The entire expenditures for both children and adults are modelled using graphs and formulae. y = 1.25x + 10 y = 0.75x + 5 a.
What is the linear equation for total cost?The equation C(x)=mx+b represents a linear cost function, where mx stands for the variable cost, b for the fixed cost, and m for the marginal cost.
Admission is $10 for adults, and ride tickets cost $1.25; the line's a y-intercept value is 104.
Admission is $5 for children, and ride tickets cost $0.75 each. When X=0,Y=5, the line b's y-intercept is 54.
When X=20 for a child, y=0.75.20+5=20.
It crosses line 20 and 20.
When X=20 and Y=1.25, 20+10 equals 35 for an adult.
Line an is passed at (20, 35).
A linear model is described by the equation y=mx+b. The y denotes the result, the m denotes the rate of change, the x denotes the input, and the b denotes the constant.
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Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches (5in.), and the other was a large cheese pizza with a 7in. radius. The circumference of the larger pizza is how much longer than the circumference of the smaller pizza?
The circumference of a circle is C=2πr.
Use π≈3.14 for the calculations.
Round your answer to the nearest hundredth.
The circumference of the larger pizza is 12.56 longer than the smaller pizza.
What is circumference?The length around the circle or the perimeter of the circle is called its circumference.
Given that, Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches, and the other was a large cheese pizza with a 7 in. radius.
We need to find how much longer than the circumference of the smaller pizza,
We know that,
Circumference of a circle = 2πr.
Therefore,
Circumference of the larger pizza = 2 × 3.14 × 7 = 43.96 in
Circumference of the smaller pizza = 2 × 3.14 × 5 = 31.4 in
Therefore,
Subtracting the circumference of smaller pizza from larger pizza to get the difference = 43.96 - 31.4 = 12.56 in
Hence, the circumference of the larger pizza is 12.56 longer than the smaller pizza.
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A college is building a new basketball court that is 94 feet long and 50 feet wide, but the wood for the court comes only in 10-meter planks that are 8 centimeters wide. How many planks are needed to surface the court?
Using the formula of area of a rectangle, the number of planks that will surface the court is approximately 55
What is Area of a RectangleThe area of a rectangle is calculated by multiplying the length of the rectangle by its width. The formula is:
Area = length x width
In this problem, we can find the area of the court and the area of the plank and divide both to determine the number of plank that would suffice.
Area of court = length * width
length = 94 feet = 28.64m
width = 50 feet = 15.24m
Area of court = 28.64 * 15.24 = 436.47m²
Area of plank = length * width
Area of plank = 10 * 0.8
Area of plank = 8m²
The number of planks required = 436.47 / 8 = 54.55 ≅ 55 planks
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The user manual for Layla's phone notes that the device can be damaged
when operated at temperatures below -20°C and above 45°C. Layla wants to
know what these ranges are in degrees Fahrenheit and writes these
inequalities to rewrite the relationship where F is degrees Fahrenheit.
(F32) < -20 or (F32) > 45
Which statement best describes the temperature ranges Layla should avoid
while using her phone?
OA. Layla should avoid using her phone in temperatures below 21°F
and above 57°F.
OB. Layla should avoid using her phone in temperatures above -4°F
and below 113°F.
OC. Layla should avoid using her phone in temperatures below -4°F
and above 113*F.
OD. Layla should avoid using her phone in temperatures above 21°F
and below 57°F.
In temperatures between -4°F and 113°F, Layla should refrain from using her phone.
Which of the following best sums up the temperature ranges Layla ought to stay away from when using her phone? In temperatures between -4°F and 113°F, Layla should refrain from using her phone.Maintaining your smartphone's working temperature between 0° and 35° C (32° to 95° F).The device may behave differently at lower or higher temperatures.(-4° to 113° F) for storage between -20° and 45°When temperatures exceed specified thresholds, stay out of parked cars and out of the sun.The recommended temperature range for users' devices is between -4 and 113 degrees Fahrenheit, according to their manufacturers.If you go lower, the phone might freeze; if you go higher, you run the risk of lasting harm.Most smartphones are built to operate between 32 and 95 degrees Fahrenheit.Apple Watches fall within this temperature range as well.To learn more about temperatures refer
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Use distributive property to create and equivalent expression to 9x + 21
HELP ITS DUE WENSDAY
Answer:
[tex]3(3x+7)[/tex]
Step-by-step explanation:
[tex]9x=3(3x), 21=3(7) \implies 9x+21=3(3x+7)[/tex]
Someone please help I’ll give good points for help !!! And explain please
The length of a rectangle is 20 cm greater than the width. The area is 125 sq cm. Find the dimensions of the rectangle.
On solving the provided question, we can say that Area of rectangle, A = x(25+x) => A = 20x + x^2 => x^2 +20x - 125 = 0 => x^2 + 25x - 5x - 125 = 0 => x = -25, +5
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
The length of a rectangle is = 20 cm greater than the width
The area is 125 sq cm.
let width be x
let length be 20 + x
Area of rectangle, A = x(25+x)
A = 20x + x^2
x^2 +20x - 125 = 0
x^2 + 25x - 5x - 125 = 0
x = -25, +5
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For one month diera calculated her home towns average high temperature
The answer for this question is Celsius for Fahrenheit.
The Formula for Converting TemperatureTo convert temperatures from degrees Fahrenheit to degrees Celsius, multiply the result by.5556 (or 5/9) after subtracting 32.
(50°F - 32) x.5556 = 10°C, for instance.
When converting from degrees Celsius to Fahrenheit, multiply the result by 1.8 (or 9/5) and then by 32.
For instance, (30°C x 1.8) + 32 = 86°F'
Here are two useful charts that translate between F and C as well as between C and F.
How to calculate her home towns average high temperature?The temperature of f degrees Fahrenheit converted to degree Celsius.
(( f)=5/9 (f-32)
represent the temperature of f degrees Fahrenheit converted to degree Celsius.
The function C(F) will be "C of F" it will be converted Fahrenheit to Celsius.
So that means if the temperature is in Fahrenheit it will be converted to Celsius.
So that means the C(F) represents the Celsius temperature.
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Complete Question -
For one month diera calculated her home town's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees FAhrenheit to degrees Celsius using the function C(F) = 5/9(F-32). What does C(F) represent?
In the diagram, which pair of angles are vertical angles?
A transversal intersects 2 lines to form 8 angles. Clockwise from the top, the angles are 1, 2, 3, 4; 5, 6, 7, 8.
Angle 1 and Angle 2
Angle 4 and Angle 6
Angle 6 and Angle 8
Angle 5 and Angle 3
Step-by-step explanation:
opposite interior angles
26
Consider the diagram below.
y
C
y₁ = x + 6-
5
-y = x - 6
J9
K 12
L 18
M 36
N 72
5
5+
A
x² + y² = 36
5
B
x
What is the area, in square units, of
A ABC?
The diagram's area at x is [tex]$$x=\sqrt{-y^2+36} \text { or } x=-\sqrt{-y^2+36}$$[/tex], and at y is [tex]$$y=\sqrt{-x^2+36} \text { or } y=-\sqrt{-x^2+36}$$[/tex].
What is the value of x² + y² = 36 ?Let's try to find x.
[tex]$$x^2+y^2=36$$[/tex]
Phase 1: Add [tex]$-y^{\wedge} 2$[/tex] to both parties.
[tex]$$\begin{aligned}& x^2+y^2+-y^2=36+-y^2 \\& x^2=-y^2+36\end{aligned}$$[/tex]
Take the square root in step two.
[tex]$$x=\sqrt{-y^2+36} \text { or } x=-\sqrt{-y^2+36}$$[/tex]
Solve for y now.
[tex]$$x^2+y^2=36$$[/tex]
Phase 1: Add [tex]$-x^{\wedge} 2$[/tex] to both parties.
[tex]$$\begin{aligned}& x^2+y^2+-x^2=36+-x^2 \\& y^2=-x^2+36\end{aligned}$$[/tex]
Take the square root in step two.
[tex]$$y=\sqrt{-x^2+36} \text { or } y=-\sqrt{-x^2+36}$$[/tex]
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What is the length of segment EA?
Answer:
Step-by-step explanation:
CA=64 √2
BA=BC=64
AG=137-64=73
AG=X
EG=X √3
EA=2X=73*2=146
What is the domain and range? Of f(x)1/4x+3?
The domain of the function f(x) = 1/4x + 3 is all real numbers except x = 0, since division by 0 is undefined.
The range of the function is all real numbers. For any real number x, f(x) = 1/4x + 3 will always produce a real number, so the range is (-infinity, +infinity).
how much of a radioactive kind of chromium will be left after 4 months if you start with 6080 grams and the half life is 1 months
The amount of chromium left after 4 months of decay is 380 grams.
What is the half-life of the element?The half-life of the element is defined as the time span in which the element grows or decays half of its whole composition of growth and decay.
Here,
Let y be the amount of decay for x months
y = 6080aˣ
Half-life
1 / 2 = a¹
a = 1/2 = 0.5
Now,
y = 6080[0.5]⁴
y = 380
Thus, the amount of chromium left after 4 months of decay is 380 grams.
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A bag contains 50 marbles, 28 red ones and 22 blue ones. A marble is picked at random from the bag. What is the probability of picking a blue marble?
a
11/25
b
25/11
c
11/14
d
14/25
The probability of blue marbles is 11/25.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
Given red marbles in the bag = 28
blue marbles in bag = 22
total marbles = 50
probability = favorable outcome/total outcome
P(blue marbles) = 22/50
P(blue marbles) = 11/25
Hence the probability is 11/25.
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We can multiply or divide radicals regardless of their index.
True
Or
False
What is the measure of one exterior angle of a 15-sided regular polygon?
O 12 degrees
O 168 degrees
O24 degrees
O 156 degrees
Answer:
24°
Step-by-step explanation:
For an n-sided regular polygon, the sum of internal angles = (n-2)×180°
Since all internal angles are equal, the internal angle can is given as:
Here, it is given that the polygon has 15 sides.
So n = 15
So each internal angle is 156°.
Internal and external angles are always supplementary. So the sum of the internal and external angles is 180°.
So external angle = 180° - 156° = 24°.
The measure of each external angle is 24°.
Simplify -5(7+x)+2/2/6x
DUE SOON PLEASE HELP
The ratio of their volumes is equal to: D. 27:125.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this formula:
Volume = 4/3 × πr³
Where:
r represents the radius.
Based on the information provided about the two spheres, an expression which models their surface areas (S) with respect to volumes (V) is given by;
S₁/S₂ = V₁/V₂
S₁/S₂ = 9/25
(4πr₁²)/(4πr₂²) = 9/25
r₁²/r₂² = 9/25
Taking the square root of both sides of the expression, we have:
r₁/r₂ = 3/4
From the volume of a sphere formula, we have:
V₁/V₂ = (4/3 × πr₁³)/(4/3 × πr₂³)
V₁/V₂ = r₁³/r₂³
V₁/V₂ = 3³/4³
V₁/V₂ = 27/125.
Therefore, the required ratio is 27:125.
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A data set with whole numbers has a low value of 20 and a high value of 94 for seven classes
The 7 classes are provided in the frequency table.
What is a frequency table ?
A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.
e.g.
A, A, A, B, B, B, B, C, C, D
Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:
Frequency of A = 3
Frequency of B = 4
Frequency of C = 2
Frequency of D = 1
Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.
Now,
Class width=94-20/7
=74/7
=10+4/7
class width=11
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22. Julianne works as a waitress. She carns $13 per hour plus tips.
a. Today she worked x hours. Express her pay for these hours algebraically.
b. She served nine tables. The total bill for these nine tables was y dollars.
Julianne received 18% in tips from these bills, Express the amount she
received in tips algebraically.
c. Express Julianne's total earnings for the day algebraically.
a. To express Julianne's pay for these x hours algebraically, you would use the equation: pay = 13x + tips
b. To express the amount Julianne received in tips algebraically, you would use the equation: tips = 0.18y
c. To express Julianne's total earnings for the day algebraically, you would add her pay (13x) to the amount of tips she received (0.18y) to get the equation: total earnings = 13x + 0.18y.
How to solve the given equation?a. Julianne earns $13 per hour plus tips, so her pay for working x hours can be expressed algebraically as pay = 13x + tips. This equation means that her pay is equal to $13 multiplied by the number of hours she worked, plus any additional tips she received. The variable "x" represents the number of hours she worked, and "tips" represents the additional money she earned from tips.
b. Julianne received tips from serving 9 tables, and the total bill for these tables was y dollars. We can express the amount she received in tips algebraically as tips = 0.18y. This equation means that the amount of tips she received is equal to 18% of the total bill for the 9 tables, represented by the variable "y". The 0.18 represents 18% in decimal form.
c. To find Julianne's total earnings for the day, we need to add her pay (13x) to the amount of tips she received (0.18y). This can be expressed algebraically as total earnings = 13x + 0.18y. This equation means that her total earnings for the day is equal to her pay for working x hours plus the amount of tips she received. The variable "x" represents the number of hours she worked, the variable "y" represents the total bill for the nine tables, and the product of 0.18 * y represents the amount she received as tips.
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There are two words or phrases in this problem that tell you what operations will be in the algebraic expression. Choose the correct meaning for each.
Answer:I need to know what the phrases are.
Step-by-step explanation:
I can't answer this unless you do so.
Which of these is a simplified form of the equation 7x + 4 = 5 + 3x + 1x?
a 3x=9
b 3x=1
c 11x=9
d 11x=1
Answer:
b [3x = 1]
Step-by-step explanation:
7x + 4 = 5 + 3x + 1x
Combine like terms:
7x + 4 = 5 + 4x
Subtract 4 from both sides:
7x = 1 + 4x
Subtract 4x from both sides:
[3x = 1]
What is an equation of the line that passes through the points through (0,-6) and (6,2)?
Answer: y= [tex]\frac{4}{3}[/tex]x - 6
Refer to the images to see the explanation I wrote down :)
A bookstore has 4320 books and magazines. It has 2169 books. The rest are does the bookstore have? magazines. How many magazines
Answer: 2151 magazines
Step-by-step explanation: First subtract the whole number of books and magazines by the number of books and you'll find your answers.
the area of rectangular ballroom is 800m2 and perimeter is 120
find the dimension
The ballroom is 40m by 20m
just think of numbers that times together to get 800 and then check if the perimeter is right.
How to find the dimension?A rectangular ballroom has two dimensions: length and width,
The perimeter is the sum of all the sides of the rectangle,
P=L+LW+W=2L+2W
The area is the product of these two dimensions,
A=L,W
We know that the perimeter is 120m and the area is 800m². Replacing in the equations above, we have two equations with two variables L and W,
120=2L+2W
=800LW
Solve the first equation for W. Subtract 2L from both sides,
120-2L=2L-2L+2W
120-2L=2W
And divide both sides by 2,
120-2L/2=2W/2
60-L=W
The next step is to replace W by this expression in the second equation,
800=L(60-L)
Now we have to solve this equation for L. Apply the distributive property on the right side of the equation,
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Allen Siegell has a personal injury protection policy that covers each person in, on, around, or under his car for medical expenses up to $50,000. He is involved in an accident and five people in his car are hurt. One person has $3,000 or medical expenses, three people each have $500 worth of medical expenses, and Allen himself has medical expenses totaling $62,000. How much money must the insurance company pay out for these five people?
The total medical expenses for the five people in the car are $3,000 + $3*$500 + $62,000 = $3,000 + $1,500 + $62,000 = $66,500
What does a math word problem entail?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Since Allen's personal injury protection policy covers each person up to $50,000, the insurance company must pay out $50,000*5 = $250,000 for the five people in the car.
Since the total medical expenses for the five people are $66,500, the insurance company will pay out the total medical expenses for the five people, which is $66,500.
Therefore, the insurance company must pay out $66,500 for these five people.
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Ozzie's loan for $500,000 has a term of 15 years and a payment of $4,778.26 per month. What is the annual interest rate on this loan?
The annual interest rate on this loan is 4.8%.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Given that,
Principal amount, P = $500,000
Loan term, t = 15 years
Loan payment = $4,778.26 per month
= $57339.12 per year
= $860,086.8 in 15 years
We know that final amount for simple interest is,
A = P(1 + r t)
860,086.8 = 500,000(1 + 15r)
1.7201736 = 1 + 15r
r = 0.04801
r = 4.8%
Hence the annual interest rate is 4.8%.
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Student bring 8 7/8 gallons of lemonade to a picnic They drink 5 2/8 for lunch. then that drink 2 1/8 with a snack How much Lemonade is left
Answer:
1 4/8
or
1 1/2
or
1.5
Step-by-step explanation:
8 7/8 - 5 2/8 - 2 1/8
mark brainliest
Nena is going to ride her bicycle from the
city park to a nearby lake, a distance of
49 miles. She will ride at an average rate
of 14 miles per hour. What is the latest
Nena can leave the park in order to
arrive at the lake at 1:00 PM?
8:30 AM
9:00 AM
9:30 AM
D
10:00 AM
E 10:30 AM
A
B
C
Answer:
To solve this problem, we need to use the concept of distance, rate and time (D = R x T)
We know that the distance is 49 miles and the rate is 14 miles per hour.
We want to find the time T.
We can use the formula D = R x T, to find the time T:
T = D/R = 49 miles / 14 miles/hour = 3.5 hours
So it takes Nena 3.5 hours to ride from the city park to the nearby lake.
Now we know that she needs to arrive at the lake at 1:00 PM, so we have to work out what time she needs to leave the park. We can subtract the time T from the arrival time to find the departure time:
1:00 PM - 3.5 hours = 9:30 AM
Therefore, the latest Nena can leave the park in order to arrive at the lake at 1:00 PM is 9:30 AM
How many yards are in 288in
Answer:
In 288 in there are 8 yd . Which is the same to say that 288 inches is 8 yards. Two hundred eighty-eight inches equals to eight yards.
Step-by-step explanation:
Answer:
There are 8 yards in 288 inches
Step-by-step explanation:
To turn inches into yards you need to convert.
First, turn the inches into feet
1 ft = 12 in
take 288 in and find how many feet there are
288 / 12 = 24 feet
There are 3 feet in 1 yard
take 24 and divide it by 3
24 / 3 = 8 yards
Can I get help with this
The distance between Sam's head and the helicopter is 28.36 m
Step 1: Find the vertical distance travelled by the helicopter in 10 seconds
The vertical distance travelled by the helicopter in 10 seconds = 5 m/sec x 10 sec = 50 m
Step 2: Find the horizontal distance between Sam and the helicopter
We can use the trigonometric relationship, tan 62° = Opposite/Adjacent
Therefore, the horizontal distance between Sam and the helicopter = 50 m/tan 62°
= 50 m/1.8813
= 26.56 m
Step 3: Find the distance between Sam's head and the helicopter
Since Sam is 1.8 m tall, the distance between Sam's head and the helicopter = 26.56 m + 1.8 m
= 28.36 m
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