanation:

Absolute Error = Measured Value - Actual Value

17m - 15m = 2m

Answer:

2m and 11.8%

Step-by-step explanation:

Absolute error is defined mathematically as;

Error/original value

[Original value - estimated value]

[17-15 ] = 2m

The percentage error would be

[Original value - estimated value]/ original value

[17-15 ] /17 × 100%

0.1176 × 100% = 11.76%

11.8%[ to the nearest tenth]

Answer:

C.

Step-by-step explanation:

Some rectangles can be squares, since they fit the criteria for both if it is a square, but not ALL rectangles can be squares, since squares have ALL 4 sides congruent, whereas rectangles only have 2 sets of sides congruent.

Answer:

The total length of the tunnel when the crew has finished digging is 1078 meters

Step-by-step explanation:

total length of the tunnel dug by the crew =  573 meters

let the halfway point of the tunnel = h

if the crew digs 34 meters past the halfway point, then we will this equation below;

h + 34 meters = 573 meters

h = 573 - 34

h = 539 meters

halfway point of the tunnel is 539 meters

Then, the total length of the tunnel when the crew has finished digging = 2h

= 2 x 539 meters

= 1078 meters

Therefore, the total length of the tunnel when the crew has finished digging is 1078 meters

Answer:

[tex]p = \frac{4}{9}[/tex]

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Sample space:

All posible outcomes.

First answer - Second answer:

A - A

A - B

A - C

B - A

B - B

B - C

C - A

C - B

C - C

9 possible outcomes.

Probability that neither is B.

A - A

A - C

C - A

C - C

4 possible outcomes.

So

[tex]p = \frac{4}{9}[/tex]

Answer: 2^4*3^5*19

Step-by-step explanation:

You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.

The largest prime factor of 309² - 147² is, 19.

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The expression is,

⇒ 309² - 147²

Now, We can simplify as;

⇒ 309² - 147²

⇒ (309 - 147) (309 + 147)

⇒ 162 × 456

⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19

Thus, The largest prime factor of 309² - 147² is,

⇒ 19

Learn more about the Greatest common factors visit:

https://brainly.com/question/219464

#SPJ2

Hi!

So for this you need an equation. It will be 72 • 0.8 - 2.88 • 3

this is bc 12 x 6 is 72 and 3 bc 2 x 3 is 6.

so after you solve it you should get : $48.96..Hope this helped! :))

Answer:

For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:

[tex]\frac{70000}{12} = \frac{x}{100}[/tex]

Where x represent the total of restaurants representing the 100% and if we solve for x we got:

[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]

So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.

Step-by-step explanation:

For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:

[tex]\frac{70000}{12} = \frac{x}{100}[/tex]

Where x represent the total of restaurants representing the 100% and if we solve for x we got:

[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]

So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.

Answer:

  y = 3

Step-by-step explanation:

It can work well to start by eliminating parentheses.

  6(y -1/3) = 4(3y -5)

  6y -2 = 12y -20

  18 = 6y . . . . . . . . . add 20-6y to both sides

  3 = y . . . . . . . . . . . divide by 6

Answer:

y=3

Step-by-step explanation:

6(y−13)=4(3y−5)

(6)(y)+(6)(−13)=(4)(3y)+(4)(−5)(Distribute)

6y+−2=12y+−20

6y−2=12y−20

Step 2: Subtract 12y from both sides.

6y−2−12y=12y−20−12y

−6y−2=−20

Step 3: Add 2 to both sides.

−6y−2+2=−20+2

−6y=−18

Step 4: Divide both sides by -6.

−6y−6=−18−6

y=3

Answer:

$ 402,722.01

Step-by-step explanation:

C is parameterized by

[tex]\vec r(t)=\langle x(t),y(t),z(t)\rangle=\left\langle12\cos t,12\sin t,t\right\rangle[/tex]

for 0 ≤ t ≤ 2π. In the integral, replace y and z as above, and the line element ds is

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt=\sqrt{145}\,\mathrm dt[/tex]

So the integral is

[tex]\displaystyle\int_C(y-z)\,\mathrm ds=\sqrt{145}\int_0^{2\pi}(12\sin t-t)\,\mathrm dt[/tex]

sin(t) has period 2π, so that term contributes nothing to the integral, leaving us with

[tex]\displaystyle\int_C(y-z)\,\mathrm ds=-\sqrt{145}\int_0^{2\pi}t\,\mathrm dt=\boxed{-2\pi^2\sqrt{145}}[/tex]

Answer:

For 2 loaves of bread, 4 cups of flour, 24 tablespoons of water, and 2 teaspoons of salt are required

For 4 loaves of bread,  8 cups of flour, 48 tablespoons of water, and 4 teaspoons of salt are required

Step-by-step explanation:

Given: A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt

To find: the missing terms in the box

Solution:

As for 1 loaf of bread, 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt are required

So, for 2 loaves of bread, double the quantity.

So, for 2 loaves of bread, 2×2=4 cups of flour, 12×2=24 tablespoons of water, and 1×2=2 teaspoons of salt are required

For 4 loaves of bread, double the quantity used to make 2 loaves of bread.

For 4 loaves of bread,  4×2=8 cups of flour, 24×2=48 tablespoons of water, and 2×2=4 teaspoons of salt are required

See the image attached.

Answer:

There are two possibilities:

[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]

[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]

Step-by-step explanation:

Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:

[tex]x + y = 9.9[/tex]

[tex]x^{2} + y^{2} = 53.21[/tex]

First, [tex]x[/tex] is cleared in the first equation:

[tex]x = 9.9 - y[/tex]

Now, the variable is substituted in the second one:

[tex](9.9-y)^{2} + y^{2} = 53.21[/tex]

And some algebra is done in order to simplify the expression:

[tex]98.01-19.8\cdot y +2\cdot y^{2} = 53.21[/tex]

[tex]2\cdot y^{2} -19.8\cdot y +44.8 = 0[/tex]

Roots are found by means of the General Equation for Second-Order Polynomials:

[tex]y_{1} \approx \frac{32}{5}[/tex] and [tex]y_{2} \approx \frac{7}{2}[/tex]

There are two different values for [tex]x[/tex]:

[tex]y = y_{1}[/tex]

[tex]x_{1} = 9.9-6.4[/tex]

[tex]x_{1} = 3.5[/tex]

[tex]y = y_{2}[/tex]

[tex]x_{2} = 9.9 - 3.5[/tex]

[tex]x_{2} = 6.4[/tex]

There are two possibilities:

[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]

[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]

Answer:

2.9375

Step-by-step explanation:

3/4×47/12

3×47/4×12

141/48

2.9375

Answer:

4x12=48

48+7=55

4 7/12 as an improper fraction is 55/12

multiply the numerator with numerator and denominator with denominator

3x55=165

4x12=48

165/48 can be divided by 3

165/3=55__48/3=16

55/16 is simplified

55/16=3 r 7 so the fraction is 3 7/16

Hope this helps

Step-by-step explanation:

Answer:

a) 120

b) 10

c) 1/12

Step-by-step explanation:

The number of ways that a sample of r can be selected from a population of n is:

nCr = n! / (r! (n−r)!)

a) 3 people selected from a group of 10

₁₀C₃ = 120

b) 3 women selected from a group of 5

₅C₃ = 10

c) Of the 120 committees that can be chose, 10 are all women.  So the probability is 10/120 = 1/12.

Answer:

E) B < A < C

Step-by-step explanation:

Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower.

Initial Values are: A, B and C

After one year, A was up 20%, B was down 25%, and C was unchanged.

Values after one year:

For the second year, A was down 20% from the previous year, B was up 25% from the previous year, and C was unchanged.

Values after the second year

Therefore, from the final values of the stock, we have that:

B<A<C

The correct option is E.

Answer:

Step-by-step explanation:

(a)

   [tex]= kr^2(r_0 - r )[/tex]

 [tex]= ( kr_0)r^2 - kr^3 \\\\=>v '(r) = ( 2kr_0 )r -3kr^2\\\\= ( -3k)r^2 + ( 2kr_0 )r[/tex]

v has an absolute maximum when v '(r) = 0

v '(r) = 0 =>

( -3k )r2 + ( 2kr0 )r = 0 =>

r = [ -( 2kr0 ) ± sqrt[ ( 2kr0)2 - ( 4 )( -3k )( 0 ) ] ] / [ ( 2 )( -3k ) ]

= [ -2kr0 ± 2kr0 ] / ( -6k)

= 0 or ( -4kr0 / -6k )

= 0 or (2/3)r0

since [tex]r > (1/2)r_0[/tex] in the given interval,[tex]r =(2/3)r_0[/tex], which matches its experimental value.

Answer:

  13

Step-by-step explanation:

The line is the hypotenuse of a right triangle that is 5 units high and 12 units wide. The Pythagorean theorem, or the distance formula, tells you the length is ...

  length = √(5² +12²) = √(25+144) = √169

  length = 13

Answer:

ⁱ ʰᵒᵖᵉ ᵗʰⁱˢ ʷᵒᵘˡᵈ ʰᵉˡᵖ ʸᵒᵘ ᵗᵒ ᵍᵉᵗ ʳᵉᵃˡ ᵃⁿˢʷᵉʳ...

Answer:

10.99 inches

Step-by-step explanation:

7*2=14

diameter=14

circumference=diameter*pi

14*3.14=43.96

quarter circle

43.96/4=10.99

10.99 inches

Answer:

the quarter circle's perimeter = 24.99 inch

Step-by-step explanation:

1. Calculate circumference of a complete circle.

2. Divide by 4 and you have the quarter part. (This is the same as multiplying by 0.25).

3. Just like a pie chart, there are 2 sides from the center to the left and right side edge of the quarter circle. Both are equal to the radius r.

4. Add the numbers found in step 2 and step 3 and you will have found the quarter circle's perimeter.

Given: use 3.14 for pi and r = 7 inch

1. Circumference = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * 7 ) = 10.99 inch

3 Since r = 7 and we have to sides.

So you just add 2 * 7 = 14 inch

4. Add 10.99 + 14 = 24.99 inch