A)
motorcylcist: 2 hoursbus: 2.5 hourstruck: 3 hoursbicyclist: 7.5 hoursB) It is a matter of definition: speed = distance/time. Speed is proportional to distance and inversely proportional to time.
Step-by-step explanation:Speed is defined as the ratio of distance to the time required to cover that distance:
... speed = distance/time
Solving this relation for time, we have ...
... time = distance/speed
a) For each of the modes of transportation, we can find the time by using this relation.
... motorcyle: (150 km)/(75 km/h) = 2 h
... bus: (150 km)/(60 km/h) = 2.5 h
... truck: (150 km)/(50 km/h) = 3 h
... bicycle: (150 km)/(20 km/h) = 7.5 h
b) For a given distance, speed and time are inversely related as a matter of definition.
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Try this option. Answer: 72+18π
Step-by-step explanation:
Formula is:
Area= 2*Area_of_two_squares + 1/2 *Area_of_the_circle, where
Area_of_1_square=6*6=36 cm²;
Area_of_the_circle=π*6²=36π cm²;
finally, according to the formula above Area=2*36+0.5*36π=72+18π
Answer:
Step-by-step explanation:
72+18pi
Use the APR table in the Business Math Handbook to estimate the APR for the following installment purchase. You received a $2,000 rebate that brought the price of your car down to $20,000; the financing was for 48 months, and your total interest was $3,279.
7.65%
Step-by-step explanation:There are 200 times $100 in $20,000, so the interest amount per $100 is ...
... $3,279/200 = $16.395 per hundred
In the row of the given table corresponding to 48 months, the smallest amount of interest listed is $23.48 per $100. The APR on the loan of concern is clearly less than 10.75%.
A financial calculator says the interest rate on a loan of $20,000 with 48 monthly payments of ($20,000 +3,279)/48 = $484.98 is about 7.65%.
5x^6–3x^2+7–2x^6–3x^6+4x^2 for x=−10
Answer:
107
Step-by-step explanation:
These are easier to do if you simplify them first.
... = x^6(5 -2 -3) +x^2(-3 +4) +7
... = x^2 +7
For x = -10, this is
... (-10)^2 +7 = 100 +7 = 107
adult tickets to the fall play cost $8 and student tickets cost $4. The drama calss sold 20 more adult tickets than student tickets to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
Answer:
80 adult tickets were sold
Step-by-step explanation:
If you subtract the extra 20 adult tickets from ticket numbers and revenue, you get ...
equal numbers of $4 and $8 tickets were sold for a total of $720 collected
Since that is some number of ticket pairs worth $12 per pair, there must have been ...
$720/12 = 60 pairs of $4 and $8 tickets
The number of adult tickets is 20 more than this, so is
60 + 20 = 80 . . . . adult tickets sold
_____
If you feel better with an equation, rather than numerical reasoning, you can let n represent the number of adult tickets. Then n-20 is the number of student tickets and total revenue is ...
8n +4(n-20) = 880
12n -80 = 880 . . . . . simplify
12n = 960 . . . . . . . . . add 80
n = 80 . . . . . . . . . . . . divide by 12
_____
Comment on the different solutions
Using n for the number of adult tickets, we effectively chose a scenario where we added 20 student tickets to bring the total to $960 for some number of $12 pairs of tickets. That number is 80, the number of adult tickets.
In the "word solution" given at first, we effectively solved for the number of student tickets, then added 20 to get the number of adult tickets. The corresponding equation would be ...
4s +8(s+20) = 880 . . . s = number of student tickets sold
12s = 720 . . . . . . . . . subtract 160, the price of the 20 extra adult tickets
please help!!! I am so confused
The exercise is asking you to compute the volume of five different spheres and cylinders, choosing 5 different random values.
Remember the formulas for the volumes: given a radius [tex] r [/tex], the volume of the sphere is
[tex] \dfrac{4}{3}\pi r^3 [/tex]
Whereas the volume of the cylinder is
[tex] \pi h r^2[/tex]
In this specific case, you're told that the height of the cylinder is the same as the diameter of the sphere (i.e. twice the radius). So, the formula of the cylinder updates to
[tex] \pi (2r) r^2 = 2\pi r^3 [/tex]
So, all you need to do is to pick 5 random numbers, use them as the radius [tex] r [/tex], and for each of them compute the volume and cylinder sphere as indicated above.
For example, if you choose a radius [tex] r=5 [/tex], you will have
[tex] \text{Sphere: } V = \dfrac{4}{3}\pi 5^3 = \dfrac{500\pi}{3} [/tex]
[tex] \text{Cylinder: } V = 2\pi 5^3 = 250\pi [/tex]
Now choose your 5 random values and do the same!
Find the slope of the line between points A and B. Simplify your answer.
-2
2
-1
1
Answer:
-2
Step-by-step explanation:
From the given graph, the point A(1, -4) and B(-1, 0)
Slope (m) = (y2 - y1) / (x2 - x1)
x1 = 1, y1 = -4, x2 = -1 and y2 = 0
Slope (m) = (0 - (-4))/(-1 - 1)
= 4/-2
Slope = -2
Thank you.
What are the solutions to the quadratic equation 4x2 = 64?
x = −16 and x = 16
x = −8 and x = 8
x = −4 and x = 4
x = −2 and x = 2
Answer:
x = −4 and x = 4
Step-by-step explanation:
4x² = 64
Lets get x² on its own. To do this we divide each sides by 4:
x² = 16
Now to get just x, we need to square root this answer:
√x² = √16
x = √16
x = 4
But this can be ±4 as it -4 and 4 squared both give 16.
So your answer is x = −4 and x = 4
Answer:
x = −4 and x = 4
Step-by-step explanation:
c on edg
The formula Q=MCT where Q=heat flow M=mass, C specfic heat, and T change of temperature is used to calculate heat flow Solve this formula for t
Answer:
q/mc=t
Step-by-step explanation:
q=mct
q/mc=t
Answer:
The formula for t is [tex]T=\frac{Q}{MC}[/tex]
Step-by-step explanation:
Consider the provide formula.
[tex]Q=MCT[/tex]
Where Q=heat flow M=mass, C specific heat, and T is the change of temperature is used to calculate heat flow.
We need to solve the above formula for T.
Divide both the sides by MC.
[tex]\frac{Q}{MC}=\frac{MCT}{MC}[/tex]
[tex]\frac{Q}{MC}=T[/tex]
[tex]T=\frac{Q}{MC}[/tex]
Hence, the formula for t is [tex]T=\frac{Q}{MC}[/tex]
Find the value of x.
10
8.3(repeating)
7
5
Answer:
5
Step-by-step explanation:
So the triangle to the right is similar to the big triangle by SAS similarity with a ratio of 1:2. So (3x-5):20 is 1:2. So 3x-5=10 or 3x=15. So x=5.
Answer:
5
Step-by-step explanation:
good luck on the test babes <3
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than a certain number of inches.
Sketch and label the sides of this rectangle. Use an algebraic expression to represent the length of the long sides.
Let x be the certain number of inches mentioned in the problem. So, three less than this quantity is [tex] x-3 [/tex]
This means that you have to sketch a rectangle labelling the short side with 2, and the long sides with [tex] x-3 [/tex]
The Shop and Save is starting their annual clearance and the store has sent out to all their customers a coupon book offering a variety of savings on their products. The LCD television that you have wanted was reduced by 35% prior to the annual clearance. In addition, the coupon book has a 10% off coupon for the LCD television. Determine what you would pay after applying the discounts given that the price of the LCD television was $1,325. Round your answer to the nearest cent.
a. $728.75
c. $596.25
b. $775.13
d. $46.38
Answer:
A
Step-by-step explanation:
First discount is the original price reduced by 35% prior to the annual clearance.
So, 35% of 1325 = 0.35 × 1325 = 463.75.
After the discount of $463.75, the price that remains = 1,325 - 463.75 = $861.25.
Then, additional disount of 10%.
10% of $1,325. = 0.10 × 1,325. = 132.50
The final price after discount of 10% = 861.25 - 132.50. = 728.75.
Round to the nearest cent, we get 728.75.
Therefore, you would pay $ 728.75 after applying the discounts.
Answer:
B. 775.13
Step-by-step explanation:
Edge says A was wrong.
Find a recursive formula for the sequence:
1, -1, -7, -25
[tex]a_n=3a_{n-1}-4[/tex]
Step-by-step explanation:Try the answers
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
_____
Derive it
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
[tex]a_n=p\cdot a_{n-1}+q[/tex]
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...
[tex]a_n=3a_{n-1}-4[/tex]
Geo usually drinks 36 ounces of water per day. He read that he should drink 64 ounces of water per day. If he starts drinking 64 ounces, what is the percent increase? Round to the nearest percent.
78%
Step-by-step explanation:The percentage change is calculated from ...
... percent change = ((new amount) -(old amount))/(old amount) × 100%
... = (64 -36)/36 × 100%
... = 28/36 × 100%
... ≈ 0.78 × 100%
... ≈ 78%
Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side BC at point M. What is the length of MC?
16 mm
24 mm
32 mm
48 mm
Answer:
16 mm
Step-by-step explanation:
Since ABC is an equilateral triangle, all three sides are the same length. The perimeter is found by adding together all of these equal sides; letting x represent the length of a side of the triangle, this gives us
x + x + x = 96
Combining like terms,
3x = 96
Dividing both sides by 3,
3x/3 = 96/3
x = 32
Since AM is a perpendicular bisector, it splits BC into two congruent sections. This means the length of MC, half of BC, will be 32/2 = 16.
Option (B) is correct which is 24 mm
Step 1:
Find the length of each side.
Let the side be a,
3×a = 96mm
⇒ a = 96/3
⇒ a = 32 mm
Step 2:
Length of MC = length of BC/2 (As AM is a perpendicular bisector)
⇒ MC = 32/2 = 16 mm
Step 3:
Now, in the triangle, AMC, using Pythagoras theorem,
AC² = MC² + AM²
⇒ (32)² = MC² + (16)²
After solving,
⇒ MC = 16√3 = 27.77 mm
This is closest to option (B) which is 24 mm
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Which number completes the Pythagorean Triple of 14, 48, x?
50
Step-by-step explanation:These numbers are double those of the (7, 24, 25) triple. 2×25 = 50.
You can also figure it out from ...
... x = √(14² +48²) = √(196 +2304) = √2500 = 50
Joseph needs to find the quotient of 3216/8. In what place is the first digit in the quotient????
Answer:
hundreds
Step-by-step explanation:
The quotient of 3216/8 is 402. 4 is the first digit, and is in the hundreds place.
At the book store, a bag of chips sells for $2.30 each and candy sells for 1.23 each. You have $23 to spend. Write an equation to describe this situation. What does the y represent? What does the x represent?
Answer:
2.3x + 1.23y = 23
Step-by-step explanation:
The bag of chips is x because it is getting multiplied by 2.3.
The candy is y because it is getting multiplied by 1.23.
The reason they equal 23 is to figure out the maximum amount of each snack you can get without going over the money limit.
In △ABC, CM is the median to AB and side BC is 12 cm long. There is a point P∈CM and a line AP intersecting BC at point Q. Find the lengths of segments CQ and BQ, if P divides CM into CP:PM=1:2.
Answer:
CQ = 2.4 cmBQ = 9.6 cmStep-by-step explanation:
This development is ugly, but it works.
Let area ΔABC = 6a. Then area ΔAMC = 3a, and area ΔAPC = a. Similarly, area ΔBMC = 3a, and area ΔBPC = a.
Let area ΔCPQ = x. Then ...
... area ΔACQ = area ΔAPC + area ΔCPQ
... area ΔACQ = a + x
Define k such that BQ : CQ = k : 1. Then ...
... area ΔBPQ + area ΔCPQ = area ΔBPC
... kx + x = a = (k +1)x
The division of BC into parts of ratio k : 1 means ...
... area ΔABQ = k × area ΔACQ
... area ΔABQ + area ΔACQ = area ΔABC
... k × area ΔACQ + area ΔACQ = area ΔABC
... (k +1)(x +a) = 6a . . . . . . . area ΔACQ = x+a
... (k +1)x +(k +1)a = 6a . . . . . distributive property
... a + (k +1)a = 6a
... k +2 = 6 . . . . . . . . . . . . . . . divide by a, simplify
... k = 4
Now, we know BQ : CQ = 4 : 1, so ...
... BQ = 4/5 × 12 cm = 9.6 cm
... CQ = 1/5 × 12 cm = 2.4 cm
There are 650 visitors to an art gallery on Friday. There are 10% more visitors on Saturday than on Friday. How many visitors are there on Saturday?
Answer:
10% of 650 visitors is:
650 visitors* (10/100)= 65 visitors.
650 visitors+ 65 visitors= 715 visitors.
There are 715 visitors on Saturday
Step-by-step explanation:
Ans7wer:
715 people
Step-by-step explanation:
650÷100=6.5
6.5X10=65
650+65=715
Help plzzzzz I don’t know this
Answer:
$6
Step-by-step explanation:
The graph shows you that 4 pounds of apples (and no cranberries) can be purchased for $24. Thus each pound costs ...
... $24/(4 pounds) = $6/pound
What is the measure of angle N to the nearest whole degree?
Answer:
9°
Step-by-step explanation:
You can make use of any of the trigonometric ratios to determine N, or you can let your calculator tell you what it is by solving the triangle.
SOH CAH TOA reminds you that
... sin(N) = 13/85 . . . . N = arcsin(13/85)
... cos(N) = 84/85 . . . N = arccos(84/85)
... tan(N) = 13/84 . . . . N = arctan(13/84)
all will tell you N ≈ 8.79741° ≈ 9°
_____
If you use inverse functions on your calculator, be sure it is in degrees mode.
Factor completely −5x2 + 10x − 15. −5(x2 − 2x + 3) −1(x2 − 10x + 15) −5x(x2 − 2x + 3) −5(x2 − 2x − 3)
Answer:
-5(x² -2x +3)
Step-by-step explanation:
5 is a factor common to all of the coefficients. It is convenient to have the x² coefficient be positive in the factored form, so the result of factoring out -5 is ...
... -5((-5x²/-5) +(10x/-5) +(-15/-5)) = -5(x² -2x +3)
Answer:
-5(x² -2x +3) your welcome
Step-by-step explanation:
Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+5
-2
Step-by-step explanation:20 greater than 8x +5 is ...
... 8x +5 +20 = 8x +25
We want this value to be -3(2x +1), so we want to solve the equation ...
... 8x +25 = -3(2x +1)
... 8x +25 = -6x -3 . . . . . . eliminate parentheses
... 14x = -28 . . . . . . . . . . . add 6x-25
... x = -2 . . . . . . . . . . . . . . divide by the coefficient of x
The desired value of the variable is -2.
_____
Check
-3(2x+1) = -3(2(-2)+1) = -3(-3) = 9
8x+5 = 8(-2) +5 = -11
9 is 20 greater than -11, so the answer checks OK.
Answer:
X = -2
Step-by-step explanation:
If zb⊥ya , find m
A. 28
B.46
C.56
D.62
I'll give you brainliest
A. 28
Step-by-step explanation:We assume m is the measure of the marked unknown angles: ∠BZY ≅ ∠BZA
(5x +3)° = (2x +18)°
Divide by ° and subtract 2x+3:
... 3x = 15
... x = 5
Then ∠BZA = (2·5 +18)° = m = 28°
What is a quartic polynomial function in standard form with zeros -2,4,4,and 3
We can simply multiply the roots together to find the original function.
(x + 2)(x - 4)(x - 4)(x - 3)
FOIL.
x^2 - 4x + 2x - 8(x - 4)(x - 3)
Combine like terms.
x^2 - 2x - 8(x - 4)(x - 3)
FOIL.
x^3 - 2x^2 - 8x - 4x^2 + 8x + 32(x - 3)
Combine like terms.
x^3 - 6x^2 + 32(x - 3)
FOIL.
x^4 - 6x^3 + 32x - 3x^3 + 18x^2 - 96
Combine like terms.
x^4 - 9x^3 + 18x^2 + 32x - 96 is the original function with the given roots.A quartic polynomial function with roots at -2,4,4,and 3 can be written in standard form as f(x) = (x + 2) * (x - 4)^2 * (x - 3)
Explanation:A quartic polynomial function is a function of the fourth degree. Its general form is f (x) = ax^4 + bx^3 + cx^2 + dx+ e, where a, b, c, d, and e are constants, and a ≠ 0. Given the roots or zeros of the function (-2,4,4,3), we can construct the quartic polynomial function.
The quartic polynomial with roots r1, r2, r3, r4 is represented by: f(x) = a(x - r1)(x - r2)(x - r3)(x - r4). The roots of your polynomial function are -2, 4, 4, and 3. So, we substitute those roots into the equation:
f(x) = a(x - (-2)) * (x - 4) * (x - 4) * (x - 3). We may choose the leading coefficient a to be 1 (a ≠ 0) for simplicity's sake. Thus, the quartic polynomial function in standard form with zeros -2,4,4, and 3 is:
f(x) = (x + 2) * (x - 4)^2 * (x - 3)
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Could someone help me with these please!?
Answer:
7. The sum of the measures of the interior angles of this polygon is 900°.
8. The sum of the measures of the interior angles of this polygon is 540°.
9. The polygon has 10 sides.
10. The polygon has 5 sides.
Step-by-step explanation:
7. Vertices: A, B, C, D, E, F and G
Number of vertices: n=7
Sum of the measures of the interior angles of the polygon: S=?
S=180°(n-2)
Substituting n by 7 in the formula above:
S=180°(7-2)
S=180°(5)
S=900°
8. Vertices: A, B, C, D and E
Number of vertices: n=5
Sum of the measures of the interior angles of the polygon: S=?
S=180°(n-2)
Substituting n by 5 in the formula above:
S=180°(5-2)
S=180°(3)
S=540°
9. Each interior angle of a regular polygon (i) measures 144°:
i=144°
How many sides does the polygon have?
n=?
i=180°(n-2)/n
Substituting i by 144° in the formula above:
144°=180°(n-2)/n
Solving for n: Cross multiplication:
144°n=180°(n-2)
Eliminating the parentheses on the right side of the equation applying the distributive property:
144°n=180°(n)-180°(2)
Multiplying
144°n=180°n-360°
Grouping n's on the right side of the equation: Subtracting 144°n both sides of the equation:
144°n-144°n=180°n-360°-144°n
Subtracting:
0=36°n-360°
Adding 360° both sides of the equation:
0+360°=36°n-360°+360°
Adding:
360°=36°n
Dividing both sides of the equation by 36°:
360°/36°=36°n/36°
10=n
n=10
The polygon has 10 sides.
10. Each interior angle of a regular polygon (i) measures 108°:
i=108°
How many sides does the polygon have?
n=?
i=180°(n-2)/n
Substituting i by 108° in the formula above:
108°=180°(n-2)/n
Solving for n: Cross multiplication:
108°n=180°(n-2)
Eliminating the parentheses on the right side of the equation applying the distributive property:
108°n=180°(n)-180°(2)
Multiplying
108°n=180°n-360°
Grouping n's on the right side of the equation: Subtracting 108°n both sides of the equation:
108°n-108°n=180°n-360°-108°n
Subtracting:
0=72°n-360°
Adding 360° both sides of the equation:
0+360°=72°n-360°+360°
Adding:
360°=72°n
Dividing both sides of the equation by 72°:
360°/72°=36°n/72°
5=n
n=5
The polygon has 5 sides.
If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following must be true?
f(x) and g(x) have the same x-intercepts.
f(x) and g(x) have the same y-intercepts.
f(x) and g(x) have the same number of zeros.
f(0) = g(0) – 2
Answer:
Choice D) which is f(0) = g(0) - 2
Step-by-step explanation:
Plug x = 0 into the g(x) function to find that....
g(x) = f(2*x) + 2
g(0) = f(2*0) + 2 .... replace every x with 0
g(0) = f(0) + 2
g(0) - 2 = f(0) + 2 - 2 .... subtract 2 from both sides
g(0) - 2 = f(0)
f(0) = g(0) - 2
i will give brainlest answer quickly please
A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below.
Plan A: 27 text, 21 Internet
Plan B: 13 text, 10 Internet
Answer the questions to determine a conditional probability.
How many customers are on payment plan B?
____ customers
How many of the customers on plan B text?
____ customers
What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
_____
Answer:
23 are on plan B13 on plan B text13/23 is the probability a customer on plan B will textStep-by-step explanation:
Assuming the categorization is mutually exclusive (customers either text or internet, but not both), the total number of Plan B customers in the sample is the sum of those in each category:
.... 13 + 10 = 23 . . . . plan B customers
The problem statement tells you
... 23 plan B customers text
Since 13 out of 23 customers surveyed use the phone for text, the empirical probability that a plan B customer will use the phone for texting is ...
... 13/23 . . . . probability that text is used most
There are 23 customers are on payment plan B.
There are 13 customers who are on plan B text.
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
Given
A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet.
They sort the data by payment plans, as shown below.
Plan A: 27 texts, 21 Internet
Plan B: 13 texts, 10 Internet
What is probability?The probability is defined as the ratio of the sum of all observations and the total number of observations.
The total number of observation is;
= 13 +10 = 23
1. How many customers are on payment plan B?
There are 23 customers are on payment plan B.
2. How many of the customers are on plan B text?
There are 13 customers who are on plan B text.
3. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text?
[tex]\rm Probability = \dfrac{Customer \ plan \ B}{Total \ number \ of \ customers}\\\\Probability = \dfrac{13}{23}[/tex]
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
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can someone help wil mark brainest if u can help and show work please help if u can
Answer:
-24>Step-by-step explanation:
1. You can use a calculator if your knowledge of arithmetic fails you.
... 98 +17 +37 -176 = 152 -176 = -24
___
2. -37/8 = -(32 +5)/8 = -4 5/8 = -4.625
This number is on the left side of zero on the number line, but is slightly closer to zero than -4.63, so is "greater than" -4.63.