Answer:
Step-by-step explanation:
"The equation of the cross-sectional parabola of the dome is [tex]\( y = -\frac{1}{800}x^2 + 50 \).[/tex]
To find the equation of the cross-sectional parabola of the dome, we can use the standard form of a parabola, which is[tex]\( y = ax^2 + bx + c \).[/tex]Since the parabola is symmetric and the vertex is at the origin (0,50), the equation simplifies to [tex]\( y = ax^2 + c \),[/tex]where determines the width of the parabola and \is the maximum height of the dome.
Given that the maximum height of the dome is 50 feet, we have[tex]\( c = 50 \)[/tex]. The diameter of the dome is 2002 feet, so the radius is half of that, which is 1001 feet. The radius corresponds to the x-coordinate at the base of the dome where the height \ is 0.
Using the point (1001, 0) and the vertex (0, 50), we can set up the equation [tex]\( 0 = a(1001)^2 + 50 \).[/tex] Solving for [tex]\( a \)[/tex]gives us:
[tex]\[ 0 = a(1001)^2 + 50 \] \[ -50 = a(1001)^2 \] \[ a = -\frac{50}{(1001)^2} \] \[ a = -\frac{50}{1002001} \] \[ a \approx -\frac{1}{20040} \][/tex]
For simplicity, we can round [tex]\( a \) to \( -\frac{1}{2000} \)[/tex]or even more simply to [tex]\( -\frac{1}{800} \)[/tex] to make the calculations easier without significantly changing the shape of the parabola for practical purposes.
Thus, the equation of the cross-sectional parabola of the dome is:
[tex]\[ y = -\frac{1}{800}x^2 + 50 \]"[/tex]
Anna has a rectangular that is 33 inches and 75 inches. Find the perímeter of the rectangular in yards
Answer:
6 yards
Step-by-step explanation:
Perimeter of a rectangle: 2a + 2b
2(33) + 2(75)
66 + 150
216 inches
216/12 gives us feet
18/3 gives us yards
6 yards
Answer: 6 yards
Your math test has 38 questions and is worth 200 points. The test consists of
multiple-choice questions worth 4 points each and open-ended questions
worth 20 points each. How many of each type of question are there?
The test has 35 multiple-choice questions and 3 open-ended questions.
To solve this, we can set up a system of linear equations. Let x represent the number of multiple-choice questions and y represent the number of open-ended questions.
Equation 1: x + y = 38 (total questions)
Equation 2: 4x + 20y = 200 (total points)
By solving this system of equations, we can find the values of x and y. First, multiply equation 1 by 4 and subtract it from equation 2:
4(x + y) = 4(38) => 4x + 4y = 152
4x + 20y = 200 - (4x + 4y = 152) gives: 16y = 48 or y = 3.
Substituting y = 3 into equation 1 gives: x = 38 - 3 = 35.
Therefore, there are 35 multiple-choice questions and 3 open-ended questions on the test.
Evan enjoys eating fresh fruits and vegetables. This
year, he decided to grow his own garden. The diagram
shows the dimensions of his garden
He fills his garden with enriched topsoil at a height of 2
inches. How much topsoil does Evan use?
48 in
cubic inches
24 in
Answer:
[tex]2304 \ in^3[/tex]
Step-by-step explanation:
Given the surface dimensions of the garden as 24 inches by 48 inches:
#Calculate surface area of the garden's top:
[tex]A=lw\\\\=48\times 24\\\\=1152 in^2[/tex]
Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:
[tex]V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3[/tex]
Hence, the amount of soil used is 2304 cubic inches.
Answer: those are right!
Hope this helps ❤️
Translate the phrase into an algebraic expression. 9 more than x
Answer: 9+x
Step-by-step explanation:
If you have x apples, and you need nine more, you would need to ADD 9 and "x".
Gaby would like to order a Cobb salad and a drink. What is the minimum amount of money she will have to borrow?(Total money they have is $50 and a Cobb salad costs $8.95 a drink costs $1.55)
Answer:
Gaby do not need to borrow money and they are left with $39.5
Step-by-step explanation:
We are given the following in the question:
Total money = $50
Cost of a Cobb salad = $8.95
Cost of a drink = $1.55
Order: A Cobb salad and a drink
Cost of order =
[tex]= 8.95 + 1.55\\=\$10.5[/tex]
Thus, the total cost of order is $10.5
Money left =
= Total money - Order bill
[tex]=50 - 10.5\\=\$ 39.5[/tex]
Thus, Gaby do not need to borrow money and they are left with $39.5.
One cup of cooked spinach contains 377% of the recommended value of vitamin A. What fraction of the recommended daily value of vitamin A is in one cup of cooked spinach?
Answer:
[tex]\frac{337}{100}[/tex]
Step-by-step explanation:
It is given that one cup of cooked spinach contains 337% of the recommended value of vitamin A.
Therefore, vitamin A is present in one cup of cooked spinach by 337%.
Hence, to represent the fraction of the recommended daily value of vitamin A in one cup of cooked spinach, it will be [tex]\frac{337}{100}[/tex]. (Answer)
{Converting the percentage into fraction}
Why do basic exponential functions always have a horizontal asymptote at y = 0?
Answer:
becouse the value of the exponential function cant go negative... there is no exponent that makes a number negative if the base is positive..
Step-by-step explanation:
Basic exponential functions have a horizontal asymptote at y = 0 because as the input x increases, the output of the function approaches zero but never touches it due to exponential decay.
Explanation:Basic exponential functions always have a horizontal asymptote at y = 0 because as the value of x becomes very large, the value of the exponential function approaches zero. This is due to the nature of exponential decay, where the function's rate of change decreases exponentially. Exponential functions are of the form f(x) = a^x, where a is a positive constant different from 1. When a is less than 1, the function represents exponential decay, and as x approaches infinity, f(x) approaches zero, but never actually reaches it, hence creating a horizontal asymptote at y = 0.
The five-number summary for the number of accounts managed by each sales manager at Force Inc. is shown in the following table. \text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 353535 454545 505050 656565 858585 The five-number summary suggests that about 50\%50%50, percent of sales managers at Force Inc. manage fewer than what number of accounts?
The median is is the midpoint of the data. This means half is below 50 and half is above 50.
The answer would be they handle less than 50 accounts.
50% of sales managers at Force Inc. manages fewer than 50( = the median given) number of accounts.
Given that:
[tex]Min = 35\\Q_1 = 45\\Median = 50\\Q_3 = 65\\Maximum = 85[/tex]
These 5 numbers summary tells the partition of data or quartiles with endpoints as minimum and maximum.
The median is a point for which the counts of data lying above it is equal to the counts of data lying below it.
Since the question asks about :
50% Sales managers manage < ? number of accounts
and since 50% of data lie below and above the median which is 50 given in the table.
Thus we have:
50% of the Sales manager at Force Inc. managing fewer than 50(the median given) number of accounts.
Learn more here:
https://brainly.com/question/300591
Solve the word problems. Round the answer to the nearest tenth.
Mark is on his way home for work. He drives 35 miles due North and then 42 miles due west. Find the shortest distance he can cover to reach home early.
54.7 miles
54.785 miles
547 miles
54 miles
Option A:
The shortest distance Mark can cover to reach home early is 54.7 miles.
Solution:
Towards North = 35 miles
Towards West = 42 miles
Using Pythagoras theorem,
In right triangle, squares of the hypotenuse is equal to the sum of the squares of the other two sides.
Let x be the hypotenuse.
[tex]x^2=35^2+42^2[/tex]
[tex]x^2=1225+1764[/tex]
[tex]x^2=2989[/tex]
Taking square root on both sides, we get
[tex]\sqrt{x^2}=\sqrt {2989}[/tex]
x = 54.67
x = 54.7
The shortest distance Mark can cover to reach home early is 54.7 miles.
Option A is the correct answer.
How do you answer this question??
Answer:
1) { 2,3,4,6,8,9,10,12,15} , {2,4,8,10}, { 2,4,8,10}
Step-by-step explanation:
£ = [ 1,2,3,4,6,8,12,16,24 48}
A = { 2,4,6,8,10}
B = { 3,6,9,12,15}
1) AUB = all members in A and B
= { 2,3,4,6,8,9,10,12,15}
2) AnB' = members in A not in B
{2,4,8,10}
3) A - B = take away members of B in A that is B from A
= { 2,4,8,10}
I hope this was helpful, please mark as brainliest
1.
Simplify: 2.6 x 8.4-5.4
A. 2.32
B. 7.8
C. 16.44
D. 21.3
Answer:
b
Step-by-step explanation:
Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
what is the measure of a? ab=15, bc=15,ac=15
Answer:
5 or 3
Step-by-step explanation:
Mary delivers 32 newspapers to her costumers in 25 minutes these deliveries represent 64% of her costumers
Mr. Allen bought a new computer. His monthly payment plan is shown in the table.
Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).
Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).
The initial values and rates of change for Mr. Allen's and Mr. Jessup's payment plans can be compared based on the given information.
1. Initial Values:
- Mr. Allen's initial amount S: $560
- Mr. Jessup's initial amount: $400
Difference in initial values: $560 - $400 = $160
Mr. Allen's initial value is $160 more than Mr. Jessup's.
2. Rates of Change:
- Mr. Allen's rate of change: $80 per month
- Mr. Jessup's rate of change: $40 per month
The rate of change represents the amount by which the owed amount decreases each month. Mr. Allen's rate of change is greater because he pays off $80 per month, while Mr. Jessup pays off $40 per month.
In summary:
Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).
Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).
Complete question:
Mr. Allen bought a new computer. His monthly payment plan is shown in the table.
Month 0 1 2 3 4 5 6 7
Amount Mr. Allen Owes (S) 560 480 400 320 240 160 80 0
Mr. Jessup buys a new computer for $400. He makes monthly payments of $40 until the computer is paid for. Compare the initial values and rates of change of each function.
You can graph both functions to show that the amount Mr. Allen owes starts at $560 and decreases $80 per month. The amount that Mr. Jessup owes starts at $400 and decreases $40 each month.
Mr. Allen's initial value is $160 more than Mr. Jessup's. Mr. Allen's rate of change is greater than Mr. Jessup's rate of change.
To calculate Peter's monthly expenses, add up the amounts in row 5 of the table. Compare the total expenses with different salaries to determine if Peter can meet them. Advise Peter to create a budget and prioritize expenses if he wants to move out.
Explanation:To calculate Peter's monthly expenses, we need to add up all the amounts in row 5 of the table. Assuming each amount represents a monthly expense, we can sum them up to get the total monthly expenses. To determine if Peter can meet his expenses with different salaries, we compare the total expenses with each salary. If the salary is greater than or equal to the total expenses, Peter can meet his expenses. If the salary is less than the total expenses, Peter cannot meet his expenses.
If Peter wants to move out of his parent's house, I would advise him to create a budget and prioritize his expenses. He should also consider finding ways to increase his income or reduce his expenses to make moving out more affordable.
a dog and a cat together weigh 27 pounds if the dog's weight is an odd number and if he weighs twice as much as she does how much do each weight.
Answer:
Dog: 9 pounds
Cat: 18 pounds
Step-by-step explanation:
x + y= 27
y = 2x
2x + x = 27
3x = 27
x = 9
y = 2x = 18
what is 9/7+5/8 as a fraction
Answer:9/7+5/8=72/56+35/56
Step-by-step explanation:9/7 times 8 by both 9 and 7 and times 7 by both 5 and 8 and you will get your answer
Answer:
[tex]1\frac{51}{56}[/tex]
Step-by-step explanation:
In order to find the answer to this question you will have to find the common denominator, (CD) multiply the denominators by the amount it takes to receive the common deliminator then do the same with the numerators without finding the common numerator, and then add the two numerators together and reduce if needed.
[tex]\frac{9}{7} +\frac{5}{8}[/tex]
Find the common denominator:
[tex]CD=56[/tex]
[tex]9\times 8 =72[/tex]
[tex]7 \times 8 = 56[/tex]
[tex]= \frac{72}{56}[/tex]
Do the same with the second fraction:
[tex]5\times7=35[/tex]
[tex]8\times7=56[/tex]
[tex]=\frac{35}{56}[/tex]
Then you would have:
[tex]\frac{72}{56} +\frac{35}{56}[/tex]
Add the numerators:
[tex]72+35=107[/tex]
[tex]=\frac{107}{56}[/tex]
Turn the improper fraction into a mixed number:
[tex]\frac{107}{56} = 1\frac{51}{56}[/tex]
You get this by dividing 107 by 56 which should give you 1 with the remainder of 51 and you keep the denominator the same.
[tex]=1\frac{51}{56}[/tex]
Hope this helps.
In 20 years, Sam will be 2 times Mary's age. 20 years ago Sam was 4 times Mary's age. How old are Sam and Mary now?
Answer:
in 20 years Sam = 32 = same as Mary so 20 years before Mary was 12 and Sam was 4 times older when she was 48. Sam is now 48 and Mary is 48.
Step-by-step explanation:
Divide. Reduce the answer to lowest terms. 3/7 / 1 1/6
first off let's convert the mixed fraction to an improper fraction and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{3}{7}~~}{\frac{7}{6}}\implies \cfrac{3}{7}\cdot \cfrac{6}{7}\implies \cfrac{18}{49}[/tex]
what is 240,000,591 divides by 176
Answer:
240,000,591÷176= 1363639.72159
Answer:
1,363,639.721590909
Step-by-step explanation:
Make sure to pick ALL and It needs To BE CoRRECt
Answer:
(a): 9x + 45
Option A, 9(x + 5) because it distributes into 9x + 45
Option B, 9 * x + 9 * 5 because it multiplies into 9x + 45
(b): 13 + 9y - 3 - y
Option D, 8y + 10 because it combines into this number
3x+4y-6z=-60
7x-5y+z=-37
2x+3y-z=-29
Answer:
{x,y,z}={-8,-3,4}
Step-by-step explanation:
Luna buys a shirt that costs $15.65. She gives the cashier $20 and receives $3.25 in change. What is the percent error in the amount of change she was given?
The error in the amount of change she was 25.28%.
Step-by-step explanation:
Given,
The actual price = 15.65$
The amount Luna gives to cashier = 20$
The change she receives = c = 3.25$
The actual amount of changes = x = total amount - actual price:
20$ - 15.65$ = 4.35
The percentage of error can be found using: [tex]\frac{x-c}{x}[/tex]
By putting the values in equation, we get
=> [tex]\frac{4.35 - 3.25}{4.35} * 100[/tex]
=> [tex]\frac{1.10}{4.35} * 100[/tex]
=> 25.28 %
Hence, the error in the amount of change she was 25.28%.
The percent error in the amount of change Luna was given is:
[tex]\[\boxed{25.29\%}\][/tex]
To determine the percent error in the amount of change Luna was given, we need to compare the actual change received to the correct change she should have received.
Step 1: Calculate the Correct Change
Luna gave the cashier $20 for a shirt that costs $15.65. The correct amount of change should be:
[tex]\[\text{Correct Change} = 20 - 15.65 = 4.35 \, \text{dollars}\][/tex]
Step 2: Calculate the Error
The cashier gave Luna $3.25 instead of $4.35. The error in the change given is:
[tex]\[\text{Error} = \text{Correct Change} - \text{Actual Change Given} = 4.35 - 3.25 = 1.10 \, \text{dollars}\][/tex]
Step 3: Calculate the Percent Error
Percent error is given by the formula:
[tex]\[\text{Percent Error} = \left( \frac{\text{Error}}{\text{Correct Change}} \right) \times 100\][/tex]
Substitute the values into the formula:
[tex]\[\text{Percent Error} = \left( \frac{1.10}{4.35} \right) \times 100\][/tex]
Perform the division:
[tex]\[\frac{1.10}{4.35} \approx 0.2529\][/tex]
Convert to a percentage:
[tex]\[0.2529 \times 100 \approx 25.29\%\][/tex]
The percent error in the amount of change Luna was given is:
[tex]\[\boxed{25.29\%}\][/tex]
A water park conducted a study to investigate the relationship between outdoor temperature and the number of park visitors. The correlating linear model is shown, where x represents the number of degrees over 70°F, and y represents the number of park visitors.
y= 42 + 15x
What is the correct interpretation of the y-intercept?
A.
When the temperature is 70°F, the park can expect 0 visitors.
B.
When the temperature is 70°F, the park can expect 42 visitors.
C.
When the temperature is 70°F, the park can expect 57 visitors.
D.
When the temperature is 70°F, the park can expect 15 visitors.
Answer:
b) When the temperature is 70°F, the park can expect 42 visitors.
Step-by-step explanation:
Given that y represents the number of park visitors and x is the number of degrees over 70°F. The equation of the model is given as:
y = 42 + 15x
The general equation of a straight line plotted y against x with an intercept(c) on the y-axis and a slope(m) is given by the equation:
y = mx + c
comparing y = mx + c with y = 42 + 15x, the slope of the line y = 42 + 15x is 15 and its intercept on the y axis is 42.
This means that at temperature 70°F, x is 0.
therefore y = 42 + 15(0) = 42
Therefore when the temperature is 70°F, the park can expect 42 visitors.
HELP PLEASE BE QUICK
Answer:
8
Step-by-step explanation:
Area of a circle = πr^2
64π / π = πr^2 / π
sqrt(64) = sqrt(r^2)
8 = r
Answer: 8
PAGE 11
2) 4x+2(x*3)=6x-6
A x=0
B x=6
C INFINITE SOLUTIONS
D NO SOLUTION
ye boi its A | SMART BOIS
In the diagram ABCD is a rectangle and PQ is parralell to AD
For the given rectangles, [tex]f=4[/tex] cm and [tex]g = 6[/tex] cm.
Step-by-step explanation:
Step 1:
The area of a rectangle is calculated by multiplying its length with its width. Both the rectangles APQD and PBCQ have the same width.
The second rectangle PBCQ has a length of 9 cm. Its area is determined by subtracting the area of APQD from the area of ABCD.
The area of the rectangle PQBC [tex]= 60 - 24 = 36[/tex] [tex]cm^{2}[/tex].
Step 2:
The length of rectangle PBCQ is 9 cm and the area is 36 [tex]cm^{2}[/tex] so the width can be determined.
[tex]Width = \frac{area}{length} = \frac{36}{9} = 4[/tex] cm. So [tex]f=4[/tex] cm.
Step 3:
The width of the rectangle APQD is also 4cm.
The width of the rectangle APQD is 4 cm and the area is 24 [tex]cm^{2}[/tex].
[tex]length = \frac{area}{width} = \frac{24}{4} = 6[/tex] cm. So [tex]g = 6[/tex] cm.
I need help on something on my Math assignment. In this problem, they already have the final answer to the volume of a half-sphere (1,071.79) in^3. the problem wants me to find the radius of the half-sphere, so I figured if I want to find radius, I must do the formula backward. But I only end up with a number like 0.00195311892566 and I don't think that is the correct answer.
Can you help me?
Sarah has a pond in the shape of a half sphere in her back yard. The pond currently holds 1,071.79 cubic inches of water. What is the radius of the pond?
Show your work and explain your answer.
Answer:
Hi I am cool
Step-by-step explanation:
Answer:
Don't you just divided that by 3?
Step-by-step explanation:
Subtract.
Your answer should be a polynomial in standard form.
(
6
y
2
−
9
y
+
4
)
−
(
−
7
y
2
+
5
y
+
1
)
Answer:
Step-by-step explanation:
(−8* y^2−9*y)+(8*y^3+9*y^2−2*y)
first, remove extraneous parentheses (or distribute if negative)
=−8* y^2−9*y+8*y^3+9*y^2−2*y
then group terms in decreasing degree of y (variable)
=+8*y^3 −8* y^2+9*y^2 −9*y−2*y
simply expression by adding/subtracting similar terms
=+8*y^3 +y^2 −11*y
to give the final answer.
Helpppppppppppppppppp
Option D:
[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]
Solution:
Given expression is [tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex].
To find the product of the expression:
[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex]
Multiply each term of the first term with each term of the 2nd term.
[tex]=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)[/tex]
Using the exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)[/tex]
[tex]=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7[/tex]
Arrange the terms with same power.
[tex]=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7[/tex]
[tex]=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]
Hence option D is the correct answer.
[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]