Answer:
12.56cm.
Step-by-step explanation:
Given that the diameter of a circle is 4 centimeters
The equation to find the circumference would be C=πd
C=3.14x4
=12.56
The circumference of the circle would be 12.56cm.
Hope this helps :)
Here's Robert's spending diary for one week. It may not look like he's spending much. Use a calculator to add up Robert's total spending for the week. Monday Tuesday Wednesday Thursday Friday Saturday Sunday Lunch $7.00 Shampoo $6.00 Lunch $7.00 Jacket $40.00 Lunch $7.00 Breakfast $4.50 Coffee $2.00 Bus $3.00 CD $14.00 Lunch $7.00 Lunch $7.00 Movie $12.00 Haircut $40.00 Total: $21.00 $13.00 $10.00 $47.00 $19.00 $44.50 $2.00 How much does Robert spend on lunch in a week, in a year? If Robert continues to buy his lunch every weekday, he will be spending /week. S weeks in a year = $ spent during the year.
ROOM
Write an equation in function notation for each situation.
1. The admission fee to a local carnival is $8. Each ride costs
$1.50
2. Steven buys lettuce that costs $1.69/1b.
3. An amusement park charges a $6.00 parking fee plus $29.99
per person.
4. A math tutor charges $35 per hour
5. A fitness center charges a $100 initiation fee plus $40 per
month
Answer:f(x)=1.5-x + 8
Step-by-step explanation:
Find the equation of the line through P=(8,7) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area.
The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]Reasons:
The area of the triangle, A = 0.5·x·y
Where;
x and y are the values of the line at the intercepts
The equation of the line is; (y - 7) = m·(x - 8)
At the y-intercept, x = 0, therefore;
(y - 7) = m·(0 - 8) = -8·m
At the y-intercept, y = 7 - 8·m
At the x-intercept, y = 0, therefore;
(0 - 7) = m·(0 - 8) = -8·m
At the x-intercept, -7 = m·x - 8·m
8·m - 7 = m·x
[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]
Therefore;
[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]
When the area is minimal, we have;
[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]
m² × 0 = 24.5 - 32·m²
[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]
[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]
[tex]\displaystyle m = \pm \frac{7}{8}[/tex]
The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;
(y - 7) = m·(x - 8)
[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]
[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]
[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]
[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]
The x and y intercept of the above line are 0
When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;
[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]
Which gives;
[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]
The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;
[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]
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The table gives the temperature (in °F) in five citiesſat 6 a.m. on the same day. Use the table to answer the questions.
City
Temperature
(°F)
Toronto
-16
Fairbanks
:-24
Dayton
43
San Antonio
74
Buffalo
-3
5
?
(a) By noon, the temperature in Buffalo had risen by 10 °F.
What was the temperature there
at noon
How much higher was the 6 am temperature in Toronto than in Fairbanks
Answer:
a) buffalo will be at 7
b) it will be -8
Step-by-step explanation:
a) because if u add - 3 + 10 it will equal 7
b) reason why is because if u substract -24 from - 16 it will be - 8
I took a test on the same thing thats why i kno it
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis. Given the three events, which of the following statements is true? Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Answer:
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis.
Given the three events, which of the following statements is true?
Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Select all that apply:
Event A and Event B are mutually exclusive.
Event B and Event C are mutually exclusive.
Event A and Event C are not mutually exclusive.
Event A and Event C are mutually exclusive.
Event A and Event C are not mutually exclusive.
Remember that in general, A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.
In this question, note that if the mother or father carries the recessive gene for cystic fibrosis, the baby is at risk. So here, A and C are not mutually exclusive, and B and C are not mutually exclusive.
A and B are not mutually exclusive because they share an outcome: the father carrying the recessive gene.
Step-by-step explanation:
Find the equation of the line L.
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (8, 0) ← 2 points on the line
m = [tex]\frac{0-4}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex]
The line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line L
How do you write 8 whole and 1/2 + whole 7 2/3 as a mixed number
The answer is 16 1/6
Step-by-step explanation:
1. make both of the denominators into six : 1/2=3/6 and 2/3=4/6
2. add them all together 8+7=15, 4/6+3/6=7/6
3. make the 7/6 into a mixed number so 1 1/6 add that to the 15 so 16 1/6
Answer: 16 1/6
To add mixed numbers, the first thing you do is convert the mixed numbers into improper fractions. How?
You multiply the whole number with the denominator of the proper fraction, then you'll add the numerator.
First mixed number is 8 1/2.
So, you'll multiply 8 by 2 then add 1.
(8 × 2) + 1 = 17
Next is 7 2/3.
Repeat this process.
(7 × 3) + 2 = 23
When your done, plug in the denominator and find the LCD, since the denominators are unlike. (First find the LCM of 2 and 3, which is 6). Our improper fractions should be:
8 1/2 = 17/2 × 3/3
7 2/3 = 23/3 × 2/2
Multiply the LCD, which is 2 and 3 and you'll get:
LCD of 8 1/2 ⇒ 51/6
LCD of 7 2/3 ⇒ 46/6
Now we can add. (You DO NOT add the denominator).
51/6 + 46/6 = 97/6
Since 97/6 is an improper fraction, we must convert it into a whole number.
Divide 97/6 and you'll get 16 with a reminder of 1.
16 is the whole number.
1 is the numerator.
Hence, the answer is 16 1/6.
Find the number of integers between 1 and 1000 that are divisible by 12 or 15, but not by both 12 and 15.
Count the multiples of 12:
⌊1000/12⌋ = 83
(where ⌊x⌋ denotes the "floor" of x, or the largest integer that is less than or equal to x)
These are the integers
{12, 24, 36, 48, …, 996}
Count the multiples of 15:
⌊1000/15⌋ = 66
These are
{15, 30, 45, 60, …, 990}
Count the multiples of both 12 and 15; these are multiples of LCM(12, 15) = 60:
⌊1000/60⌋ = 16
These are
{60, 120, 180, 240, …, 960}
Now use the inclusion/exclusion principle to count the multiples of either 12 or 15, but not both:
83 + 66 - 2•16 = 117
Among the multiples of 12 and the multiples of 15, we count the numbers that are multiples of both 12 and 15. By subtracting the number of multiples of both (16), we get the count of integers that are either divisible by 12 or 15. We subract 16 again to remove those that are divisible by both 12 and 15.
A world-famous prix fixe menu includes the following choices.
Beverage (choose one): wine, soft drink, coffee, tea, milk, juice, or cappuccino
First course (no choice): baguette, bruschetta, whole roasted garlic, and butter
Second course (choose one): quesadilla, onion soup, salad, Caesar salad, lettuce wedge, spinach salad, or romaine salad
Third course (choose one): rib eye steak, swordfish, rack of lamb, whitefish, grilled chicken, southern fried chicken, lobster, or vegetarian plate
if you choose steak, then choose one of the following: fries, mashed potatoes, creamed corn, spinach, broccoli, or grilled onions
Fourth course (choose one): chocolate cake, cinnamon tart, apple tart, pecan tart, creme brulee, mango sorbet, or chocolate tart
How many different choices are possible?
Using the fundamental counting theorem, it is found that 107,016 different choices are possible.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
For the beverage, there are 7 options, hence [tex]n_1 = 7[/tex]For the first course, there are no choice, hence an arrangement of 4 options, that is, [tex]n_2 = 4! = 24[/tex]For the second course, there are 7 options, hence [tex]n_3 = 7[/tex]For the third course, there are 7 non-steak options, plus 6 steak options, hence [tex]n_4 = 13[/tex]For the fourth course, there are 7 choices, hence [tex]n_4 = 7[/tex]Then, applying the theorem:
[tex]N = 7(24)(7)(13)(7) = 107016 [/tex]
107,016 different choices are possible.
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When Li Juan's auto yard is filled to capacity with only cars, it has 60 cars. When it is filled to capacity with only vans, it has 50 vans. Which linear equation models the number of cars, c, and vans, v, that could be in Li Juan's auto yard when it is filled to capacity? А c/60 + v/50 =1 B. 60c + 50v =1 C. c/50 + v/60 =1 D. 50c + 60v =1
The linear equation that could be used to model Li Juans auto yard is c/60 + v/50 = 1
A linear equation is in the form:
y = mx + b;
where m is the rate of change, b is the initial value of y and y, x are variables.
Let c represent the number of cars and v represent the number of vans.
Hence when it is filled to capacity:
c/60 + v/50 = 1
The linear equation that could be used to model Li Juans auto yard is c/60 + v/50 = 1
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What fraction of an hour is 21 minutes in simplest form
7/20
Step-by-step explanation:
21 ÷ 3 = 7
21 - 1 = 20
7/20
how can you determine whether two systems of equations are equivalent?
Two systems of equations are equivalent if they have they have the same solution/solutions.
someone help me on these 2 questions asap! 50 points!!
Step-by-step explanation:
earbuds
we have a 1in : 0.2in scale of drawing to reality.
0.2 = 2/10 = 1/5
so, 1in in the drawing is actually 1/5in in reality.
how long are the 4in in the drawing ?
well, 4 times the 1in thing.
4×1/5 = 4/5 = 0.8in long
again the similar triangles
similar triangles means that each pair of corresponding lines (sides, heights, ...) in the triangles follows the same scaling factor for the length.
so, what do I need to multiply the side of the large triangle with to get the corresponding side length of the small triangle ?
27 × x = 9
x = 9/27 = 1/3
and that is the scale factor.
I don’t understand any of the below. Can you please help?
-25 + (-12)
14 - (-20)
-4 + (-10)
Answer:
1. -37
2. -34
3. -14
Step-by-step explanation:
1. -25 then ++- is negative so -25-12 so add them becuase negative + negative adds then keep the negative sign. THIS HELPS WITH EVERYTHINGB
The question is in the photo. Answer part d
Answer
your equation in part c is wrong
Step-by-step explanation:
part c
y=mx+c
11=2m+c-----------(1)
15=3m+c----------(2)
(2)-(1)
15-11=(3m+c)-(2m+c)
4=3m-2m+c-c
m=4
substitute in (1)
2m+c=11
2*4+c=11
8+c=11
c=3
so equation should be y=4x+3
what led to the creation of the free-soil party?
A. To stop immigrants from entering the United States
B. To promote slavery across the West
C. To stop the spread of slavery
D. To achieve Manifest Destiny
Answer:
The answer is C
Step-by-step explanation:
brainliest plss
helpppp please!!!!!!!
Answer:
a
Step-by-step explanation:
a
2^x+2=4081
Solve the following exponential equation
Find the volume of a cylinder either enter. An exact answer in terms of pie or 3.14
Answer:
Step-by-step explanation:
V = πR²h
V = π3²6
V = 54π units³
If π = 3.14, V = 169.56 units³
If two events (both with probability greater than 0) are mutually exclusive, then:
Answer:
they are not independent
Step-by-step explanation:
they are not independent they would be independent if they didn't depend on each other or if the probability didn't affect the other.
Phyllis invested $50,000 in two different types of stock. The first type earned 10% and the second type earned 15%. If the profit on the 15% stock was $2,500 more than the profit on the 10% stock, how much did Phyllis invest in the 15% stock?
Answer:
$ 30,000
Step-by-step explanation:
0.15(50,000 - x) - 0.1x = 2,500
7,500 - 0.15x - 0.1x = 2,500
7,500 - 2,500 = 0.15x + 0.1x
5,000 = 0.25x
5,000/0.25 = x
x =20,000
50,000 - 20,000 = 30,000
0.15 * 30,000 = $4,500
0.1 * 20,000 = $2,000
$4,500 - $2,000 = $2,500
Kathy is following a recipe for punch that calls for 3 liters
of juice. She has 3 quarts of juice. Without using an equation, does Kathy
have enough juice for the punch? Explain.
Answer:
Yes, Kathy does have enough juice.
Step-by-step explanation:
Kathy does have enough because quarts are a little bigger than liters, so the 3 quarts she has will cover the liters.
Can somebody please help this is honestly due tomorrow
Answer:
I am almost completely sure its 4.
Step-by-step explanation:
I dont mind brainiests by the way
Only answer this if you know the answer.
Find The nth Term of this number sequence
18, 16, 14, 12
Answer:
2
Step-by-step explanation:
18,16,14,12,10,8,6,4,2
5x + 5 = x + 25 what is x?
Answer:
x = 5
Step-by-step explanation:
5x + 5 = x + 25
subtract 5 from both sides
5x = x + 20
subtract x from both sides
4x = 20
divide both sides by 4
x= 20/4
x= 5
Use the figure below to find the values of x and y
Answer:
x=68 and y = 112
Step-by-step explanation:
angles of a triangle must equal 180, so
52°+60°+x°=180
112+x=180 <-- subtract 112 to get x on one side.
x=68
To solve for y, a straight line = 180 so
68+y=180 --> just subtract 180-68
y=112
The average of 5 consecutive whole numbers is 2021. What is the average of the first 3 of these numbers?
Answer:
2020
Step-by-step explanation:
if it is 5 consecutive numbers, it means it needs to be 2019, 2020, 2021, 2022, 2023
it is the number in the middle.
for the first 3 numbers, it is 2019, 2020, 2021
the middle number is 2020
Mr. And mrs. Samson decide to go with design a and purchase the materials. Their total bill is 356.88. If they pay 220 in cash and charge the remainder, how much did they charge?
Answer:
136.88
Step-by-step explanation:
Subtract 356.88 - 220 = 136.88
How long would it take to earn Php 8,000 on a principal of Php 20,000 at 5% simple interest rate?
The length of time it would take the given principal to become Php 8,000 is 8 years.
The formula that would be used to determine the length of time it would take Php 20000 to accumulate an interest of Php 8000 can be determined using this formula:
Time = Interest earned / (principal x interest rate)
8000 / (20,000 x 0.05)
= 8 years
To learn more about simple interest, please check: brainly.com/question/9352088?referrer=searchResults
can someone help me with this and also happy thanksgiving if you celebrate it
My ans is C
24 - 6x + 40 = 34
24+40 - 6x = 34
64 - 6x = 34
6x = 64-34
6x = 30
x = 5 ^^