The inequality representing p, the number of people who can go to the amusement park, is given as follows:
10.5p + 16.5 ≤ 90.
How to build the inequality?The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:
C(p) = mp + b.
In which the parameters are given as follows:
m is the slope, representing the cost of the ticket per person.b is the intercept, representing the cost of parking.Parking is $16.50, and tickets cost $10.50 per person, hence the numeric values of the slope and the intercept are given as follows:
m = 10.50, b = 16.50.
Thus the cost function is given as follows:
C(p) = 10.5p + 16.5.
They have no more than $90 to spend on parking and admission, hence the inequality is defined as follows:
C(p) ≤ 90.
10.5p + 16.5 ≤ 90.
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The height of the apple trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.2 feet what percentage of the apple trees are taller than 14.9 ft
Answer:
2.275%
Step-by-step explanation:
z = (x-μ)/σ, where
x is the raw score = 14.9 ft
μ is the population mean = 12.5 ft
σ is the population standard deviation = 1.2 ft
We are to find the percentage of the apple trees are taller than 14.9 ft,
This means x > 14.9, x greater than 14.9
Hence,
z = (14.9 - 12.5)/1.2
z = 2
Probability value from Z-Table:
P(x<14.9) = 0.97725
P(x>14.9) = 1 - P(x<14.9) = 0.02275
Converting to Percentage
= 0.02275 × 100
= 2.275%
Therefore, the percentage of the apple trees that are taller than 14.9 ft is 2.275%
A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at 14 miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of 3 miles per hour. How long will it be before the rescued sailors are 57 miles from their lifeboat?
The time it will take for the rescued sailors to be 57 miles from their life boat is given as follows:
3.35 hours.
What is relative velocity?Relative velocity is obtained considering the direction in which the objects are traveling, as follows:
Opposite direction: the relative velocity is given by the sum of the velocities of each object.Same direction: the relative velocity is given by the subtraction of the velocities of each object.For this problem, the sailors and the lifeboat are traveling in opposite directions, hence the relative velocity, considering each of their velocities is given as follows:
v = 14 + 3 = 17 miles.
(meaning that they get 17 miles farther each hour).
Velocity is distance divided by time, hence the time it will take for them to be 57 miles apart is given as follows:
17 = 57/t
17t = 57
t = 57/17
t = 3.35 hours.
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Moana sold
packets of seeds to help raise funds for a sports trip. Each packet earned
her $0.65. Afa sold calendars, which earned him $1.50 each. Altogether they earned
$84.70. If they sold a total of 95 items between them, how many did each student
sell?
9514 1404 393
Answer:
Moana: 68 seed packetsAfa: 27 calendarsStep-by-step explanation:
Let c represent the number of calendars sold. Then 95-c is the number of seed packets sold. The total revenue is ...
0.65(95-c) +1.50c = 84.70
0.85c = 22.95 . . . . . . . . . . . . subtract 61.75
c = 27
95 -c = 68
Moana sold 68 seed packets; Afa sold 27 calendars.
If y varies directly as x, and y = 15 when x = 10, then what
is y when x = 6
Answer:
y = 9.
Step-by-step explanation:
y = kx where k is a constant.
Substituting the given values:
15 = k*10
k = 15/10 = 1.5 so
y = 1.5x is the relation.
When x = 6
y = 1.5 * 6
= 9..
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
y = kx
k = 1.5 and x = 6
The value of y when x = 6 is 9.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
3x = 5 is an equation.
We have,
If y varies directly as x.
This means,
y ∝ x
y = kx
where k is the constant of proportionality.
Now,
y = 15 when x = 10
This means,
15 = 10k
k = 15/10
k = 1.5
Now,
y = kx
k = 1.5
x = 6
y = 1.5 x 6
y = 9
Thus,
y = kx
k = 1.5 and x = 6
The value of y when x = 6 is 9.
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Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter how many quizzes will Baldwin have taken in total
The total number of quizzes in 9 weeks will be 45.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Baldwin took a total of 35 quizzes over the course of 7 weeks. After attending 9 weeks of school this quarter.
The number of quizzes in 9 weeks will be,
7 weeks = 35 quizz
1 week = 35 / 9 quizz
9 week = ( 35 x 7 ) / 9
9 weeks = 45 quizzes.
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Z is a standard normal random variable. The P(Z > 2.11) equals
0.4821
0.9821
0.5000
0.0174
Ellie bought snacks for her team's practice. She bought a bag of oranges for
$2. 66 and a 5-pack of juice bottles. The total cost before tax was $7. 46. Write
and solve an equation which can be used to determine j, how much each
bottle of juice costs?
The linear equation for jj is ($7.46 - $2.66) / 5 and the cost of each bottle of juice is $0.96.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The first step to take in order to determine jj, is to determine the total cost of the 5-pack of juice bottles.
Cost of the 5-pack of juice bottles = Total cost before tax - cost of the bag of oranges
Cost of the 5-pack of juice bottles = $7.46 - $2.66 = $4.80
The second step is to determine the cost of each bottle of juice
The cost of each bottle of juice = Cost of the 5-pack of juice bottles / total number of bottles
$4.80 / 5
= $0.96
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40 points!!!! What’s the answer???Please help!!!!! Please Tell me how you got it!!!
Please answer I’ll give brainliest!!! Fake answers such as links will get reported.
Answer:
1 : 64Step-by-step explanation:
Without calculation, we should get:
(1/8)² = 1/64Lets confirm
Area of the drawing:
4.875 * 14 = 68.25 in²Area of the wing:
39*112 = 4368 ft²Divide the area of the wing by the area of the drawing:
4368/68.25 = 64As we see the ratio is same, drawing to wing:
1 : 64how do i do this question
The slope of the line is given by the equation slope m = 3/2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , let the first point be P = P ( 0 , 1 )
Let the second point be Q = Q ( 2 , 4 )
Now , the slope of the line between the two points is
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 4 - 1 ) / ( 2 - 0 )
On simplifying the equation , we get
Slope m = ( 3 / 2 )
Therefore , the value of m is 3/2
Hence , the slope of the line is 3/2
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Caleb bought groceries for $68.48, including sales tax. If sales tax was 7%, how much was the groceries before tax?
pls help me
Answer:
$64.00
Step-by-step explanation:
Let the amount for the groceries before tax be Y
If the cost inclusive of tax at 7% is $68.48, then
Y + 7% * Y = $68.48
100%Y + 7%Y = $68.48
107%Y = $68.48
Recall that 107% = 1.07
1.07Y = $68.48,
Divide both sides by 1.07
Y = $68.48/1.07
Y = $64.00
Hence the cost of the groceries before tax is $64
I don't get the problem! No links please!
Answer:
5
Step-by-step explanation:
Would this equal 0 (zero): (put yes/no as your answer)
Sandy's rose bush grew 8 inches in the spring. Then, she pruned it back 8 inches in the fall.
I need help ASAP!!!!!!!!! Plz & thx. I will give the correct answer a crown.
Also, have a great day/night
Answer:
Yes, that would be 0
As simple as 8-8=0
You have a great day/night too :)
..Solve multi step problems
Help me.....
Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards
What is MultiplicationMultiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.
In this problem, we may require the use of some mathematical operators to find the solution to the problem.
1.
He currently has 216 cards, but he needs 15 sets of cards.
1 set of card = 72 cards
Let's calculate the number of sets he currently has.
1 set of card = 72 cards
x set = 216 cards
cross multiply both sides and solve for x.
x * 72 = 216 * 1
x = 216 / 72
x = 3 sets
He currently has 3 sets of cards.
Since he wants 15 sets of cards, we will need 12 more set of cards.
The number of cards can be calculated by multiplying 12 by 72
Number of cards = 12 * 72 = 864
He needs 864 more cards.
2.
1 set of card = $27
1 set = 72 cards
But she's bringing $9 to join, we can calculate the ratio of cards she will get.
1 / 27 = x / 9
x = 9 / 27
x = 1/3
She will get 1/3 of the cards bought which will be
72 * 1/3 = 24 cards
She will get 24 cards
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hELP before my mom gets mad at me for bad grades
All must add up to 360°
100+44=144°
360-144
= 216°
Answer:
144°
Step-by-step explanation:
Every possible triangle's 3 angles add up to 180.
So when you are given 2 angles of a triangle (100° and 44°), you can find the 3rd one by subtracting the given angles from 180°.
100°+44°=144°
180°-144°=36°
That's the missing angle inside the triangle.
We need that to find angle 1 because 2 angles that make up a straight line add up to 180°. So 180-36°=144°.
Write a proportion to find how many points az a student needs to score on a test worth 50 points
to get a test score of 40%.
Answer:The student needs to score 20 points
Step-by-step explanation:
? /50= 40/100Cross multiply:100*? = 40*50⇒? = 40*50/100= 20
George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be modeled by x2 + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by 2 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r - c)(5) mean about George's new store? The new store will sell 900 items in its fifth month in business. The new store will have a profit of $900 after its fifth month in business. The new store will have a profit of $5400 after its fifth month in business. The new store will sell 5400 items in its fifth month in business.
Answer:
pls can you explain further
N plus 75 used in a real world sentence.
Answer:
Laura has "n" amount of nickels. She receives 75 more from her grandmother.
Explanation:
(If this is not what the question meant, please let me know!)
Because the question is asking us to write a sentence for an addition problem, we need to write a sentence that involves two amounts of one thing being combined, in this case nickels.
write a verbal expression for the algebraic expression
please help
A verbal expression for the given algebraic expression are as follows:
10. The product of a and b
11. Four times the sum of x and seven
12. Twice the value of x
13. The cube of m
14. The difference between x and six
15. Eight hundred twelve
16. The value of y
17. The average of x and y
18. Three times x minus four
19. Five times the difference of a and b
Write the difference between verbal expression and algebraic expressions?Verbal expressions are sentences that express a mathematical concept or equation. They use words, such as "twice the number," "the product of," or "sum of," as opposed to symbols and operations. Verbal expressions are often used to explain math problems or to pose questions.Algebraic expressions, on the other hand, use symbols and operations to express mathematical concepts. Symbols such as +, -, x, and / can be used to represent addition, subtraction, multiplication and division, respectively. Algebraic expressions are also used to simplify equations and can be used to solve math problems. For example, an algebraic expression such as "2x + 3y" can represent the sum of two numbers multiplied by two and three, respectively.The main difference between verbal expressions and algebraic expressions is that verbal expressions use words to explain a mathematical concept while algebraic expressions use symbols and operations. Verbal expressions are often used to explain a problem while algebraic expressions are used to solve the problem.To learn more about algebraic expressions refer to:
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help i have 5 mins left
Answer: c = P - a - 5
Step-by-step explanation:
P= a + 5 + c
P - a - 5= c
2. If tan theta = 2 , find cot theta
Answer:
1/2
Step-by-step explanation:
cot∅ = 1/tan∅
cot∅ = 1/2
Two-fifths of a number is 2/5 greater than 1/3 of the number. What is the number?
Please help me! i do t know....
Answer:
[tex]-3/\sqrt{58}[/tex]
Step-by-step explanation:
tan = opposite / adjacent
opposite side is the y-coordinate of a point on the terminal side
adjacent side is the x-coordinate of a point on the terminal side
if the terminal side is in the second quadrant (the top-left quadrant), a coordinate on the terminal side would have a negative x-coordinate and a positive y-coordinate
This being the case:
the opposite side (y) would be -3 and the adjacent side (x) would be 7
using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
[tex]7^2+(-3)^2=c^2[/tex]
The hypotenuse is c, so it equals [tex]\sqrt{58}[/tex]
sin = opposite / hypotenuse
so sin(theta) = [tex]-3/\sqrt{58}[/tex]
PLEASE ANSWER!! I WILL GIVE BRAINLIEST AND 50 PTS!!
Coordinate plane with triangle EFG with E at 0 comma 5, F at 1 comma 1, and G at negative 2 comma 1. Point H at 1 comma 1 is on segment GF, and points E and H are connected with a segment.
Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the dilation?
segment EH and segment E prime H prime both pass through the center of dilation.
The slope of segment EF is the same as the slope of segment E prime H prime.
segment E prime G prime will overlap segment EG.
segment EH ≅ segment E prime H prime.
Answer:
See below and the attachedStep-by-step explanation:
Given triangle EFG:
E(0, 5), F(1, 1), G(-2, 1)Center of dilation is H(0, 1)Scale factor is k = 3The rule for this dilation is:
(x, y) → (k(x - a) + a, k(y - b) + b) (x, y) → (3x, 3(y - 1) + 1) = (3x, 3y - 2)The coordinates of E'F'G' are:
E → E' = (0, 5) → (0, 13)F → F' = (1, 1) → (3, 1)G → G' = (-2, 1) → (-6, 1)Points H and H' overlap as center of dilation at (0, 1)Options (verified with the graph):
Segment EH and segment E prime H prime both pass through the center of dilation.
TrueThe slope of segment EF is the same as the slope of segment E prime H prime.
FalseSegment E prime G prime will overlap segment EG.
FalseSegment EH ≅ segment E prime H prime.
Falseanswer is A gl on ur test
S(5-4-2) and y (1 7)
Answer:
i do not not the answer of this question
Find the missing value to the nearest hundredth.
tan ___ = 73
A. 81.61°
B. 64.61°
C. 60.61°
D. 89.22°
Answer:
The answer is 89.22
Step-by-step explanation:
A circle has a circumference of 1,133.54 units. What is the diameter of the circle?
Answer:
360.82
Step-by-step explanation:
Answer: A circle has a circumference C=1133.54 units. Substitute the value, Therefore, the diameter of the circle is 361 units.
Step-by-step explanation:
Lily purchases 3 gallons and two quarts of ice cream. How much ice cream did she purchase, in QUARTS
Answer:
14 Quarts
Step-by-step explanation:
1 Gallon = 4 Quarts.
3x4 = 12 + 2 = 14 Quarts.
Given f(x) = −x² – 8x, find ƒ(−3)
Answer:
15
Step-by-step explanation:
To find f(-3), substitute x with (-3)
f(x) = -x² - 8x
f(-3) = - (-3)² - 8*(-3)
= - (9) + 24
= - 9 + 24
= 15
Answer:
15
Step-by-step explanation:
f ( x ) = - x² - 8x
Accordingly, to find the value of f ( -3 ) you have to replace x with ( - 3 ).
f ( -3 ) = - (-3)² - 8 × -3
f ( -3 ) = - 9 + 24
f ( -3 ) = 15
The radius of a circle is 6 centimeters. What is the circle's circumference?
Answer:
37.7 cm
Step-by-step explanation:
C=2πr=2·π·6≈37.69911
Answer:
37.68 cm.
Step-by-step explanation:
The formula for circumference of a circle is: πd (diameter)
The radius of this circle is 6 centimeters.
To find the diameter, multiply the radius by 2.
6 × 2 = 12.
12 is the diameter.
Lastly, multiply the diameter by pi.
**3.14 IS A SUBSTITUTE FOR PI**
3.14 = 37.68.
Therefore, the circumference of this circle is 37.68 cm.
How do you explain irrational numbers to children?
The irrational numbers to children can be explained as the numbers that can be written as a nonrepeating or nonterminating decimal .
What are Irrational Numbers ?
The real numbers that can be represented as a nonrepeating or a nonterminating decimal but not as a fraction, and the decimal that goes on forever without repeating.
For Example : [tex]\sqrt{2} , \sqrt{5} , \sqrt{7}[/tex] are few example of irrational numbers .
In simpler words : the irrational number is a number that is not rational. which means It is a number which cannot be written as a ratio of two integers or cannot be written as fraction.
and If a fraction has a 0 in the denominator , it is an irrational number .
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