If the daily prices are $1.50 for children and $2.00 for adults , then the number of adults swam at public pool is 302 and number of children who swam at public pool is 258 .
let the number of children swam at swimming pool be = c ;
let the number of adults swam at swimming pool be = a ;
the total number of person who used the swimming pool is = 560 ;
the equation is ⇒ c + a = 560 ...equation(1) ;
the price for 1 child is $1.50 and price for 1 adult is = $2 ;
the total money collected can be written as :
= (price of children tickets)×(number of children that swam)+(price of adults tickets)×(number of adults that swam) ;
⇒ 1.5c + 2(560 - c) = 991 ;
⇒ 1.5c + 1120 - 2c = 991 ;
⇒ -0.5c = 991 - 1120 ;
⇒ -0.5c = -129 ;
⇒ c = 129/0.5 = 258 ;
So , adults (a) = 560 - 258 = 302 ;
Therefore , the number of adults are 302 and number of children are 258 .
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Find the volume of a cone, to the nearest cubic inch, with a height of 24 in. And diameter of 40 in. Use 3. 14 for pi
The volume of the cone with mentioned dimensions of height and diameter are 10,048 cubic inches.
The volume of come can be calculated by the formula -
V = πr²h/3, where V represents volume of the cone, r represents radius of the cone and h represents height of the cone. Furthermore, radius is half of the diameter. Hence, calculating radius first.
Radius = 40/2
Performing division on Right Hand Side of the equation
Radius = 20 inches
Keep the values in formula of cone to find the volume of the cone
Volume of the cone = (3.14 × 20² × 24)/3
Performing division on Right Hand Side of the equation
Volume of the cone = 3.14 × 20² × 8
Performing multiplication on Right Hand Side of the equation
Volume of the cone = 10,048 inch³
Thus, the volume of cube is 10,048 cubic inches.
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In parallelogram ABCD, AB = 6x-4, CD = 5x + 1, and BC = 2x.
What is the perimeter of ABCD?
D
Perimeter =
A
units
C
B
Answer:
15x-3
Step-by-step explanation:
Recall that parallelograms, as the name implies, have two pairs of parallel sides. In this case, line segments AB and CD are parallel to each other, and then BC and DA are parallel to each other:
Perimeter = AB + BC + CD + DA = (6x-4) + (2x) + (5x+1) + (2x) = 15x - 3
heellllpp guys i will give brainlist
A farmer is tilling his rectangular field. The length of the field is 54 meters and distance
between opposite corners is 90 meters. How wide is the farmer's field?
As per the Pythagoras theorem, the width of the farmer's field is 74.83 meters.
In math the term Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
The general form of the Pythagoras theorem is written as,
=> hypotenuse² = opposite side² + adjacent side²
Here we have know that a farmer is tilling his rectangular field.
Where the known length of the field is 54 meters and distance between opposite corners is 90 meters.
As we all know that here we have here is a triangle.
And then here we need to use Pythagorean Theorem is calculated as,
=> 50² + w² = 90²
When we simplify this one then we get,
=> 2500 + w² = 8100
=> w² = 5600
=> w = 74.83
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A local hamburger hop old a combined total of 491 hamburger and cheeeburger on Friday. There were 59 fewer cheeeburger old than hamburger. How many hamburger were old on Friday?
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
432 hamburgers.
We can write an equation to represent the information given.
Hamburgers + Cheeseburgers = 491
Cheeseburgers = Hamburgers - 59
Substitute the second equation into the first equation:
Hamburgers + (Hamburgers - 59) = 491
Solve for 'Hamburgers':
2Hamburgers - 59 = 491
2Hamburgers = 550
Hamburgers = 275
Since the question asks for the number of hamburgers, the answer is 275 hamburgers.
The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.
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Find a unit vector that has the same direction as the given vector. -3i + 7j
The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
The given vector(v) is -3i+7j
The unit vector is found by dividing the vector by its magnitude
Unit vector of [tex]$v=\frac{v}{\|v\|}$[/tex]
A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.The formula of unit vector in the direction of a given vector is:
Unit Vector = Vector/Vector's magnitudeWe have to find the magnitude first
So,
[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]
[tex]& \|v\|=\sqrt{58}[/tex]
The unit vector is:
The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,
|i| = 1|j| = 1|k| = 1[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]
Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].
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solutions to y<-x and 2x+y>2
The solution to the inequality is (2, -2)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y<-x and 2x+y>2
Express them as equations
So, we have
y = -x and 2x + y = 2
This gives
2x - x = 2
Evaluate
x = 2
Recall that
y = -x
So, we have
y = -2
Hence, the solution is (2, -2)
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find the measures of <X <Y.
The missing interior angles of the hexagon is as follows:
∠X = 135 degrees
∠Y = 135 degrees
How to find the angles in a polygon?The polygon above has 6 sides. Therefore, the polygon is a hexagon. The sum of interior angles of a polygon is ( n − 2 ) × 180°.
where
n = number of sidesThe sum of interior angles in an hexagon is calculated as follows:
180(6 - 2) = 180(4) = 720 degrees
Therefore, the angles of x and y are congruent.
Hence,
let
∠x = ∠y = a
Therefore,
2a + 91 + 149 + 100 + 110 = 720
2a = 720 - 450
2a = 270
a = 270 / 2
a = 135 degrees
Therefore,
∠x = ∠y = 135 degrees.
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a family eats at a restaurant. the bill is $38.00. the family leaves a tip and spends $44.27. how much was the tip as a percentage of the bill?
Answer:
14.16%
Step-by-step explanation:
[tex]=(\frac{44.27-38}{44.27} )(100)=(\frac{6.27}{44.27} )(100)=\frac{627}{44.27} =14.16[/tex]
Hope this helps
Enter the resulting inequality.
11 > −2; Subtract 11 from both sides.
The resulting inequality is
If 11 is Subtracted from both sides, the resulting inequality is 9 > -4
How find the resulting inequality?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
Initially, you have 11 > −2
If you subtract 11 from both sides, you will have:
11 -2 > −2-2
9 > -4
Thus, the resulting inequality will be 9 > -4
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find the rate of change between the points (-1,30) and (-6,10)
Answer:
Step-by-step explanation:
The rate of change, also known as the slope, between two points can be found using the formula:slope = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two points.To find the slope between the points (-1, 30) and (-6, 10), we can plug in the coordinates into the formula:slope = (10 - 30) / (-6 - (-1)) = -20/-5 = 4So the rate of change or the slope between the points (-1,30) and (-6,10) is 4.This means that the y-value of the second point is 4 units lower than the y-value of the first point for every unit you move to the left on the x-axis.
with an average, you add everything up and then divide the total by the number of items you are adding. this gives every number equal weight in the average. but what if you want to weight one item more than others? you will use a weighted average. this can be used, for example, to determine your grade in a class. follow these steps to find the weighted average in the problem below. first, convert each percentage to a decimal. then, multiply each percentage in decimal form by its respective grade. and lastly, add everything up to find the weighted average. for example, emily received a 67 on her first economics exam, which counts for 20% of her grade; an 84 on her second exam, which counts for 30% of her grade; and a 78 on her third exam, which counts for 50% of her grade. what is her weighted average in the class?
Answer:
Based on the weights assigned to these grades, Emily's weighted average in the class would be 77.6 marks.
Somebody help me please with this question!!
an automobile manufacturer claims that their van has a 57.2 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van. after testing 91 vans they found a mean mpg of 56.9 with a standard deviation of 1.8 mpg. is there sufficient evidence at the 0.025 level that the vans underperform the manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.
The null and alternative hypotheses for the above scenario are
H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon
Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon
Given that,
One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level
To find: state the null and alternative hypotheses for the above scenario.
The null and alternative hypotheses for the above scenario are
H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon
Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon
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What is the length of CD when;
C: (-3 , -4)
D: (1 , -2)
CD is about 2.83 in length when C: (-3 , -4) D: (1 , -2) in coordinate geometry.
How is this determined?In coordinate geometry, the distance formula, which is the square root of (x2 - x1)2 + (y2 - y1)2, can be used to determine the length of CD.
In this instance, point C's coordinates are (-3, -4) and point D's coordinates are (1, -2). Using the distance formula with these values as input, we obtain:
√((1 - (-3))^2 + ((-2) - (-4))^2) = √(4 + 4) = √8 = 2.8284271247461903
In simpler terms, you can use the distance formula, which is the square root of the sum of the differences of their x- and y-coordinates squared, to determine the separation between two points in a coordinate plane.
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What is the expanded form for 72 cubed?
Answer:373248
Step-by-step explanation:
72^3 = 373248
D. Ray saved $4 on a shirt that was was originally
$32. What percent was the discount?
Answer: The percent was 12.5%
What is the equation of the following graph? Use equation y = mx + b (picture included)
Selina had been renting for 13 months when there was a flood. The total cost to replace her damaged belongings was $1,960.00. What percent would Selina have saved if she had a renters' insurance policy at a monthly cost of $21.00? Round to the nearest tenth of a percent.
Answer:
13 × 21=293
10/100×293=$29.3
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
When y = 5x the possible outcome of table is 2.8 when x = 4 , 3.88 when x= 7 and 3.33 when x= 4 .
Function range :A function's range can refer to one of two closely related ideas: The function's image is its codomain. Given two sets, X and Y, a function is a binary relation between X and Y if, for every x in X, there is exactly one y in Y that corresponds to f. Take a look at the function y = f(x). The range of the function is the spread of all the y values from the lowest to the highest. Substitute all of x's values into the given expression for y to determine whether it is positive, negative, or equal to other values.
if y=5 x
y= 7 and X = 4 , then
7= 5(4)
7 = 20
= 20/7
= 2.8
when Y =9 and X = 7 then,
9 = 5(7)
9 = 35
35/9
= 3.88
when Y = 6 and X = 4 then,
6= 5(4)
6= 20
20/6
= 3. 33
Missing function of table are 2.88 , 3.88,3.33
What is the range of the function?
The range is (0;+∞). The values are all positive (if a positive number is raised to a power, the result cannot be negative), and the value cannot be zero, so the range is (0;+∞).
Incomplete question :
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
Complete the table for the given rule.
Rule:y=5x
x, y
5,4,2
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A painter is making a mural on the side of a building. In planning this project, he first creates the same painting on a normal sized sheet of paper at a scale of 2 in. to 5 ft. If the width of the paper drawing is 4.9 inches, what will be the width of the mural (in feet) when it is finished?
The width of the mural (in feet) when it is finished is equal to 12.25 feet.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Scale factor = 2/5
For the width of the mural (in feet), we have:
2/5 = 4.9/x
x = (5 × 4.9)/2
x = 24.5/2
x = 12.25 feet.
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a credit card company looking for unusual activity examines the number of transactions on a credit card in each of the last 10 months. these numbers are given below. 10 8 7 9 10 6 8 7 9 9 use a calculator to create a frequency distribution. in how many months have 10 transactions occurred?
10 transactions have occurred in 2 months.
In frequency tables or charts, frequency distributions are displayed. The actual number of observations that fall into each range can be seen in frequency distributions, as well as the proportion of observations that do.
To create a frequency distribution:
Count the number of occurrences for each value (in this case, transactions).
Group the values into ranges (if applicable).
Tabulate the frequency (number of occurrences) for each value or range.
For this set of numbers, the frequency distribution is:
Transactions | Frequency
6 | 1
7 | 2
8 | 2
9 | 3
10 | 2
So, in 10 months, 10 transactions have occurred in 2 months.
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Please Help. I'll give Brainliest
Answer: Number 2
Step-by-step explanation:
Angle 1 + Angle 2 + Angle 3 = 180 degrees because its a straight line, so we immediately eliminate number 1 and 4 (Because it says the angles add up to 270). Next, we look at 2 and 3. 3 is incorrect because with just 1 right angle, QRST might be a rectangle. Therefore, number 2 is correct. :>
hi help pls n thanks
The required domain is x ≥ -4.So option(4) is correct.
What is domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
According to question:From the graph, we can see that curve is starting from -4 to infinity in x direction.
By baby curve method
x ≥ -4
Thus, required domain is x ≥ -4.So option(4) is correct.
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Find the values of the variables for the parallelogram.
Answer:
which parallelogram?
Step-by-step explanation:
repost it and add a pic
The equation y =7400x represents the number of miles, y, that the satellite Space Explorer flies in x hours. Find the rate of change.
If the equation "y = 7400x" represents the number of miles(y) , that satellite space explorer files in x hours , then the rate of change is 7400 miles per hour.
The Rate Of Change is also known as "Slope" ,
The rate of change can be found by taking the derivative of the equation ⇒ y = 7400x with respect to x.
The derivative of the equation "y = 7400x" with respect to x is ;
⇒ dy/dx = d/dx(7400x) = 7400 .
Therefore , rate of change of the equation "y = 7400x" is 7400 miles per hour , that means the satellite explorer files will cover 7400 miles in 1 hour .
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In the figure, ABCD is a square, E is the midpoint of side AD, and F is the midpoint of side BC. The area of the shaded region is
what fraction of the area of square region ABCD?
Answer:
option (D) is the correct one ...
MARK ME AS BRAINLIEST ...How do you solve it WITHOUT using graph paper?
Line A passes through the points (-4, 3) and (-2, -1).
Line B passes through the points (-4, 4) and (-5, 7).
At what point do the lines intersect?
A step by step explanation please!
Answer: To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.
First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.
Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.
So, the slope-intercept form of Line A is y = -2x + 11
We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.
So, the slope-intercept form of Line B is y = 3x + 16
Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:
-2x + 11 = 3x + 16
Subtracting 3x from both sides:
-5x = 5
Dividing both sides by -5:
x = -1
Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:
y = -2(-1) + 11 = -2 + 11 = 9
So the point of intersection of Line A and Line
Step-by-step explanation:
Mrs.Henderson has 16 boys in her class of 24 students. Mr.Gregory has 18 boys in his class of 30. Which class has the greater ratio of boys to student s? Explain
The greater ratio of boys to students in the class of Mrs. Henderson's class is, 0.67
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Mrs. Henderson has 16 boys in her class of 24 students
Mr. Gregory has 18 boys in his class of 30
Greater ratio = ?
Ratio in Mrs. Henderson = number of boys/total students
= 16/24
= 2/3
= 0.67
Ratio in Mrs. Gregory = number of boys/total students
= 18/30
= 3/5
= 0.6
Hence, the ratio is greater in Mrs. Henderson's class 0.67
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X
y
1
17
2
24
3
31
ept of the line represented by the table.
4
38
The slope is of m = 7 and the y-intercept is of b = 10.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the table, when x increases by one, y increases by 7, hence the slope m is given as follows:
m = 7.
Hence:
y = 7x + b.
When x = 1, y = 17, hence the intercept b is given as follows:
7 + b = 17
b = 10.
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