Answer:
Part a) [tex]V(h)=6.25\pi h\ in^3[/tex]
Part b) [tex]V(3)=18.75\pi\ in^3[/tex] (see the explanation)
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of cylinder
h is the height of the cylinder
we have that
[tex]B=\pi r^{2}[/tex]
Part a) Write the function, V(h), that represents the volume of the cylinder
we have
[tex]r=5/2=2.5\ in[/tex] ----> the radius is half the diameter
substitute
[tex]B=\pi (2.5)^{2}[/tex]
[tex]B=6.25\pi\ in^2[/tex]
The volume is
[tex]V(h)=6.25\pi h\ in^3[/tex]
Part b) Find V(3) and tell what it represents
V(3) represent the volume of the cylinder with a height of 3 inches
so
For h=3 in
substitute
[tex]V(3)=6.25\pi(3)\ in^3[/tex]
[tex]V(3)=18.75\pi\ in^3[/tex]
Final answer:
The function for the volume of the cylinder with diameter 5 inches is V(h) = π * (2.5 inches)² * h. To find V(3), we calculate the volume with height 3 inches, which represents the physical volume of the cylinder at that height.
Explanation:
To find the volume of the cylinder, V(h), we must use the formula V = πr²h, where r is the radius of the base, and h is the height of the cylinder.
Part A: Given that the diameter is 5 inches, the radius is half of the diameter, so r = 5 / 2 = 2.5 inches. Thus, the function representing the volume is V(h) = π * (2.5 inches)² * h.
Part B: To find V(3), we substitute h with 3 inches into the function: V(3) = π * (2.5 inches)² * 3 inches. This gives us the volume of the cylinder when the height is 3 inches.
Put these numbers to greatest to least negative 1 3/8 negative 0.4 negative 1.55 negative 9/16
Answer:
[tex]-0.4, -\frac{9}{16}, -1\frac{3}{8}, -1.55[/tex]
Step-by-step explanation:
The list of numbers given:
[tex]-1\frac{3}{8}, -0.4, -1.55, -\frac{9}{16}[/tex]
We need to arrange from greatest to least.
In order to arrange the numbers in descending order we will find the equivalent decimal value of each number.
a)[tex]-1\frac{3}{8}=-1.375[/tex]
b) [tex]-0.4[/tex]
c) [tex]-1.55[/tex]
d) [tex]-\frac{9}{16}=-0.5625[/tex]
Arranging the numbers in descending order
[tex]b>d>a>c[/tex] [since all the numbers are negative, so the number closest to 0 is the greatest]
Thus the correct order from greatest to least is:
[tex]-0.4, -\frac{9}{16}, -1\frac{3}{8}, -1.55[/tex] (Answer)
Point P' is the translation of P (5, -5) under translation of 2 units to the left and 5 units up. What are the coordinates of P'?
(Graph up top)
(A.) (7, 0)
(B.) (7, 5)
(C.) (3, 5)
(D.) (3, 0)
Answer:
i dont know
Step-by-step explanation:
i dont know
What is 724 times 41,000
Pls help me ASAP it needs to be turned in today pls help
Answer:
13x-12 the last one
Step-by-step explanation:
Answer:
13x-12
Step-by-step explanation:
4(3x-5)+x+8
12x-20 +x+8
13x-12
Sonia is making a quilted wall hanging that is 38 in wide.if each quilt square is 4 3/4 inches wide, how many squares will she need to complete one row of the wall hanging?
A. 6 1/2
B.8
C.42 3/4
D.190
Answer:
b
Step-by-step explanation:
2,319 rounded to hundreds
Answer:
2,300
Step-by-step explanation:
see attached to identify the hundreds digit.
How we round the hundreds digit depends on the number in the tens place.
If the number in the tens places is less than 5, then we keep the hundreds digit the same (i.e we round down)
If the number in the tens place is greater or equal to 5, then we increase the hundreds digit by 1 (i.e round up)
in this case, the digit in the tens place is 1 (i.e less than 5) hence we round down by keeping the hundreds place the same
we end up with 2,300
2,319 rounded to the nearest hundreds is 2,300.
To round the number 2,319 to the hundreds place, follow these steps:
Identify the hundreds place, which is the digit in the second position from the right. In 2,319, the hundreds place digit is 3.Look at the digit immediately to the right of the hundreds place, which is the tens place. In this case, it's 1.Apply the rounding rule: if the digit in the tens place is 5 or higher, round up. If it is lower than 5, do not round up. Since 1 is less than 5, we do not round up.Replace all digits to the right of the hundreds place with zeros. Thus, 2,319 rounded to the nearest hundreds becomes 2,300.Therefore, the answer is 2,300.
please send help my way ty :)
Answer:
○ A. Graph C
Step-by-step explanation:
Starting from the y-intercept of [tex]\displaystyle [0, -4],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving one block south over four blocks west or one block north over four blocks east. Now, you have to figure out which graph follows the inequality symbol in the inequality. In this case, two answer choices match this because the less than inequality will result in a dashed line, so we can automatically eliminate answer choices D. and B.. Now, to figure out our graph once in for all, we need to use the zero-interval test [test point [0, 0]] to ensure if we either shade the opposite portion [the portion that does NOT contain the origin] or the portion that DOES contain the origin. We then need to verify it as false or true:
[tex]\displaystyle 0 < \frac{1}{3}[0] - 4 → 0 ≮ -4[/tex]
This is a FALSE statement, so instead of shading above the dashed line, we shade below the dashed line, and that answer choice is A..
>, < → Dashed Line
≥, ≤ → Solid Line
I am joyous to assist you anytime.
1. What is the percent change from 1000 to 80?
2. What is the percent change from 45 to 63?
3. What is the percent change from 250 to 60?
4. What is the percent change from 60 to 99?
Step-by-step explanation:
1.-92%
2.40%
3.-76%
4.65%
The percent changes for each scenario is: 1. From 1000 to 80: -92% 2. From 45 to 63: +40% 3. From 250 to 60: -76% 4. From 60 to 99: +65%.
To calculate the percent change between two values, we use the formula:
[tex]\[ \text{Percent Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\% \][/tex]
1. The percent change from 1000 to 80 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{80 - 1000}{1000} \right) \times 100\% = \left( \frac{-920}{1000} \right) \times 100\% = -92\% \][/tex]
So, the percent change is a 92% decrease.
2. The percent change from 45 to 63 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{63 - 45}{45} \right) \times 100\% = \left( \frac{18}{45} \right) \times 100\% = \frac{2}{5} \times 100\% = 40\% \][/tex]
So, the percent change is a 40% increase.
3. The percent change from 250 to 60 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{60 - 250}{250} \right) \times 100\% = \left( \frac{-190}{250} \right) \times 100\% = -76\% \][/tex]
So, the percent change is a 76% decrease.
4. The percent change from 60 to 99 is calculated as follows:
[tex]\[ \text{Percent Change} = \left( \frac{99 - 60}{60} \right) \times 100\% = \left( \frac{39}{60} \right) \times 100\% = \frac{13}{20} \times 100\% = 65\% \][/tex]
So, the percent change is a 65% increase.
A school is arranging a field trip to the zoo. The school spends 875.49 dollars on passes for 29 students and 4 teachers. The school also spends 279.56 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
Money spent on each student is $36.17
Step-by-step explanation:
$875.49 = 29 students & 4 teachers
33 people = $875.49
1 person = $26.53 (pass)
29 students = $279.56
1 student = $9.64 (lunch)
each student = $9.64 + $26.53
= $36.17
the amount spent on a pass and lunch for each student is approximately $26.56 + $9.63 = $36.19.
To find out how much money was spent on a pass and lunch for each student, we need to calculate the total amount spent on passes and lunch and then divide it by the total number of students.
Given:
- Total amount spent on passes for 29 students and 4 teachers: $875.49
- Total amount spent on lunch for just the students: $279.56
- Total number of students: 29
1. First, let's find the total amount spent on passes for just the students:
Total amount spent on passes for students and teachers = $875.49
Total amount spent on passes for 4 teachers = ?
Total amount spent on passes for students = $875.49 - (amount spent on passes for teachers)
Since each pass costs the same amount for students and teachers, we can divide the total amount spent on passes by the total number of passes (students + teachers) to find the cost per pass.
Total number of passes (students + teachers) = 29 students + 4 teachers = 33 passes
Cost per pass = Total amount spent on passes / Total number of passes
= $875.49 / 33
≈ $26.56 (rounded to two decimal places)
2. Now, let's find out how much money was spent on lunch for each student:
Total amount spent on lunch for students = $279.56
Cost per student for lunch = Total amount spent on lunch for students / Total number of students
= $279.56 / 29
≈ $9.63 (rounded to two decimal places)
So, the amount spent on a pass and lunch for each student is approximately $26.56 + $9.63 = $36.19.
I’ll put you as brainiest
A 25 kilogram object is placed on a compression spring, and it creates a displacement of 0.15 meters.
What is the weight of an object that creates a displacement of 0.23 m on the same spring?
Step-by-step explanation:
If [tex]mKg[/tex] of mass is placed on spring with spring constant [tex]k[/tex],
[tex]mg=kx[/tex]
where [tex]g[/tex] is universal gravitational constant
[tex]x[/tex] is the displacement in the spring.
In case 1:
[tex]25g=k(0.15)\\k=\frac{25g}{0.15}[/tex]
In case 2:
[tex]mg=k(0.23)[/tex]
Using result from case 1,
[tex]mg=\frac{25g}{0.15}\times 0.23[/tex]
[tex]m=[/tex][tex]38.33Kg[/tex]
A photocopier is making reduced copies of a photo that measures
25 centimeters in height. The height of the first copy is 80% of the
height of the original. Another copy is made using the first copy, and
the height of this copy is 85% of the height of the first copy.
What is the height of the first copy?explain your answer
Answer:
The height of First Copy is 20 cm.
Step-by-step explanation:
Given:
Original Height = 25 cm
First copy is reduce to 80% of Original height.
Therefore to find the height of first copy can be find out by multiplying 80 with original height and then dividing by 100.
∴ Height of First Copy = [tex]\frac{80}{100} \times \textrm{original height}= 0.8\times 25 cm = 20cm[/tex]
Hence Height of first copy is 20 cm
Now Another copy is reduce to 85% of First Copy.
Therefore to find the height of another copy can be find out by multiplying 85 with first copy height and then dividing by 100.
∴ Height of Another Copy = [tex]\frac{85}{100} \times \textrm{first copy height}= 0.85\times 20 cm = 17cm[/tex]
Hence Height of Another copy is 17 cm
Answer:
To find the height of the first copy,
multiply 0.8 by 25.
The height of the first copy is
20 cm.
To find the height of the second copy,
multiply 0.85 by the height of the first copy.
The height of the second copy is
17 cm.
Step-by-step explanation:
Aylin is making a scrapbook using 18 photos and 20 newspaper clippings.She wants all the pages to be set up in the same way,With the combination of photos and newspaper clippings on every page.She also wants to make sure that no items are left over.What is the greatest number of scrapbook pages that Aylin can create?
Answer:
2 scrapbook pages
I found the answer online
Aylin can create a maximum of 19 scrapbook pages by dividing the total number of items by the number of items on each page.
Explanation:Aylin wants to set up all the pages of her scrapbook in the same way, with a combination of photos and newspaper clippings on every page.
She wants to make sure that no items are left over.
To find the greatest number of scrapbook pages Aylin can create, we need to divide the total number of items -
= 18 photos + 20 newspaper clippings
= 38 items
Now,
Since she wants each page to have the same combination, we can find the greatest common divisor (GCD) of 18 and 20, which is 2.
Therefore, Aylin can create a maximum of 38/2 = 19 scrapbook pages.
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A clothes line is connected from a window on one building to a window in a building across the alley. The clothesline is 10 yards long with an angle of depression of 17°. How far apart are the buildings?
Answer:
The distance between the two buildings is 9.563 yards.
Step-by-step explanation:
See the diagram attached.
AB and CD are two buildings AC distance apart.
Now, AC = ED.
The angle of depression of clothesline BD is 17 Degrees.
Now, given that BD = 10 yards.
And ∠ OBD = ∠ BDE = 17° {Alternate angles}
Now, from the right triangle Δ BED, we have
[tex]\cos 17 = \frac{ED}{BD} = \frac{ED}{10}[/tex]
⇒ ED = 10 cos 17 = 9.563 yards.
Therefore, the distance between the two buildings is 9.563 yards. (Answer)
-0.06 m = 7.2
m =
what is m equal to.
Answer: m = -120
Step-by-step explanation: In this equation, m is being multiplied by -0.06 so we will need to divide both sides of the equation in order to get m b itself.
On the left side of the equation, the -0.06's cancel and we are left with m. On the right side of the equation, we divide -7.2 by -0.06 and we get -120.
Now we have m = -120
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper/or digitally too. It will really pay off for you down the line.
Image provided.
I need help please match the careers with the career clusters!!!
Career clusters are groups of related careers. In the example given, careers in biological sciences like microbiologist, ecologist, neurologist, and forensic scientist form one cluster, while allied health professions such as medical technician, medical examiner, and neurophysiologist form another. Matching careers to clusters involves identifying commonalities such as educational requirements, tasks, and industry.
Explanation:It looks like you are trying to match careers with specific career clusters. Career clusters represent a group of careers that share common features. If we consider biological sciences, we'd have a cluster including careers such as a microbiologist, ecologist, neurologist, and forensic scientist. These professions are heavily involved in studying living organisms and their environments.
On the other hand, if we consider allied health, this would be another cluster including careers like medical technician, medical examiner, and neurophysiologist. These professions are more orientated towards applied sciences in healthcare.
I hope this helps you understand how to match careers with their respective career clusters. A good approach is to identify commonalities between various jobs such as their educational requirements, day-to-day tasks, and the industry they belong to.
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E
1. If 3x + 7x + 9 = 35, then x= ?
Answer:
Step-by-step explanation:
16
The value of x in the equation 3x + 7x + 9 = 35 is 2.6 after simplification and carrying out the necessary algebraic steps.
Explanation:The subject of your question is Mathematics, specifically algebra. Now, let's solve the equation: 3x + 7x + 9 = 35.
To start, combine like terms on the left side of the equation. That gives us 10x + 9 = 35. Next, subtract 9 from both sides to isolate the term with x. This gives us 10x = 26. Finally, divide both sides by 10 to find the value of x. So, x = 2.6.
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Please help me you guys
Answer:
g(x) = |x+3| - 5
Step-by-step explanation:
Let y = f(x)
⇒y = |x+3|
When y is replaced by Y + k, the graph of y = f(x) shifts k units down
⇒ y replaced by Y + 5 translates the graph of y = f(x) 5 units down
∴ Y = g(x) is represented by Y + 5 = |x+3|
⇒ Y = |x+3| - 5
or g(x) = |x+3| - 5
Y+1=2/5(x+3) in standard form?
For this case we have that by definition, the equation of a line in the standard form is given by:
[tex]ax + by = c[/tex]
According to the statement we have the following equation of the line:
[tex]y + 1 = \frac {2} {5} (x + 3)[/tex]
We manipulate algebraically to write in the standard form. To do this we follow the steps below:
We apply distributive property on the right side of the equation:[tex]y + 1 = \frac {2} {5} x + \frac {6} {5}[/tex]
We subtract [tex]\frac {6} {5}[/tex] on both sides of the equation:
[tex]y + 1- \frac {6} {5} = \frac {2} {5} x\\y- \frac {1} {5} = \frac {2} {5} x[/tex]
We multiply by 5 on both sides of the equation:
[tex]5y-1 = 2x[/tex]
We subtract 5y on both sides of the equation:
[tex]2x-5y = -1[/tex]
Finally, the equation in its standard form is:
[tex]2x-5y = -1[/tex]
Answer:
[tex]2x-5y = -1[/tex]
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≤ −x − 4
(1, 10)
(−1, 10)
(10, 1)
(1, −10)
Answer:
Step-by-step explanation:
y ≤ x − 5
1<10-5
1<5
Pair: (10,1)
y ≤ −x − 4
-10<-1-5
-10<-6
Pair: (1,-10)
Answer:
(1, −10)Step-by-step explanation:
If we graph this system of inequalities, we could find the solution.
From the graph you can deduct that the only right answer is the last one (1,-10), because the area of solution is only for negative values of y.
Therefore, the right choice is the last one.
If you can't graph, you can try another method. If we replace the value in the system, it should satisfy it, that is, it should gives us a true result like 0<1 for example. Let's try
For x=1 and y=-10, we have
-10 ≤ 1 − 5
-10 ≤ −1 − 4
-10 ≤ -4
-10 ≤ -5
As you can see, the result is true, because -10 is less than -4 and -5, so that's the right answer.
solve for y then graph -12x+15=60
The sale price of a trampoline before tax is $300 the sales tax is 4% find the sales tax in the total price of the trampoline
The trampoline will attract a sales tax of $12 which will take its total price to $312.
The trampoline costs $300 without taxes being accounted for yet.
The tax is 4%. In dollar terms this is:
= Sales tax percentage x Cost of trampoline
= 4% x 300
= $12
The total price of the trampoline will therefore be:
= Cost of trampoline + sales tax
= 300 + 12
= $312
In conclusion, the sales tax would be $12 and the total price would be $312.
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The Dowers make pumpkin pie. If each person wants three slices of pie,and each pie is Cut into 9 slices, how many pies do they need to make for 15 people?
Answer:
They need to make 5 pies for 15 people.
Step-by-step explanation:
15*3=45 slices of pie in total,
each pie is cut into 9 slices,
45/9=5 pies
a countey fair charges $7 and $0.75 for each ride token. you have $15 write a exspression that represents the amount (in dollars) you have left after entering the fair and purchasing n tokens. how many tokens can you purchase? how much money do you have after purchasing 6 tokens
Answer:
$3.50
Step-by-step explanation:
15.00 - 7.00 = 8.00
6 x .75 = 4.50
8.00- 4.5 = 3.50
The equation for the total amount for the fair and rides is given by the relation y = 0.75n + 7 where n is the total number of rides
The amount left after purchasing 6 tokens is $ 3.50
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount be represented as = y
Now , the number of rides be = n
The cost of entry fee = $ 7
The cost for each ride = $ 0.75
The total amount available = $ 15
So , the equation will be
total amount = cost for each ride x number of rides + cost of entry fee
Substituting the values in the equation , we get
Total amount y = 0.75n + 7
y = 0.75n + 7
So , the equation is y = 0.75n + 7
Now , when purchasing 6 tokens , we get the remaining amount as
Substituting the value of n = 6 in the equation , we get
y = 0.75 x 6 + 7
y = 4.5 + 7
y = $ 11.5
So , the amount left = 15 - y
The total amount left = 15 - 11.5
The total amount left = $ 3.50
Hence , The equation for the total amount for the fair and rides is given by the relation y = 0.75n + 7 where n is the total number of rides
The amount left after purchasing 6 tokens is $ 3.50
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I really need help getting this done, I have questions 1,2 and 5 done but can’t figure out the other. Can anyone help
Answer:
Step-by-step explanation:I could help
PLEASE HELP ASAP!!!!
Compose two complete sentences that each include a dependent clause and an independent clause. Identify the subject and predicate of each. Do not use any of the examples in #1 above.
Example: After the meal (S) was served (P), we (S) lounged around with full bellies (P).
Answer:
An independent clause is a group of words that contains both a subject and a predicate. It expresses a complete thought and can stand alone as a sentence. It can also be joined to other dependent or independent clauses to make a more interesting and complex sentence.
Step-by-step explanation:
Graph a line that contains the point ( − 6 , 1 ) and has a slope of 5
The graph of the line that contains the point ( − 6 , 1 ) and has a slope of 5 is shown below in the attachment.
How to graph a line?
To graph a line with a given point (-6, 1) and a slope of 5 without explicitly finding the equation, you can start from the given point (-6, 1) and use the slope (5) to find other points.
Move up by 5 units (rise) and to the right by 1 unit (run) from the given point, and you'll get another point on the line. Repeat this process to plot multiple points and then connect them to graph the line.
The graph of the line is attached below.
Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary of $650 per week. How much did she earn last week if she sold $4,400 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Danielle earned $969 last week.
Step-by-step explanation:
Base salary per week = $650
Commission = 7.25%
Worth of electronics sold = $4400
Commission = 7.25% of 4400
[tex]Commission = \frac{7.25}{100}*4400\\Commission = \frac{31900}{100}\\Commission = \$319[/tex]
Earning of last week = Base salary per week + commission
[tex]Earning\ of\ last\ week=650+319=\$969[/tex]
Danielle earned $969 last week.
Keywords: percentage, division
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What is the value of m < a + m < b
34°
56°
90°
180°
Answer:
90°
Step-by-step explanation:
step 1
Find the measure of angle b
we know that
(m∠b+90°)=124° ----> by vertical angles
so
m∠b=124°-90°
m∠b=34°
step 2
Find the measure of angle c
(m∠c+124°)=180° ----> by supplementary angles (form a linear pair)
m∠c=180°-124°
m∠c=56°
step 3
Find the measure of angle a
m∠a=m∠c ----> by vertical angles
so
m∠a=56°
step 4
Find the value of m∠ a + m∠b
m∠a=56°
m∠b=34°
m∠ a + m∠b=56°+34°
m∠ a + m∠b=90°
Which of these is usually true of a convenience sample?
A. It consists of the entire population.
B. It is randomly chosen.
C. It gives reliable results.
D. It excludes those who are indifferent.
Answer:
The correct answer is C = It gives reliable results
Answer:
D. it excludes those who are indifferent
Step-by-step explanation:
If the distance between Sydney and Goulburn is 200 km, find the average speed to
complete the journey in 2hr 30mins (hint: speed = distance/time).
Answer:
Average Speed to complete the journey = 80 km/h
Step-by-step explanation:
Given,
The distance between Sydney and Goulburn = 200 kilometer.
Time to complete the journey = 2 hour 30 minutes
Converting the time into minutes -
2 hour 30 minutes
= (2 x 60) minutes + 30 minutes
= 120 minutes + 30 minutes
= 150 minutes
We know, to determine average speed, we have to divide the distance by time.
Therefore, Speed = [tex]\frac{Distance}{Time}[/tex]
Speed = [tex]\frac{200 km}{150 minutes}[/tex]
Speed = 1.33 km/minutes
Speed = (1.33 km x 60) km/hour (To convert it to hour, we have to multiply by 60)
Average Speed per hour = 80 km/h