Your math teacher tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 2 points each and word problems are worth 5 points. How many of each type of question are there?
Answers
x isthe number of multiple choice questions, and y is the number of word problems, we can write a system of equations like:
{ x + y = 38
{ 2x + 5y = 100
If we multiply the first equation by -2 we get:
{ -2x-2y = -76
{ 2x + 5y = 100
Now if we add both equations we get only equation with 1 unknown (y) :
3y = 24 ⇒ y = 8
Substituting the calculated value to the first equation we get:
x + 8 = 38 ⇒ x = 30
The solution:
{ x = 30
{ y = 8
means that:
The test had 30 multiple choice questions, and 8 word problems.
Related Questions
in one year a company found 9 defective parts out of 4500 parts picked for testing
Answers
Answer:
hdhdhdjdmkdjddbgdgdhdjoudhnskshgebdlejdbdhjdjdjdk
As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3.
How many squares should he use for the sixth stage?
Answers
Answer:
15 square for six stage
Answer:
21
Step-by-step explanation:
stage 1: 1
stage 2: 3
stage 3: 6
the pattern is that the number of squares increases everytime by the stage number it is. for example stage 2 has 3 squares. to find stage 3 you start off with 3 squares (from stage 2), and add the stage number (stage 3). 3+3=6 so stage 3 has 6 squares.
stage 4: 10 (6+4)
stage 5: 15 (10+5)
stage 6: 21 (15+6)
What the answer fast
Answers
Answer:
∠CDE
Step-by-step explanation:
Name it by the order of the letters with the point of the angle in the middle
2. The box and whisker plot below shows the starting salaries for 120 graduates of a small college.
a) What is the range of the starting salaries?
b) About 30 graduates make below what amount?
c) How many graduates have a salary above $33,000 ?
d) $25 of the graduates make above what amount?
Answers
The range of the starting salaries is 53,000
Given,
The box and whisker plot below shows the starting salaries
The number of graduates in a small college = 120
We have to find the range of the starting salaries;
Range of a data;
The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
Here,
Lowest value = 19,000
Highest value = 72,000
Then,
Range of the set = 72,000 - 19,000 = 53,000
That is,
The range of the given data set is 53,000
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I would appreciate if someone could solve this problem and explain it :)
Ps. I will give a brainless also :)
Answers
Answer:
Step-by-step explanation:
Givens
C is the midpoint of AE
D is the midpoint of BE
DC is given as 46
Remark
Triangle CED is similar to AEB by SAS for similarity
Therefore DC is 1/2 the size of AB
Solution
1/2 AB = DC
1/2 AB = 46 Multiply both sides by 2
AB = 2*46
AB = 92
write an equation in point-slope form for the line through the given point with the given slope
(10,-9)m is -2
Answers
Answer:
Step-by-step explanation:
Point: 10,-9
k=-2
y=-2x+b
So: 9, -7
8,-5
7,-3
6,-1
5,1
4,3
3,5
2,7
1,9
0,11
y=-2x+11
Answer:
y + 9 = - 2(x - 10)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 2 and (a, b ) = (10, - 9 ) , then
y - (- 9) = - 2(x - 10) , that is
y + 9 = - 2(x - 10)
Write the ratio 3/5 to 6 as a fraction in simplest form
Answers
Answer:
1/10
Step-by-step explanation:
To convert a ratio to a fraction, you divide the number on the left by the number on the right. This gets you (3/5)/6. When dividing fractions by whole numbers, you need to convert the whole number to a fraction. I converted 6 to 6/1, so that gave me (3/5)/(6/1). You then multiply the top number by the bottom number to get the numerator of the answer, and the middle 2 numbers multiplied is the denominator. The answer is (3x1)/(5x6), or 3/30, which can be simplified to 1/10.
A suspect of a crime is traveling on 26th Street toward Cherry Street. The diagram shows the locations of the suspect and a police officer. Your friend says that the officer should wait at point C to intercept the suspect because the officer will have the same distance to travel no matter which route the suspect takes. Is your friend correct? Explain.
Answers
AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.
What is the Angle Bisector Theorem?According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.
In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.
Therefore, we can conclude as saying:
C. NO, you cannot use the angle bisector theorem to determine that AC = CE.
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The average horse requires 0.0333 Megacalories (Mcal) each day for every kilogram (kg) it weighs. If your horse weights 678 kg, and the food you are buying provides 810 kcal per pound of food, how many pounds of food do you need each day for your horse?
Use the following facts:
1000 kcal = 1 Mcal
1 pound food = 810 kcal
0.0333 Mcal = 1 kg horse
Round to the nearest whole number.
Answers
On solving the provided question, we can say that Therefore, you would need multiply approximately 27.84 pounds of food each day for your horse.
what is multiplyOne of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."
First, we need to convert the weight of the horse from kilograms to pounds, so:
678 kg x 2.20462 lbs/kg = 1495.69 lbs
Next, we need to calculate how many Mcal the horse needs per day:
0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day
Then, we can convert the Mcal to kcal:
22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day
Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:
22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day
Therefore, you would need approximately 27.84 pounds of food each day for your horse.
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A(-3,-2), B(12, 3); 3 to 2
Answers
Answer:
(6, 1)
Step-by-step explanation:
The formula for dividing segment AB into parts in the ratio M:N is ...
P = (M·B +N·A)/(M+N)
ApplicationUsing the above formula with the given values, we have ...
P = (3(12, 3) +2(-3, -2))/5 = (36 -6, 9 -4)/5 = (30, 5)/5
P = (6, 1)
The point P that divides segment AB into parts in the proportion 3:2 is ...
P = (6, 1)
Please answer this correctly without making mistakes
Answers
Answer:
3 1/4
Step-by-step explanation:
Hey there!
Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,
CO = CW - OW
CO = 8 3/4 - 5 1/2
Make the denominators the same,
5 1/2
improper
11/2
*2
22/4
Proper
5 2/4
8 3/4 - 5 2/4
3 1/4 miles
Hope this helps :)
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
I wills send you a picture
Answers
Draw the tank
we can use the formula of the volume of a cylinder
\(V=\pi\times r^2\times h\)we can repalce the value of the volume (320pi) and the height
\(\begin{gathered} 320\pi=\pi\times r^2\times20 \\ 320\pi=20r^2\pi \end{gathered}\)now solve for r^2 dividing 20pi on both sides
\(\begin{gathered} \frac{320\pi}{20\pi}=r^2 \\ \\ r^2=16 \\ \end{gathered}\)and solve for r using roots
\(\begin{gathered} r=\sqrt[]{16} \\ \\ r=4 \end{gathered}\)the value of the radious is 4ft and the diameter double, then
\(\begin{gathered} d=2\times4 \\ d=8 \end{gathered}\)diameter of the cylinder is 8 ft then rigth option is C
Fidgets cost $3 each and Pop Its cost $4 each. If you buy a total of 20 Fidgets and Pop
Its for $75, which system of equations could you use to determine how many of each
you bought? Let x represent the number of fidgets you bought and y represent the
number of pop its you bought.
Answers
The number of fidgets and pop bought was 15 each
How to determine the equationFrom the information given, we have that;
1 fidget costs $3
1 Pop cost $4
Let the number of Fidgets be x
Let the number of Pop be y
Then, we have that a total of 20 fidgets and Pop cots $75
We have that;
20x + y = 75
Now, substitute the value of x as 3, we get;
20(3) + y= 75
expand the bracket
y = 75 - 60
y = 15
The number of fidgets is expressed as;
20x/4 = 20(3) /4 = 15
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which of the following lines is perpendicular to the line Y=-3x+2 and passes through the point (-2,8)
Answers
Given the equation of the line:
y = 3x + 2
The perpendicular line passes through the point: (-2, 8)
Let's find the equatrion of the perpendicular line.
The slope of a perpendicular line is the negative reciprocal of the slope of the original line.
Apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
y = -3x + 2
The slope here is -3
Therefore, the slope of the perependicular line is the negative reciprocal of -3.
We have:
\(\begin{gathered} m_1m_2=-1 \\ \\ m_2=-\frac{1}{m_1} \\ \\ m_2=-\frac{1}{-3} \\ \\ m_2=\frac{1}{3} \end{gathered}\)The slope of the perpendicular line is ⅓.
From the slope-intercept form, substitute ⅓ for m:
y = mx + b
\(y=\frac{1}{3}x+b\)To find the value of the y-intercept, b, substitute the points (x, y) ==> (-2, 8) for x and y respectively:
\(\begin{gathered} 8=\frac{1}{3}(-2)+b \\ \\ 8=-\frac{2}{3}+b \\ \\ \end{gathered}\)Multiply all terms by 3:
\(\begin{gathered} 8(3)=-\frac{2}{3}(3)+3b \\ \\ 24=-2+3b \end{gathered}\)Add 2 to both sides:
\(\begin{gathered} 24+2=-2+2+3b \\ \\ 26=3b \end{gathered}\)Divide both sides by 3:
\(\begin{gathered} \frac{26}{3}=\frac{3b}{3} \\ \\ \frac{26}{3}=b \\ \\ b=\frac{26}{3} \end{gathered}\)Therefore, the equation of the perpendicular line is:
\(y=\frac{1}{3}x+\frac{26}{3}\)ANSWER:
\(y=\frac{1}{3}x+\frac{26}{3}\)Please help me fast!!!!. Joe and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and shop on Michigan Avenue before their dinner reservations at 5:10 P.M. They plan to spend 1 hour and 10 minutes at the Willis Tower, 3 hours and 10 minutes at Navy Pier, and 1 hour and 15 minutes shopping. What is the latest time Joe's family can start their tour of Chicago and still make it to dinner on time?
Include A.M. or P.M. in your answer.
Answers
Answer:
1:35 pm
Step-by-step explanation:
Given that:
Chicago tour schedule :
Willis tower = 1 hour 10 minutes
Navy piers = 3 hours 10 minutes
Shopping = 1 hour 15 minutes
(1 hour 10 min) + (3 hour 10 minutes) + (1 hour 15 minutes)
Total touring time in Chicago = 4 hours 35 minutes
Dinner time is slated at 5:10 pm
Latest time to start tour :
5:10 pm - 4 hours 35 minutes = 1 :35 pm
Suppose y varies directly with x. When x is 5, y is 15. What is y when x is 12?
Answers
Answer:
y = 36
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition when x = 5 , y = 15
15 = 5k ( divide both sides by 5 )
3 = k
y = 3x ← equation of variation
when x = 12 , then
y = 3 × 12 = 36
Question 1(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 10 + 20x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
Question 2(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
Question 3(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
Question 4(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 120
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 120
Question 6(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Answers
Step-by-step explanation:
and a line going from the point 0 comma 100 )
Which graph represents the equation
graph of a line passing through the points negative
two trains leave the station at the same time, one traveling due east, the other due west. After 46 minutes, they are 140 miles apart. if one trains speed is 20 mph more than the other trains, what are the speeds of the two trains?
Answers
Answer:
Train A speed = x + 20
Train B = x
We know the 46 minutes is 23/30 of an hour.
Use D = rt
Take it from it, hope its helped, have a great day!
The volume of a rectangular prism is 5,890.625 cm3. If the height is 14.5 cm and the length is 25 cm, what is the value of the width?
Answers
Answer:
Step-by-step explanation:
The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
We know that V = 5,890.625 cm^3, h = 14.5 cm, and l = 25 cm.
Substituting these values into the formula, we get:
5,890.625 = 25w(14.5)
5,890.625 = 362.5w
w = 16.25
Therefore, the width of the rectangular prism is 16.25 cm.
Answer:
It's A
Step-by-step explanation:
well all you have to do is divide like 5,890.625 dvided by 14.5 then divide again by 25 them bam you got 16.25
Represent each expression as a power of a, a cannot be equal to 0
Answers
Answer:
a^-27
Step-by-step explanation:
(a^3)^-3)^3)
(a^-9)^3)
a^-27
When we represent the expression ((a³)⁻³)³ as a power of a, the result obtained is a⁻²⁷
How to represent the expression as a power of a?The following data were obtained from the question:
Expression: ((a³)⁻³)³Representation as power of a =?We can represent the expression ((a³)⁻³)³ as a power of a by using the power law of indices as illustrated below:
((a³)⁻³)³
Recall
(Bᵐ)ⁿ = Bᵐⁿ (i.e multiply the power)
Thus,
((a³)⁻³)³ = (a⁻⁹)³
= a⁻²⁷
Thus, we can conclude from the above calculation that the representation of the expression ((a³)⁻³)³ as a power of a is a⁻²⁷
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At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year.
The average was a gain of µ = 15 pounds with a standard deviation of
= 6. The distribution of scores was approximately normal.
A sample of n = 4 students is selected, and the average weight change is computed for the sample.
What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p (M > 10) (four decimals)
Answers
The probability that the sample mean weight change is greater than 10 pounds is p(M > 10) = 0.9088.
What is the probability?To find the probability that the sample mean will be greater than M = 10 pounds, we need to standardize the sample mean using the formula for z-score:
z = (M - µ) / (σ / √n)
Substituting the given values, we get:
z = (10 - 15) / (6 / √4)
z = -1.33
Using a standard normal distribution table or calculator, we can find the probability that z is greater than -1.33, which is approximately 0.9088.
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Solve this expression: (2-i)(-3+i)
Answers
Answer:
-5+5i
Step-by-step explanation:
Answer:
D on edge
Step-by-step explanation:
-5+5i
At what point(s) does the parabola, y=x2−2, intersect the line, y=−x?
Answers
C. (-2, 2) and (1, -1)
What is the intersection of two graphs?Since the point of intersection is the sole location where the two graphs come together, the coordinates of that location provide the answer to the equations involving the two variables. There are no solutions when the graphs are in parallel.
Given, the parabola Y = X² -2 and a line Y = -X. To find the intersection points of this graph we need to compare these equations.
Let's put the value of y in equation 1
- X = X² - 2
X² + X - 2 = 0
The factor of this quadratic equation is -2 and 1. Therefore the coordinate in which both graphs will intersect is (-2, 2) and (1, -1). I am attaching an image for better understanding.
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I need help with this math problem
Answers
Answer: A) (x + 12) and (x + 9)
Step-by-step explanation:
You need to get x^2 + 21x + 108.
A) (x + 12) (x + 9) = x^2 + 12x + 9x + 108 = x^2 + 21x + 108
B) (x - 12) (x - 9) = x^2 - 9x - 12x + 108 = x^2 -21x + 108
C) (x - 27) (x - 4) = x^2 - 4x - 27x + 108 = x^2 - 31x + 108
D) (x + 27) (x + 4) = x^2 + 27x + 4x + 31 = x^2 + 31x + 31
So, the answer is A).
Has anyone done the inverse functions mastery text on edmentum it’s super hard stuck on this question and the pictures wont help
Answers
Part C: Mr. Chin wants to add a rectangular desk that is 7 feet wide by 5 feet long. He says
he has enough space in the reading room to add the desk. Do you agree with Mr. Chin's
conjecture? Why or why not? Explain.
Answers
Not agree with the Mr. Chin's conjecture, because there may be space for the desk in the room but Mr. Chin not have the actual measurement, it may or may not fit the desk in room of given length and width.
What is conjecture?A good guess or an idea about a pattern is a conjecture. Speculate (about something) We can only speculate about the killer's thoughts. speculate that... He speculated that the population might double within a decade. speculate about something She speculated about the existence of a brand-new species.
A mathematical assertion that has not yet been thoroughly established is known as a conjecture. When one observes a pattern that is consistent across many cases, speculations result. However, just because a pattern applies to a lot of cases does not mean that it applies to all of them. To fully accept the mathematical observation, conjectures must be demonstrated. A theorem is formed when a conjecture is thoroughly demonstrated.
A crucial step in solving a problem is making a guess; It's more than just a tool for professionals in math. It is extremely uncommon for a problem's solution to be immediately apparent in everyday problem solving. Instead, the process of solving problems involves looking at the problem structure, looking at the cases, making a guess about the solution, and then proving that guess.
Hence, not agree with Mr. Chin's conjecture.
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the incenter of a triangle is formed by the intersection of the of a triangle
Answers
Answer:
angle bisectors
Step-by-step explanation:
The incentre is where a triangle's three angle bisectors intersect ( an angle bisector is a ray that cuts an angle in half ). The incentre is the centre of a triangle drawn inside the triangle.
The cost of bowling is $5 per player for shoe rentals and $45 per hour to book a
lane. Suppose a group of f friends go bowling for h hours. Write an expression for
the total cost for the group of friends to go bowling.
Answers
Writing an expression consists of combining two or more variables, symbols, or numbers, with one or more mathematical operators to form a mathematical sentence that is based on a specific context
The expression for the total cost for bowling is 45·h + 5·f
The reason the above expression is correct is as follows:
The given parameters are;
The cost of shoe rentals for bowling per player = $5
The cost to book a lane per hour = $45
The number of people in the group of friends = f
The number of hours the friends go bowling = h
Required:
To write an expression for the total cost for the group of friends to go bowling
Solution:
Let the number of lanes the friends book= 1
The total cost, C, is the cost to book one lane at $45 per hour for h hours, plus the cost for the f number of friends to rent one shoe each at $5 per player (person)
Mathematically, C = 45·h + 5·f
The expression for the total cost for the group of friends to go bowling, is therefore;
45·h + 5·f
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A 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider.
What is the sample size? Give only the number:
The margin of error for this data set is 2.5%. What is the 95% confidence interval for those who say they felt fully engaged with their mortgage provider (rounded to 1 decimal place)?
Answers
The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.
First, let's calculate the margin of error:
Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055
Next, we can calculate the lower and upper bounds of the confidence interval:
Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%
Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%
Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
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