A restaurant offers a lunch special for $15 plus a $3 tip for the server. Write an expression that represents the total cost for the special in 2 different ways.

Answer:

x = (e^3 +3)/(e^3 -1) ≈ 1.20958

Step-by-step explanation:

Take the antilog and solve in the usual way.

ln(x+3) -ln(x -1) = 3

ln((x +3)/(x -1)) = 3 . . . . rearrange to a single log

(x +3)/(x -1) = e^3 . . . . take the antilog

x +3 = e^3·(x -1)

3 +e^3 = x(e^3 -1)

x = (e^3 +3)/(e^3 -1) ≈ 1.20958

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Check

This answer checks OK in the original equation:

ln(4.20958) -ln(0.20958) = 3

Answer:

C. both student 1 and student 2

Step-by-step explanation:

Dilation does not change any angles, so the triangles are similar and the trig functions of corresponding angles will be identical.

The slope of CB is -1/3 and the slope of BA is 3, so they multiply together to give -1. That means the segments are at right angles and the triangle is a right triangle.

Both the premise and the conclusion of each student is correct.

Answer:

Option A: P(Male or Type B) > P(Male | Type B)

Step-by-step explanation:

Total Female = 85 type A, 12 type B  ⇒ 97 Female.

Total Male = 65 type A, 38 type B   ⇒ 103 Male

Total type A = 65 + 85 = 150

Total type B = 12 + 38 = 50

total number of people = 97 + 103 = 200

Then the probability would be:

P(Male | Type B) = [tex]\frac{number of male in B}{total number of male}[/tex]

                           = [tex]\frac{38}{103}[/tex]

                           = 0.368

P(Male or Type B) = [tex]\frac{total number of male + (total number of people in B - total number of male in B)}{total number of male}[/tex]

                              =  [tex]\frac{103 + (50 - 38)}{200}[/tex]

                              = [tex]\frac{103 + 12}{200}[/tex]

                              = [tex]\frac{115}{200}[/tex]

                              = 0.575

 Hence, P(Male or Type B) > P(Male | Type B)

Answer:

m > -5

Step-by-step explanation:

Divide your inequality by the coefficient of m, which is -3. Doing that requires you reverse the comparison symbol:

(-3m)/(-3) > (15)/(-3)

m > -5

_____

The comparison symbol is reversed whenever an inequality is multiplie or divided by a negative number. You might be able to see why when you look at the relation between a couple of integers:

-2 < -1

2 > 1 . . . . . . multiply the above by -1

Multiplying by a negative number effectively reflects the comparison across the center of the number line. As we know from looking in a mirror; reflection reverses left and right, so numbers that were farther to the right (more positive) are now farther to the left (more negative).

Answer:

Step-by-step explanation:

Two equations in two unknowns can be written:

  3m +5v = 40

  9m +7v = 74

These can be solved a variety of ways. One of them is using Cramer's rule. It tells you the solution to

is given by ...

For the numbers above,

The rental cost for each movie is $3.75; for each video game, it is $5.75.

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The attached graph shows a graphing calculator solution to these equations.

The first one. Start at origin. Move 6 units to the right and up 2 units

Answer:

Option 1 - Start at the origin. Move 6 units to the right, then move 2 units up.

Step-by-step explanation:                  

To find : Which set of directions correctly describes how to plot the point (6,2) on the coordinate plane?

Solution :

The point (6,2) means the x-coordinate is 6 and y-coordinate is 2.

According to graphing,

As the x-coordinate is positive it moves to right side.

So, From origin there is a shift of 6 units right.

As the y-coordinate is positive it moves to upward side.

So, From origin there is a shift of 2 units up.

Therefore, 'Start at the origin. Move 6 units to the right, then move 2 units up'.

Hence, Option 1 is correct.

Answer:

x = 5/4

y = 7/4

Step-by-step explanation:

The smaller triangle and the larger one are similar, so the sides are proportional.

(x+5)/5 = 10/8

x/5 + 1 = 1/4 + 1 . . . . . divide it out

x/5 = 1/4 . . . . . . . . . . .subtract 1

x = 5/4 . . . . . . . . . . . . multiply by 5

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For y, you can do exactly the same computations, replacing every instance of 5 with a 7. Then you get ...

y = 7/4

Answer:

  p < 5

Step-by-step explanation:

We want to find p for ...

  1.5p -1 < 1 +1.1p

  0.4p < 2 . . . . add 1-1.1p

  p < 5 . . . . . . . multiply by 2.5

The desired relationship will be the case for values of p less than 5.

Answer:

46.20 square units

Step-by-step explanation:

The area of a regular polygon can be found from the side length and apothem as ...

A = (1/2)ap . . . . . where a = apothem, p = perimeter (# of sides times side length)

The total area of the pentagon is then ...

A = (1/2)(5.51)(5·8) = 110.20 . . . . . square units

__

The shaded area is the difference between the area of the pentagon and the area of a square with side length 8. The square's area is ...

A = s^2 = 8^2 = 64 . . . . . . square units

__

Then the shaded area is ...

A = (pentagon area) - (square area) = 110.20 -64.00 = 46.20 . . . . . square units

Area of a triangle = 1/2 x base x height.

Replace are and base to get:

82.5 = 1/2 x 15 x height

Multiply both sides by 2:

165 = 15 x height

Divide both sides by 15:

Height = 165 / 15

Height = 11 inches.

the answer is D because 6 and 10 aren't multiples of 8 and 12

To find the fraction that is not equivalent to 8/12, simplify each given fraction and check for equivalence.

To find which fraction is not equivalent to 8/12, we need to simplify or reduce each of the given fractions. If the simplified form of a fraction is not equal to 8/12, then it is not equivalent. Let's simplify each option:

A) 2/3 - already in simplest form, not equivalent to 8/12

B) 24/36 - can be simplified to 2/3, equivalent to 8/12

C) 4/6 - can be simplified to 2/3, equivalent to 8/12

D) 6/10 - can be simplified to 3/5, not equivalent to 8/12

Therefore, option D is NOT equivalent to 8/12.

Answer:

  D.  √((2 +4)² +(5 -8)²)

Step-by-step explanation:

The distance is found using the formula ...

  d = √((x1 -x2)² +(y1 -y2)²)

Selection D has this formula properly filled in with the values ...

  (x1, y1) = (2, 5)

  (x2, y2) = (-4, 8)

The correct answer:

B. 6 - 2

Answer:

B. 6-2

Step-by-step explanation:

We have been given expression : [tex]\left(+6\right)-\left(+2\right)[/tex]

Now we need to rewrite that expression [tex]\left(+6\right)-\left(+2\right)[/tex], without parenthesis then select which of the given choices are correct.

[tex]\left(+6\right)-\left(+2\right)[/tex]

We know that product of opposite sign is always negative sign.

Then product of - and +2 gives -2

So we can rewrite the problem as:

[tex]=6-2[/tex]

Hence choice B. 6-2 is the final answer.

Answer:

1/5  = 0.2

Step-by-step explanation:

First

[a + b] / c is an algebraic expression

Then

[(-3) + (4)] / 5

[1] / 5

1/5

Best regards

Answer:

-3 4/5

Step-by-step explanation:

a+b/c​

Substitute the values in

-3 + 4/-5

-3 + -4/5

-3 4/5

If the expression was (a+b)/c

then (-3 +4)/-5

We would do the parentheses first

1/-5

-1/5

Answer:

11 students out of 902 responded above 35

Step-by-step explanation:

Using z-score we can find what percentage of student will be above 35. Using this percentage we can calculate how many students out of 902 scored above 35.

Mean = u = 26

Standard deviation = s = 4

Target Value = x = 35

Formula for the z score is:

[tex]\frac{x-u}{s}[/tex]

Using the values in this formula, we get:

[tex]\frac{35-26}{4} =2.25[/tex]

Using the z table we can find the percentage of values that would be 2.25 standard deviations above the mean in a normal distribution. Using the z-table we get this value to be 0.0122 or 1.22%

Thus 1.22% of the values will be above 35.

1.22% of 902 is 11 (rounded to nearest whole number)

Thus 11 students out of 902 responded above 35

Answer:

the answer is 11

Step-by-step explanation:

Explanation:

Let M be the midpoint of AB. Then CM is the perpendicular bisector of AB. As such, center O is on CM, and OC is a radius (and CM). The tangent is perpendicular to that radius (and CM), so is parallel to AB, which is also perpendicular to CM.

If you need to go any further, you can show that triangles CMA and CMB are congruent, so (linear) angles CMA and CMB are congruent, hence both 90°.

Hope this helps , use SOHCAHTOA

Some

Old

Hag

Cracked

All

Her

Teeth

On

Apples

To remember, hope this helps !

[tex]\bf -15~~,~~\stackrel{-15+4}{-11}~~,~~\stackrel{-11+4}{-7}~~,~~\stackrel{-7+4}{-3}~~~~,...\qquad \qquad \boxed{d=4} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ d=4\\ a_1=-15\\ n=27 \end{cases} \\\\\\ a_{27}=-15+(27-1)4\implies a_{27}=-15+(26)4 \\\\\\ a_{27}=-15+104 \implies a_{27}=89[/tex]

[tex]\bf \rule{34em}{0.25pt}\\\\ \textit{ sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\[-0.5em] \hrulefill\\ n=27\\ a_1=-15\\ a_{27}=89 \end{cases} \\\\\\ S_{27}=\cfrac{27(a_1+a_{27})}{2}\implies S_{27}=\cfrac{27(-15+89)}{2}\implies S_{27}=\cfrac{27(74)}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill S_{27}=999~\hfill[/tex]

Answer:

2. x = √3

3. y = 3√2

4. a = (2/3)√2

Step-by-step explanation:

In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.

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2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x

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3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve

12 = 2√2y

12/(2√2) = y = 6/√2 = 3√2

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4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve

a = 2√2/3 = (2/3)√2

_____

Comment on "rationalizing the denominator"

"Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical:

1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/n

That is, ...

1/√2 = (√2)/2 . . . . for example.

Answer:

1590.4 square ft

Step-by-step explanation:

r=30 so you need to multiply that by 25% (30*.25=7.5)

30-7.5=22.5

A= pi(r)^2

A=pi*(22.5)^2

A=506.25pi

A=1590.43 or 1590.4 (to the nearest tenth)

Answer: 1590.4 square feet

Step-by-step explanation:

Given: The radius of the circular area = 30 feet

Now, 25% of the radius = [tex]0.25\times30=7.5[/tex] feet

If the we reduce the radius by 25%, then the radius of the circular area =

[tex]30-7.5=22.5\text{ feet}[/tex]

Now, the circular area of the spray is given by :-

[tex]\text{Area}=\pi r^2\\\\\Rightarrow\text{ Area}=(3.143.141592653)(22.5)^2\\\\\Rightarrow\text{ Area}=1590.43128088\approx1590.4\text{ ft}^2[/tex]

Therefore, the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity = 1590.4 square feet.

Answer:

The answer is C 5/4

Step-by-step explanation:

When lines are parallel and you know there is a scalar factor, make the ratio by putting the original over the dilation 15:12 or 15/12 this is the ratio and after you need to reduce by dividing by the greatest common factor. 15 and 12's GCF is 3 so (15/3)/(12/3) = 5/4.

Answer:

  C) In step 3, he should have determined which square is closest to 18.

Step-by-step explanation:

17.64 also rounds to 18. 17.64 differs from 18 by ...

  18 -17.64 = 0.36

whereas 18.49 differs from 18 by ...

  18.49 -18 = 0.49

Hence 17.64 is closer to 18 and we might expect 4.2 to be closer to √18 than is 4.3.

___

The actual root of 18 is about 4.243, so 4.2 is a better approximation.

 C) In step 3, he should have determined which square is closest to 18.

Answer:

see the attachment for a graph

4.53 thousand square yards remain after 6 years

Step-by-step explanation:

The area can be described by an exponential equation that multiplies the area by 0.85 when the time variable increases by 1 year. Such an equation might be ...

a(t) = 10.2·0.85^(t-1)

The graph of this is attached.

After 6 years, the equation predicts

a(6) = 10.2·0.85^(6-1) ≈ 4.53 thousand square yards

of island will remain.

Using the Pythagorean theorem:

21^2 = √(8^2 + x^2)

441 = √( 64  + x)

441 - 64 = √x

377 = √x

x = √377

x = 19.4

The answer is D.

14n+21

(distribute the 7 to the values in the parenthesis)

To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). The correct equations are: Y + 3 = 6(x - 8) and Y + 5 = -2/5(x + 3).

To write an equation in point slope form, we use the formula: y - y1 = m(x - x1). Where (x1, y1) is the given point and m is the given slope.

Question 1:

Given point: (8, 3) and slope: 6

Substituting the values into the formula, we have: y - 3 = 6(x - 8)

Therefore, the correct answer is option A: Y + 3 = 6(x - 8).

Question 2:

Given point: (-3, -5) and slope: -2/5

Substituting the values into the formula, we have: y + 5 = -2/5(x + 3)

Therefore, the correct answer is option A: Y + 5 = -2/5(x + 3).

Final answer:

The point-slope form equations for the given points and slopes are y - 3 = 6(x - 8) for the first set and y + 5 = (-2/5)(x + 3) for the second set.

Explanation:

The equation of a line in point-slope form is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a given point on the line.

1. With the given point (8,3) and slope m = 6, the equation in point-slope form will be y - 3 = 6(x - 8). This corresponds to option B. Y-3=6(x-8).

2. For the given point (-3,-5) and slope m = -2/5, the point-slope form of the equation is y + 5 = (-2/5)(x + 3), which matches option A. Y+5= -2/5(x+3).

Answer: 14 centimeters.

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere:

[tex]V=\frac{4}{3}(3.14r^3)[/tex]

Where the radius of the sphere is "r".

As you know the volume of the ball, you can susbtitute it into the formula [tex]V=\frac{4}{3}(3.14r^3)[/tex], and solve for the radius "r":

[tex]1437=\frac{4}{3}(3.14r^3)\\\\3( 1437)=4(3.14r^3)\\\\4311=12.56r^3\\\\r=\sqrt[3]{\frac{4311}{12.56}}\\\\r=7.0cm[/tex]

The diameter of the ball can be calculated with:

[tex]D=2r[/tex]

Where r is the radius of the ball.

Substituting the radius of the ball into  [tex]D=2r[/tex], you get that the diameter of the ball that she should purchase, rounded to the nearest whole number, is:

[tex]D=2(7.0cm)\\D=14.0cm\\D=14cm[/tex]

Final answer:

To solve for the diameter of the ball, the volume of a sphere formula is used. The calculated diameter is rounded to the nearest whole number, and Martha should purchase a treat ball with a diameter of approximately 14 centimeters.

Explanation:

To find the diameter of the ball that can hold 1437 cubic centimeters of treats, we need to use the formula for the volume of a sphere: V = (4/3) π r^3, where V is the volume and r is the radius. We will solve for r and then multiply by 2 to find the diameter. Given that the volume, V, is 1437 cubic centimeters, the formula becomes:

1437 = (4/3) × 3.14 × r^3

To isolate r, we first divide both sides of the equation by (4/3) × 3.14:

r^3 = 1437 / ((4/3) × 3.14)

Calculating the right side gives us the approximate value of r^3. Then, we take the cube root of both sides to solve for r:

r = ∛(1437 / ((4/3) × 3.14))

Once we find r, we can calculate the diameter, D, by:
D = 2 × r

Calculating the above with the given volume, we find:

r ≈ ∛(1437 / ((4/3) × 3.14)) ≈ 6.83 cm

D ≈ 2 × 6.83 cm ≈ 13.66 cm

So, rounding the diameter to the nearest whole number, Martha should purchase a treat ball with a diameter of approximately 14 centimeters.

Answer:

  B: quadratic model, 0.997

  Yes, 0.997 is very close to 1.

Step-by-step explanation:

In general, the better the model, the closer the R²-value is to 1. A graph shows the quadratic model to be a good fit.

_____

Comment on "better models"

A 4th-degree polynomial can be written that will fit each of the 5 points exactly and give an R²-value of 1. However, the model does not appear to interpolate or extrapolate well. The quadratic offers a reasonable fit that is better than that of the linear model and seems to have reasonable behavior between and beyond the given data points.

Answer:

Step-by-step explanation:

Mikey worked 8 hours on Wednesday, 6 hours on Thursday and 7 hours on Friday.

Total Work = 8+6+7 = 21 hours.

Gross Pay = 187.95 dollars.

Hourly Rate = (Gross pay)/(Total work) = (187.95)/21 = 8.95 dollars per hour.

Hence, option A is correct i.e. 8.95 dollars per hour.