Mathematics College

If Dr. Suzuki rides his bike to his​ office, he averages 9 miles per hour. If he drives his​ car, he averages 27 miles per hour. His time driving is one third hour less than his time bicycling. How far is his​ office?

Answers

Answer 1
Speed
Riding speed = 9 mph
Driving speed = 27 mph

Time
If x hours is the time taken when riding, (x - 1/3) hours  is the time taken when driving.

Distance in both instances is the same, D= Speed * time

Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours

Distance, D = 1/2 *9 = 4.5 miles

Related Questions

Suppose u=⟨2,−2u=⟨2,−2⟩ and v=⟨6,2⟩v=⟨6,2⟩ are two vectors that form the sides of a parallelogram. then the lengths of the two diagonals of the parallelogram are

Answers

91.7
44.6
is the answer

A 12-foot ladder is leaning against a wall. The distance from the base of the wall to the base of the ladder is feet. Given this information, what can be determined about the triangle formed by the ground, wall, and ladder? Check all that apply.

Answers

Putting into diagram the information provided. The triangle formed is a right triangle. (Find Attached).

We are given the length of the ladder and the distance of the base of the ladder from the wall. With that we can solve for the height of the triangle as well as the angle of inclination wrt to the floor and foot of the ladder or the wall to the tip of the ladder.

Pythagorean's theorem provides for the following formula

Square of hypotenuse (longest side of the triangle) equals the sum of the squares of the two other sides for right triangles.

Thus
Length of ladder being the hypotenuse we have below equation
Hypotenuse = 12
Distance from the base to the foot of ladder = 1 foot/feet
height = ?

12² = 1² + h²
h = √144-1
h=√143

Solving for inclination with respect to wall to tip of the ladder we can use rule of sine for right triangle

sineФ = opposite side / hypotenuse
sineФ = 1/12 = 0.083333
Ф = sin^-1 or inverse sine of 0.083333
Ф = 4.78017268 degrees

Note : If the distance between the base is not interpreted correctly, just change the value and plugin to the equation to get the result.

Answer:

A,B,D,E

Step-by-step explanation:

did it on edge

What is the area, in cm2, of the circle shown above? Round your answer to the nearest tenth.

Answers

Where is the circle?

hey can you please help me posted picture of question

Answers

The correct answer is option A

( 2 - 8i ) + ( 5 - i )

Real part is added in real part and the complex part is added in complex part

= 2 +5 - 8i - i

= 7 - 9i

So, the answer is 7 - 9i

You save $15,000.00. You place one-third in a savings account earning a 4.6% APR compounded annually. You then invest one quarter of the remaining balance in a 3-year U.S. Treasury bond earning a 5.2% APR compounded annually and the rest in a stock plan. Your stock plan increases in value 3% the first year, decreases 8% in value the second year, and increases 6% in value the third year. What is the balance of the savings account by the end of the third year?

$4,618.81

$2,910.63

$5,722.23

$3,910.02

Answers

Scenario:
1. You deposited 1/3 of 15,000 or 5,000 in a savings account that earns 4.6% compounded annually.  If 5,000 is already in the savings account, there is still 10,000 left. 
2. One-fourth(1/4) of 10,000 or 2,500 is invested in 3-year US Treasury bond earning 5.2% compounded annually. If 2,500 is invested, there is still 7,500 left.
3. The 7,500 was invested in the stock market. 

For the savings account
The amount of money deposited in the savings account after three years will be
    [tex]F_2=P\left(1+r\right)^t=5,000\left(1+0.046\right)^3=5,722.23[/tex]

Therefore, the balance of the savings account after three years is $5,722.23.

The diameter of a circle is 8 inches.What is the area?
A.8 inches
B.16 inches
C.32 inches
D.64 inches

Answers

The required correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.

The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. Since the given information provides the diameter (twice the radius), we need to first find the radius by dividing the diameter by 2.

Given: Diameter = 8 inches

Radius = Diameter / 2 = 8 inches / 2 = 4 inches

Now we can calculate the area using the formula:

= πr² = π * (4 inches)²
≈ 3.14 * 16 square inches
≈ 50.24 square inches

Therefore, the correct answer is not listed among the given options. The area of the circle is approximately 50.24 square inches.

Learn more about area of the circle here:

https://brainly.com/question/10043105

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Final answer:

The area of a circle with an 8-inch diameter is calculated using the formula A = πr². The correct area is around 50.27 square inches, not one of the provided options.

Explanation:

The question asks for the area of a circle with a diameter of 8 inches. To find the area, we use the formula A = πr², where π is approximately 3.14159, and r is the radius of the circle. Since the diameter is 8 inches, the radius (r) is half of that, which is 4 inches.

To calculate the area:

Divide the diameter by 2 to find the radius: 8 inches / 2 = 4 inches.Square the radius: 4 inches ² = 16 square inches.Multiply by π (pi): π × 16 square inches ≈ 50.26548 square inches.

The area of the circle is approximately 50.27 square inches, which means none of the given options A, B, C, or D is correct.

one day a store sold 12 sweatshirts white one cost $9.95 and yellow ones cost $12.50. In all 147.45 worth of sweatshirts were sold how many of each color were sold?

Answers

x= # of white sweatshirts
y= # of yellow sweatshirts

STEP 1:
set up quantity and cost equations

QUANTITY EQUATION
x + y= 12

COST EQUATION
$9.95x + $12.50y= $147.45


STEP 2:
solve for one variable in quantity equation

x + y= 12
subtract y from both sides

x= 12 - y


STEP 3:
substitute x value in step 2 in cost equation

$9.95x + $12.50y= $147.45
9.95(12 - y) + 12.50y= 147.45

multiply 9.95 by parentheses
(9.95*12) + (9.95*-y) + 12.50y= 147.45

119.40 - 9.95y + 12.50y= 147.45
combine like terms

119.40 + 2.55y= 147.45
subtract 119.40 from both sides

2.55y= 28.05
divide both sides by 2.55

y= 11 yellow


STEP 4:
substitute step 3 x value in either equation

x + y= 12
x + 11= 12
x= 1 white


CHECK:
$9.95x + $12.50y= $147.45
9.95(1) + 12.50(11)= 147.45
9.95 + 137.50= 147.45
147.45= 147.45


ANSWER: 1 white sweatshirt and 11 yellow sweatshirts were sold.

Hope this helps! :)

The ratio of the length to the width of a map is 8 to 5. The map is exactly 32 inches in length. What is the width of the map? A. 13 inches B. 20 inches C. 24 inches D. 32 inches

Answers

Ratio of length to width of a map = 8:5

Length of the map = 32 inches
Let the width of the map = x inches

So,

Length : Width = 8 : 5
32 : x= 8: 5

x = 5/8 * 32

x = 20 inches

So, the width of the map is 20 inches

Answer:

B. 20 inches

Step-by-step explanation:

Remember that when dealing with ratios or unit rates you just have to do simple rules of three to calcuate what they are asking you, in this case you have that in the map for every 8 units in the length there will be 5 in the width, so how many will there be when the map is 32 inches in length?

[tex]\frac{8}{5}= \frac{32}{x}\\x=\frac{32*5}{8}\\ x=20[/tex]

So the width of a map with a length of 32 inches and a ratio of 8:5 will be 20 inches.

please help with 23 and show how to work it out

Answers

For this problem, you best start with calculating how many miles they drive in 1 hour, by dividing 192 by 4.5, which equals 42.666. You then multiply this by 3 to get the distance after 3 hours.

To prevent rounding errors, you can put this all in one equation:

[tex]\frac{192}{4.5} \times {3} =128[/tex]

So answer C looks like the right one.

Michael bought a new soccer Jersey that was $24.99. after taxes the total cost was $28.99. What is the percent if increase

Answers

Tax = $28.99 - $24.99 = $4.00

Tax Percentage = 4/24.99 x 100 = 16%

Answer: 16%

What is the quotient of -19/2 divided by 38/ 7

Answers

This is the correct answer

Test the claim that mean gpa of a night student is significantly different than 2.1 at the 0.02 significance level

Answers

0.60. Is your answer have a nice day

Assuming boys and girls are equally​ likely, find the probability of a couple having a baby boy boy when their fourth fourth child is​ born, given that the first three three children were all boys all boys.

Answers

I am assuming the gender of each child is independent of the other.

Then the information about the first three children is irrelevant.

So then the probability of fourth child being boy is 1/2, since boys and girls are equally​ likely.

Hope this helps.

Q #5 Solve the system by graphing

Answers

That first one is correct there is no solution since they are parallel.
We have the following system of equations:
 (-1/3) x + y = -1
 y = 4 + (1/3) x
 Let's rewrite the system of equations:
 y = (1/3) x - 1
 y = (1/3) x + 4
 We note that both lines have the same slope:
 m = 1/3
 Therefore, the lines are parallel.
 The first line has a cut point with the y axis of:
 (0, -1)
 The second line has a cut point with the y axis of:
 (0, 4)
 Like the lines are parallel, the system has no solution.
 Answer:
 The system of equations has no solution.

Hey can you please help me posted picture of question

Answers

You multiply the options in each section:

Shirts x skirts x shoes
7 x 6 x 4
=168

So, there are 168 combinations- Letter answer B
The answer to the question is b

-4 log8 x - 2 = 6
Round to the nearest ten - thousandth

Answers

-4 log8 x - 2 = 6

log8 x - 2 = 6/-4 = -3/2

log(x-2)/log8 = -3/2    ; log8 = 0.903089987
log(x-2)/0.903089987= -3/2 
log(x-2)  = -1.35463498

10 ^  -1.35463498 = x-2

x = 2.044194174

your drawer contains 6 black socks and 8 white socks. what is the probability that both socks are black

Answers

[tex] \displaystyle
|\Omega|=\binom{14}{2}=\dfrac{14!}{2!12!}=\dfrac{13\cdot14}{2}=91\\
|A|=\binom{6}{2}=\dfrac{6!}{2!4!}=\dfrac{5\cdot6}{2}=15\\\\
P(A)=\dfrac{15}{91}\approx16\% [/tex]

*Please help, will mark correct answer as brainliest*
What is the formula for finding a break-even point?

Answers

The break-even point formula is calculated by dividing the total fixed costs of production by the price per unit less the variable costs to produce the product.

Break-even point in units =
                  Fixed costs/( Sales price per unit - Variable cost per unit )

Break-even point in Dollars = Break-even point in units * Sales price per unit

Answer:

break even point=(0.01)(# of points)(P)/monthly savings

Step-by-step explanation:

ap3x

A copy machine makes 132 copies in 5 minutes and 30 seconds. How many copies does it make per minute?

Answers

24 copies per minute

a man owned 75 shares of stock worth $50 each the corporation declared a dividend of 8% payable in stock how many shares did he then own

Answers

Final answer:

After receiving an 8% stock dividend on his initial 75 shares, the man will own a total of 81 shares.

Explanation:

The question is asking how many shares the man will own after a corporation where he holds stock declared a dividend payable in stock. The man initially owned 75 shares of stock, each worth $50, and the corporation declared an 8% dividend. To find out how many additional shares he receives as a dividend, we calculate 8% of his 75 shares:

Additional shares = 8% of 75 = 0.08 × 75 = 6 shares.

The man will then own his original 75 shares plus the 6 additional shares, for a total of:

Total shares owned = 75 + 6 = 81 shares.

PLEASE PLEASE PLEASE HELP ME WITH ALGEBRA 1 PLEASE!?!?!?!?!!!?!?!?!?!?! I WILL GIVE LOTS OF POINTS AND BRAINLEST PLEEEEEEEEEEEEEEEEASE!!?!?!?!?!?!!?!?!?!?


What are the different ways you can solve a system of linear equations in two variables? What is the process for solving a system using each method?

Answers

Im actually learning this myself atm, The three methods most commonly used to solve systems of equation are substitution, elimination and augmented matrices. Substitution is a method of solving systems of equations by removing all but one of the variables in one of the equations and then solving that equation. Elimination is another way to solve systems of equations by rewriting one of the equations in terms of only one variable. The elimination method achieves this by adding or subtracting equations from each other in order to cancel out one of the variables. Augmented matrices can also be used to solve systems of equations. The augmented matrix consists of rows for each equation, columns for each variable, and an augmented column that contains the constant term on the other side of the equation. For example, the augmented matrix for the system of equations 2x + y = 4, 2x - y = 0 is [[2 1], [2 -1]...[4, 0]], Good luck!
Hey mate 

It is 
________________________________
[tex]2x + y = 4, 2x - y = 0 is [[2 1], [2 -1] [4, 0][/tex]

Hope I helped have a good day

Can someone please help me with this problem. I need help solving a and b

Answers

(a) A generic quadratic expression is often written
  ax² +bx +c
Then the "a" and "b" in the expression -b/(2a) represent the coefficients of the squared term and the linear term, respectively. In your quadratic expression, the variable is "t", not "x", but that makes no difference. You have
  a = -16
  b = 96
Then the time (t) at the maximum height is
  t = -b/(2a)
  t = -96/(2(-16)) = 96/32 = 3

The ball is highest 3 seconds after being fired.


(b) Evaluating h for t=3, we get
  h = -16*3² +96*3 +11
  h = -144 +288 +11
  h = 155

The maximum height of the ball is 155 ft.

What is the y-intercept of the quadratic function fx) (x- 6)(x-2)?

Answers

Option 1
To find the y-intercept of a quadratic that is in factor formed follow the steps below:

First take the factor form and put it into standard quadratic form
Standard quadratic form:
[tex]ax^2 + bx + c[/tex]

To put the the factor form of a qudratic into standard form, we use the foil method

(x-6)(x-2) = [tex]x^2 - 8x +12[/tex]

Now to find the y-intercept, input 0 where the x is located:

[tex]f(x) = x^2 - 8x +12[/tex]
[tex]f(0) = 0^2 - 8(0) +12[/tex]
[tex]f(0) = 12[/tex]
y-intercept = (0,12)

Why did I use 0? Remember the y-intercept is where the line crosses the y axis so this means the x value of the y intercept is always = 0. Also, not, to find the y-intercept, you could of just multiplied the 6 and 2 in the factored form to get the 12 and since you know that the x is always 0 at the y-intercept, you know that the y-intercept is at (0,12)

Option 2
Input 0 for x in f(x) = (x-6)(x-2)
f(x) = (x-6)(x-2)
f(0) = (0 - 6)(0 - 2)
f(0) = (6)(2) =  12
x = 0
f(0) = y = 12
y-intercept = (0,12)

Answer:

The answer is B just took the test

Step-by-step explanation:

There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100 , or you lose. To play you roll a die. If a six appears you win; all other rolls you lose. if 1000 people played this game during one afternoon what would you expect to be the outcome?

A. the game earns $3330

B. the game earns $1660

C. the game loses $3330

D. the game loses $1660

Answers

Outcome on winning = $100 - $20 = $80
Outcome on losing = $20

Probability of winning = 1/6
Probability of losing = 5/6

Expected Value = 1/6 (80) +5/6(-20) = -3.333

This shows on average from each game, the game earns $ 3.333.

So, if 1000 such games are played, the game will earn 1000 x 3.33 = $3330 

So, the answer to this question is option A

Correct answer is Option(A) . The game earns $3330

Carnival Game Expected Outcome

To determine the expected outcome, we first need to calculate the expected value of playing this game once.

The cost to play is $20. If a six is rolled, the player wins $100; otherwise, they lose their $20.

Calculations:

Probability of rolling a six = 1/6Probability of not rolling a six (1, 2, 3, 4, or 5) = 5/6

Expected value (EV) for one game:

EV = (1/6 x ($100 - $20)) + (5/6 x (-$20))EV = (1/6 x $80) + (5/6 x -$20)EV = $80/6 - $100/6EV = -$20/6EV ≈ -$3.33

This means that on average, each player loses approximately $3.33 per game.

Outcome for 1000 Players

If 1000 people play the game, the total expected loss for the players will be:

Total Expected Loss = 1000 x EVTotal Expected Loss ≈ 1000 x (-$3.33) = -$3330

Therefore, the game earns approximately $3330.

Which statements is true

A: all rectangles are squares
B: some trapezoids are parallelogram
C: all square are rhombues
D: no rhombuses are rectangles

Answers

All squares are rectangles
all squares are rhombuses

B and D are True Statements.

Hope this Helped!

;D
Brainliest??

Please help Thankyou

Answers

Answer: B) (-∞, -1)U(-1, ∞)
----
The domain of a function is all the x values that return real y values.

If you look at your function, notice that x is in the denominator of [tex] \frac{1}{x+1} + 5[/tex]. Remember the denominator of a fraction can never equal zero because dividing by 0 isn't possible. That means x ≠ -1. All other x values work if you plug them in, so your answer must be the one that doesn't include x = -1.

As you look through your answer choices, remember that a bracket [ or ] means that the number is included and a parenthesis ( or ) means that the number is not included. The U means "union," which means both domains to the left and right of the U are included.

Your only choices that have "-1" are B and D. However, in D, there are closed brackets, and we want the "-1" to not be included. That means B is the only correct answer. 
f(x) = (1/x+1) + 5 ;

in order to make the function undefined, x must not be equal to -1 which makes the function 1/0 + 5.

It's either B or D

is 0.003km greater than, less than, or equal to 3 m

Answers

There are 1000 meters in a kilometer. 0.003 kilometers is equal to 3 meters

Refer to narrative 14-1. a house is selling for $150,000. a deposit of $20,000 was made when the sales contract was signed. the down payment is 30% and the balance will be financed with a 25-year mortgage at 11% and 4 discount points. if the sellers are responsible for the broker's commission (6% of the purchase price); $1,300 in other closing costs; and the existing mortgage, with a balance of $40,000; what proceeds will they receive on the sale of the property?

Answers

????????????????????

(a) find the slope m of the tangent to the curve y = 5 + 5x2 − 2x3 at the point where x =
a. m = (b) find equations of the tangent lines at the points (1, 8) and (2, 9). y(x) = (at the point (1, 8)) y(x) = (at the point (2, 9))

Answers

a) The slope at (1, 8) is 4.
  The slope at (2, 9) is -4.
These values are computed numerically by the graphing calculator and shown in the column f'(x) in the graphic.

The derivative is y' = 10x -6x². At x=1, y' = 10-6 = 4; at x=2, y' = 20-24 = -4.


b) In point-slope form, the equations of the tangent lines are shown in the graphic.

The slope of the tangent will be "[tex]10a-6a^2[/tex]". The equation at point (1, 8) is "[tex]y = 4x+4[/tex]" and at point (2,9) is "[tex]y = -4x+17[/tex]".

Given equation is:

[tex]y = 5+5x^2-2x^3[/tex]

(a)

The slope of the tangent to the curve point where [tex]x = a[/tex] is:

→ [tex]\frac{dy}{dx} = m = 10x-6x^2[/tex]

→              [tex]= 10a-6a^2[/tex]

(b)

The equation of tangent at point (1,8) will be:

→ Slope, [tex]m = 10-6[/tex]

                  [tex]= 4[/tex]

→ [tex]y-8=4(x-1)[/tex]

         [tex]y = 4x-4+8[/tex]

         [tex]y = 4x+4[/tex]

and,

The equation of tangent at point (2,9) will be:

→ Slope, [tex]m = 10\times 2-6\times 2^2[/tex]

                  [tex]= 20-24[/tex]

                  [tex]= -4[/tex]

→ [tex]y-9=-4(x-2)[/tex]

   [tex]y-9=-4x+8[/tex]

         [tex]y = -4x+17[/tex]

Thus the above answer is right.

Learn more about tangent here:

https://brainly.com/question/10462284

Determine if the function is an even function, an odd function or neither. y=-5x^(2)-2x+6

Answers

By definition we have:
 A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.
 A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.
 For y = -5x ^ (2) -2x + 6 we have:
 f (-x) = - 5 (-x) ^ (2) -2 (-x) +6
 f (-x) = - 5x ^ (2) + 2x + 6
 Answer:
 the function is neither

Answer:

C

Step-by-step explanation:

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