The width of the opening is 2x, which equals 2(4√2) = 8√2 feet. To solve this problem, we'll use the properties of a paraboloid of revolution.
Given that the light source is located 2 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, we have the vertex of the parabola at (0, 2). We also know the focus of the parabola is at the light source, which is at (0, 0).
Since the parabola opens downward, its equation is of the form (x - h)² = -4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus.
In our case, h = 0, k = 2, and p = 2. So the equation becomes x² = -4(2)(y - 2) or x² = -8(y - 2).
At the opening, the paraboloid is 4 feet deep, so y = -2. Substituting this value into the equation, we get:
x² = -8(-2 - 2) => x² = 32
Now, we find the width by solving for x:
x = ±√32 => x = ±4√2
Learn more about depth here:
https://brainly.com/question/13804949
#SPJ11
The width of the opening of the searchlight is 2√32 feet.
To find the width of the opening of the searchlight, we'll first determine the equation of the parabola and then use that to find the width.
Identify the vertex and focus:
The vertex is at the base of the searchlight (0, 0) and the focus is 2 feet from the base along the axis of symmetry,
so it's located at (0, 2).
Determine the equation of the parabola:
Since the parabola opens upward, its equation will be in the form [tex](x-h)^2 = 4p(y-k),[/tex]
where (h, k) is the vertex and p is the distance from the vertex to the focus.
In this case, h = 0, k = 0, and p = 2,
so the equation is [tex]x^2 = 4(2)(y) or x^2 = 8y.[/tex]
Find the width at the depth:
Since the depth of the searchlight is 4 feet, we'll find the width at y = 4. Substitute y = 4 in the equation:
[tex]x^2 = 8(4)[/tex], which gives [tex]x^2 = 32[/tex].
To find the width, we need the distance between the two points where x is positive and negative, so x = ±√32.
Calculate the width of the opening:
The width of the opening is the difference between the positive and negative values of x, which is 2√32.
For similar question on width.
https://brainly.com/question/19819849
#SPJ11
Currently, Jana's grandmother is 5.25 times older than Jana.
Jana's mother is 2.5 times older than Jana. In 3 years, the sum
of all three of their ages will be 149 years. Write and solve an
equation to find Jana's current age. Then find her mother's
and grandmother's current ages.
Step-by-step explanation:
j = jana's age
m = mom's age = 2.5 j
g = grandma's age = 5.25 j summed, they equal 149 IN THREE YEARS
j+3 + 2.5j +3 + 5.25 j + 3 = 149
8.75 j + 9 = 149
8.75 j = 140
j = 16 y/o
mom = 2.5 j = 40 y/o
g-ma = 5.25 j = 84 y/o
when we need to sample because we can't gather information from the entire population, and our population consists of a few clusters which had characteristics very similar to each other but not necessarily other groups, we can use what type of sampling?question 10 options:
If clusters have similar characteristics, it may make sense to use cluster sampling to select a representative sample of population for this study.
In situations where the population is large and it is not feasible to gather information from the entire population.
And where the population can be divided into several subgroups or clusters, stratified sampling or cluster sampling may be used.
However, based on the scenario you have described, cluster sampling seems to be the appropriate sampling method.
Cluster sampling involves dividing the population into smaller groups, or clusters.
Based on some shared characteristic or geographic location, and then selecting a random sample of clusters to survey.
This can be more efficient and cost-effective than selecting individual participants from the entire population.
Learn more about population here
brainly.com/question/31472605
#SPJ4
clerks at mosier data systems key in thousands of insurance records each day for a variety of client firms. samples of the work of 20 clerks are gathered. ceo donna mosier carefully examines 100 records entered by each clerk and counts the number of errors. mosier wants to set control limits to include 99.73% of the random variation in the data entry process. which type of process control chart should she use?
Donna Mosier should use an Individuals control chart to set control limits for the data entry process.
An Individuals control chart is a type of process control chart used to monitor the process when the sample size is one. In this case, Mosier is examining 100 records entered by each of the 20 clerks, making the sample size one.
To set control limits that include 99.73% of the random variation in the data entry process, Mosier can use the following steps:
Calculate the mean and standard deviation of the number of errors for each clerk based on the 100 records examined.Calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) using the formulas: UCL = mean + 3 * standard deviation and LCL = mean - 3 * standard deviation.Plot the individual data points for each clerk on the Individuals control chart, with the UCL and LCL as the upper and lower boundaries, respectively.Monitor the data points over time to detect any trends, shifts, or out-of-control points that may indicate a process issue.By using an Individuals control chart, Mosier can set control limits to monitor the data entry process and detect any issues before they become major problems.
Learn more about control chart
https://brainly.com/question/26478724
#SPJ4
Gina and Joey share a 20-ounce bucket of clay. By the end of the week, Gina has used
3
10
of the bucket, and Joey has used
3
5
of the bucket of clay. How many ounces are left in the bucket
2 ounces of clay left in the bucket.
If Gina has used 3/10 of the bucket, then Joey has used,
1 - 3/10 = 7/10 of the bucket
Similarly, if Joey has used 3/5 of the bucket, then Gina has used,
1 - 3/5 = 2/5 of the bucket
The total amount of clay used by both of them is,
3/10 + 3/5 = 9/10
Therefore, the amount of clay left in the bucket is,
1 - 9/10 = 1/10
Since the bucket contains 20 ounces of clay, the amount of clay left in the bucket is,
(1/10) x 20 ounces = 2 ounces
So, there are 2 ounces of clay left in the bucket.
To learn more about clay here:
https://brainly.com/question/23857396
#SPJ4
20. The wallpaper border that runs all the way around a room is 5f² +19f+ 11 long. Three sides of the room have the following lengths of border: 6f, 5f-7, 2f^2+2. What is the length of the fourth side of the room?
In linear equation, 3f² + 8f + 16 feet is the length of the fourth side of the room.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
= 5f² + 19f + 11 - 6f - 5f + 7 - 2f² - 2
= 3f² + 8f + 16 feet
Learn more about Linear equation
brainly.com/question/11897796
#SPJ1
The expression that represent the length of the fourth side of the room is [tex]3f^2 + 8f + 16[/tex].
What is expression ?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here Total length of the room = [tex]5f^2+19f+11[/tex]
Three sides length of the room = 6f , 5f-8 and [tex]2f^2+2[/tex]
Fourth side = Total length - sum of length of three sides
=> [tex]5f^2+19f+11-(6f+5f-7+2f^2+2)[/tex]
=> [tex]5f^2+ 19f + 11 - 6f - 5f + 7 - 2f^2 - 2[/tex]
=> [tex]3f^2 + 8f + 16[/tex] .
The expression that represent the length of the fourth side of the room is [tex]3f^2 + 8f + 16[/tex].
To learn more about expression refer the below link
https://brainly.com/question/112703
#SPJ1
What it the mediam of 1 3 1 3 1 7 4 5 7
Answer: 1
Step-by-step explanation: It is the middle of the sequence, so you basically count until you find the middle
In ABC, m A= 62° and mB=39⁰.
In XYZ, m Y=39° and m Z=79⁰.
Include in Your Answer:
What is mC?
What is mX?
• Is it possible for these two triangles to be similar? Why or
why not?
Please answer this geometry question
The value of cos ( 90 - x ), given the side lengths of the right triangle would be B. 3 / 5.
How to find the value of the cosine ?In a right triangle, the sum of the two acute angles is always 90 degrees. If we have a right triangle with side lengths 3, 4, and 5, then it's a 3-4-5 Pythagorean triple, which means the angles are also in a specific ratio.
Now, we want to find cos(90 - x). Since the sum of the two acute angles in a right triangle is 90 degrees, the other angle in the triangle is (90 - x). We know that sin x = opposite / hypotenuse, so in our triangle, sin(90 - x) = 3/5.
The sine and cosine of complementary angles are related by the co-function identity:
cos(90 - x) = sin x
So, cos(90 - x) = sin(90 - x) = 3/5.
The answer is 3/5.
Find out more on cosine at https://brainly.com/question/28662065
#SPJ1
HELP!! View image! THANK U
The probability of selecting no Independents is $\frac{{7 \choose 2} + {8 \choose 2}}{{20 \choose 2}} = \frac{91}{190} \approx 0.4789$.
please help! and explain and show work of how you got the answer. I will mark you brainliest.
Answer: i dont know if this is right but i put a^4+b^4=c^4
Step-by-step explanation:
I have no idea tho
I need some help bro
Answer:
first answer is correct
y = -1/2 x^2 + x + 1
Step-by-step explanation:
based on the graph, you can find two points
(2,1) and (0,1)
I input (2, 1) to each equation to check
y = -1/2 x^2 + x + 1 is correct
Find H. C. F of each set of number using long division method 80,215,245and720
The H. C. F of 80,215,245 and 720 using long division method is 5.
The long division method to find the Highest Common Factor (H.C.F.) of 80, 215, 245, and 720.
Divide the largest number by the smallest number.
720 ÷ 80 = 9 with a remainder of 0
Divide the smallest number by the remainder from the previous step.
80 ÷ 40 = 2 with a remainder of 0
Divide the remainder from the previous step by the next smallest number.
40 ÷ 5 = 8 with a remainder of 0
Divide the remainder from the previous step by the next smallest number.
5 ÷ 5 = 1 with a remainder of 0
We have reached a remainder of 0, which means that 5 is the H.C.F. of the given numbers.
Therefore, the H.C.F. of 80, 215, 245, and 720 is 5.
We can also verify this by listing the factors of each number and finding the common factors:
80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
215: 1, 5, 43, 215
245: 1, 5, 7, 35, 49, 245
720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The common factors are 1, 5, and 40.
The largest common factor is 5, which is the same as what we obtained using the long division method.
For similar question on H.C.F. :
https://brainly.com/question/21504246
#SPJ11
how would the baked loaves be different if you increased the shortening in the french bread formula (p. 135) to 7%?
Increasing the shortening in the French bread formula to 7% would result in a softer and more tender crumb due to the added fat.
French bread is typically made with a small amount of fat, such as butter or oil, to enhance its flavor and texture. However, increasing the shortening to 7% would significantly increase the amount of fat in the formula, which would have several effects on the final product.
Firstly, the added fat would make the dough more extensible, resulting in a softer and more tender crumb. This is because the fat coats the gluten strands in the dough, reducing their ability to form a strong network and resulting in a more open and airy crumb.
Additionally, the added fat would also make the crust softer and less crispy. This is because the fat prevents the crust from drying out and developing a hard, crispy texture.
Learn more about french bread
https://brainly.com/question/8613013
#SPJ4
a circle has a radius of 5 centimeters. what is the radian meausre of the center angle coresponding to the arc length of 10 centimeters
The radian measure of the center angle corresponding to the arc length of 10 centimeters is 2 radians.
Describe Arc?An arc is a segment of a curve or a curved line that is a part of a circle, an ellipse, or any other curved shape. In geometry, arcs are important because they define a portion of the circumference of a circle or an ellipse.
An arc is defined by two endpoints on the curve and the points on the curve between the endpoints. The length of an arc is measured as the distance along the curve between the two endpoints. The measure of an arc is often expressed in terms of degrees or radians.
In a circle, an arc is a part of the circumference of the circle, and it is named based on the two endpoints of the arc. For example, if AB is an arc of a circle with endpoints A and B, then it can be denoted as arc AB or arc BA.
An arc can be measured in terms of its central angle, which is the angle formed by the two radii that define the endpoints of the arc and the center of the circle. The measure of the central angle of an arc is directly proportional to the length of the arc. In other words, if two arcs have central angles that are equal, then their lengths are also equal.
The radian measure of the center angle corresponding to an arc length of a circle is given by the formula:
θ = s/r
where θ is the radian measure of the center angle, s is the length of the arc, and r is the radius of the circle.
In this case, the radius of the circle is given as 5 centimeters, and the length of the arc is given as 10 centimeters. Substituting these values into the formula, we get:
θ = 10/5 = 2 radians
Therefore, the radian measure of the center angle corresponding to the arc length of 10 centimeters is 2 radians.
To know more about radian visit:
https://brainly.com/question/27025090
#SPJ1
triple the difference of c and b, then subtract the result from a
Therefore, if you triple the difference of c and b (which is 2), and then subtract the result from a (which is 10), you get the answer of 4.
The mathematical expression for "triple the difference of c and b, then subtract the result from a" is:
a - 3(c - b)
In this expression, "c" and "b" are variables representing numerical values, and "a" is another variable representing a numerical value.
To evaluate this expression, you would need to substitute specific numerical values for "a", "b", and "c". For example, if a = 10, b = 5, and c = 7, then the expression would become:
10 - 3(7 - 5) = 10 - 6 = 4
Therefore, if you triple the difference of c and b (which is 2), and then subtract the result from a (which is 10), you get the answer of 4.
To know more about subtract, visit:
https://brainly.com/question/1927340
#SPJ1
What are the domain and range of this exponential function?y=2x–9
The value of both domain and range of this exponential function is (−∞,∞).
y = 2x-9
The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).
The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).
Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).
To learn more about domain and range;
https://brainly.com/question/1045262
A rectangular prism has a volume of 180 cubic inches. How many 1/3 inch cubes fit inside?
The no of rectangular prism that fit perfectly in the system is 540.
What is prism?A rectangular prism is a three-dimensional solid object that has six rectangular faces. It is also known as a rectangular parallelepiped. The rectangular prism is characterized by its length, width, and height, which are also called its dimensions.
According to the given information:The volume of a rectangular prism can be calculated by multiplying its length, width, and height. The formula for the volume of a rectangular prism is:
Volume = length x width x height
The surface area of a rectangular prism can be calculated by adding the areas of all its faces. The formula for the surface area of a rectangular prism is:
Surface area = 2(length x width) + 2(length x height) + 2(width x height)
Rectangular prisms are commonly used in geometry and in real-world applications, such as in architecture, engineering, and manufacturing. They can be used to represent buildings, boxes, containers, and other objects with rectangular shapes.
Given, a rectangular prism has a volume of 180 cubic inches.
To find how many 1/3 inch cubes fit inside we have that,
180/(1/3)
540/1
540
Hence the no of cube fit inside is 540.
To know more about prism visit:
https://brainly.com/question/29722724
#SPJ1
Solve the equation
2x/3+1=7x/15+3
The answer is X = 10
⇒ Given [tex]\frac{2x}{3} + 1 = \frac{7x}{15} + 3[/tex]
⇒ [tex]\frac{2x+3}{3} = \frac{7x+45}{15}[/tex]
⇒ 15(2x + 3) = 3(7x + 45)
⇒ 30x + 45 = 21x + 135
⇒ 30x - 21x = 135 - 45
⇒ 9x = 90
⇒ x = [tex]\frac{90}{9}[/tex]
⇒ Therefore X = 10
To know more about Solving Equations : https://brainly.com/question/29011747
patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. assume the time that patients wait is exponentially distributed. what is the probability a randomly selected patient will see the doctor within eleven minutes of the scheduled time?
The probability is approximately 0.446 or 44.6%.
Waiting time is exponentially distributed, we can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem.
Let X be the waiting time in minutes.
X is exponentially distributed with a mean of 8 minutes.
The rate parameter λ is equal to 1/8.
The CDF of the exponential distribution is given by:
[tex]F(x) = 1 - e^(-\lambda x)[/tex]
The probability that a patient will see the doctor within eleven minutes of the scheduled time.
The value of F(11) - F(0).
[tex]F(11) = 1 - e^(-\lambda \times 11) = 1 - e^(-11/8)[/tex] ≈ 0.554
[tex]F(0) = 1 - e^(-\lambda \times 0) = 1 - e^0 = 1[/tex]
Therefore, the probability that a randomly selected patient will see the doctor within eleven minutes of the scheduled time is:
F(11) - F(0) ≈ 0.554 - 1 ≈ 0.446
For similar questions on probability
https://brainly.com/question/24756209
#SPJ11
An object moving at speed s for time t travels distance st. The Brown family is taking a road trip. This morning, they drove for 2. 5 hours at a speed of 65 miles per hour. How far did the family drive this morning?
Write your answer as a whole number or decimal
The total distance Brown family drove this morning at the speed of 65 miles per hour in 2.5 hours is equal to 162.5 miles.
Let 's' represents the speed of the moving object.
And 't' represents the time to cover distance.
The speed was 65 miles per hour.
And the time they drove was 2.5 hours.
The distance the Brown family drove this morning
= Multiplying their speed by the time they drove.
This implies,
distance = speed x time
Substitute the values we have,
The distance they drove this morning is equal to,
⇒ distance = 65 miles per hour x 2.5 hours
⇒ distance = 162.5 miles
Therefore, the distance drove by Brown family this morning is 162.5 miles at the speed of 65 miles per hour.
learn more about speed here
brainly.com/question/29801696
#SPJ4
Label the net for the cylinder. Then find the surface area of the cylinder. Give your answer in terms of π and as a decimal number rounded to the nearest tenth.
The surface area of the cylinder is approximately 94.2 ft².
What is surface area?Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.
According to the given information:
The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.
The formula for the lateral surface area of a cylinder is given:
Lateral Surface Area = 2πrh
where r is the radius of the cylinder and h is the height of the cylinder.
Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:
Lateral Surface Area = 2π * 3 * 2 = 12π ft²
The formula for the area of a circle (which represents the bases of the cylinder) is given:
Circle Area = πr²
Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:
Circle Area = π * 3² = 9π ft²
Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:
2 * Circle Area = 2 * 9π = 18π ft²
Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:
Total Surface Area = Lateral Surface Area + 2 * Circle Area
= 12π + 18π
= 30π ft²
As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²
To know more about surface area visit: https://brainly.com/question/22074027
#SPJ1
Jaxon made 5% of his free throws over the season. If he shot 220 free throws, how many did he make?
Answer:
Jaxon made 11 free throws over the season.
Step-by-step explanation:
If he made 5% of his free throws, we know that he will make 5% of the total number of free throws he took, which is 220:
We multiply 220 by 0.05, or 5% to find out how many free throws he made:
220*0.05 = 11
After that, we now know that Jaxon made 11 of his free throws out of 220 over the course of the season, or 5%.
Your friend incorrectly factors the expression below as 7x(5-2xy). Factor the expression below correctly. What error did your friend make?
35x - 14xy
Answer:
The answer is 7x(5-2y)
Step-by-step explanation:
35x-14xy
7x(5-2y)
the error made is the x in the bracket
Explain why the value of 0.6 is greater than the value of 0.39.
Answer:
B
Step-by-step explanation:
The value of 0.6 is greater than the value of 0.39 because 0.6 represents a larger proportion or fraction of a whole than 0.39 does.
To compare these two values, we can think of them as parts of a whole. For example, we can consider 0.6 as 60% of a whole and 0.39 as 39% of the same whole. When we compare 60% and 39%, it is clear that 60% is greater than 39%.
Another way to compare these two values is to convert them to fractions. 0.6 can be written as 6/10 or 3/5, while 0.39 can be written as 39/100.
When we compare 6/10 and 39/100, we can see that 6/10 is greater than 39/100 because 6/10 represents 6 parts out of 10, while 39/100 represents 39 parts out of 100.
Therefore, we can conclude that the value of 0.6 is greater than the value of 0.39 because it represents a larger proportion or fraction of a whole.
WILL MARK AS BRAINLEIST!!
Question in picture!!
The area of the region R is 4/3 square unit, while the value of c is 2 - √3.
Showing working for the area of region
To find the value of c for which the two subregions have the same area, we need to first find the points of intersection of the given curves.
Setting y = 2x - x^2 = 0, we get x = 0 and x = 2. So the curves intersect at the points (0,0) and (2,0).
Now, we can set up the integral to find the area of the region R:
A = ∫[0,2] (2x - x^2) dx
A = [x^2 - (x^3/3)]|[0,2]
A = (4/3) square units
Next, we need to find the value of c for which the two subregions of R have the same area. Let (a, 2a - a^2) be the point where the line y = cx intersects the curve y = 2x - x^2.
So we have:
2a - a^2 = ca
Rearranging, we get:
a^2 - 2a + c = 0
Using the quadratic formula, we get:
a = (2 ± √(4 - 4c))/2 = 1 ± √(1 - c)
Since a > 0, we must choose the positive root.
Now, we can set up the integrals to find the areas of the two subregions of R:
A1 = ∫[0,a] (2x - x^2 - cx) dx
A2 = ∫[a,2] (2x - x^2 - cx) dx
Setting A1 = A2, we get:
∫[0,a] (2x - x^2 - cx) dx = ∫[a,2] (2x - x^2 - cx) dx
Solving for c, we get:
c = (2a - a^2)/(2a - 2)
Substituting a = 1 + √(1 - c), we get:
c = 2 - √3
Therefore, the value of c for which the two subregions of R have the same area is 2 - √3.
Learn more about area of regions here:
https://brainly.com/question/31377501
#SPJ1
What is the solution of
x²-1/x^2+5X+4 ≤0?
O4
O x <-4 or x ≥1
O x <-4 or x>-1
O4
Answer:
use desmos or they work pretty well
The solution of the inequality is -4<x≤1 where x≠-1
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is x²-1/x²+5x+4 ≤0
Let us factor the terms in inequality to find the solution
(x+1)(x-1)/(x+1)(x+4) ≤0
(x-1)/(x+4) ≤0
Find the critical values where the inequality changes sign
Interval 1: x < -4
Interval 2: -4 < x < 1
Interval 3: x > 1
Test each interval to see where the inequality is true or false
For interval 1, we can choose x = -5 as a test point:
(x-1)/(x+4) = (-5-1)/(-5+4) = -6 < 0
Since the inequality is true for x = -5, it is also true for all x < -4.
For interval 2, we can choose x = 0 as a test point:
(x-1)/(x+4) = (0-1)/(0+4) = -1/4 < 0
Since the inequality is true for x = 0, it is also true for all -4 < x < 1.
For interval 3, we can choose x = 2 as a test point:
(x-1)/(x+4) = (2-1)/(2+4) = 1/6 > 0
Since the inequality is false for x = 2, it is also false for all x > 1.
Combine the intervals where the inequality is true -4<x≤1 where x≠-1 is the solution
Hence, the solution of the inequality is -4<x≤1 where x≠-1
To learn more on Inequalities click:
https://brainly.com/question/28823603
#SPJ5
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 13 people took the trip. She was able to purchase coach tickets for $380
and first class tickets for $1200. She used her total budget for airfare for the trip, which was $9040. How many first class tickets did she buy? How many coach tickets did she buy?
number of first class tickets bought=
Answer: Sarah bought 5 first class tickets and (13-5) = 8 coach tickets.
Step-by-step explanation: The taken a toll of one to begin with lesson ticket is $1200 and the fetched of one coach ticket is $380.
So, the full taken a toll of first class tickets would be 1200x and the entire cost of coach tickets would be 380(13-x) = 4940 - 380x.
The overall fetched of the tickets is given as $9040, so we will set up the taking after condition:
1200x + 4940 - 380x = 9040
Streamlining and tackling for x, we get:
820x = 4100
x = 5
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.
C′(−10.5, 1)
C′(−10.5, 3.5)
C′(−3, 3.5)
C′(−10.5, −3.5)
Answer:
To dilate a triangle using a scale factor of 3.5, we multiply the distance between each vertex and the center of dilation (in this case, the origin) by 3.5.
Using this information, we can find the coordinates of each vertex of triangle A'B'C':
A' = (43.5, 33.5) = (14, 10.5)
B' = (33.5, -23.5) = (10.5, -7)
C' = (-33.5, 13.5) = (-10.5, 3.5)
Therefore, the vertex of point C' is (-10.5, 3.5).
So the correct answer is C′(−10.5, 3.5).
lee had scored the following points in his first 8 games 12,14,14,15,8,10,3,15 enter the number of points lee needs to score in the nest game to increase his keam score to 13 points
Lee needs to score a total of 26 points in the next game to increase his mean score to 13 points.
Calculating the score in the next gameGiven that
Scores = 12,14,14,15,8,10,3,15
To increase his mean score to 13 points,
Lee needs to have a total of 13 x 9 = 117 points after the next game.
He has already scored a total of 12+14+14+15+8+10+3+15 = 91 points in the first 8 games.
Therefore, Lee needs to score a total of 117 - 91 = 26 points in the next game to increase his mean score to 13 points.
Read more about mean at
https://brainly.com/question/14532771
#SPJ1
A city's yearly snowfall in inches over the last 5 years is recorded.
What is the mean of the snowfall in the last 5 years and how can it be interpreted?
Responses:
A mean of 25 shows that the data values are relatively close together. It represents that typically the city's snowfall has been about 25 inches yearly the last 5 years.
A mean of 25 shows that the data values are spread out. It represents that the city's snowfall has been exactly 25 inches each year for the last 5 years.
A mean of 27.2 shows that the data values are relatively close together. It represents that typically the city's snowfall has been about 27.2 inches yearly the last 5 years.
A mean of 27.2 shows that the data values are spread out. It represents that the city's snowfall has been exactly 27.2 inches each year for the last 5 years.
Year Snowfall (inches)
2015 25
2016 27
2017 25
2018 29
2019 30
Answer:
A mean of 27.2 shows that the data values are relatively close together. It represents that typically the city's snowfall has been about 27.2 inches yearly over the last 5 years.
Step-by-step explanation:
The mean, also known as the average, is the sum of all the data values divided by the number of data points. In this case, the mean of 27.2 inches indicates that, on average, the city has experienced a snowfall of approximately 27.2 inches per year over the last 5 years. The fact that the mean is close to the individual values of 25, 27, 25, 29, and 30 inches suggests that the data points are relatively close together and do not deviate significantly from the mean, indicating that the snowfall in the city has been relatively consistent over the past 5 years.