Non-response bias can occur when subjects who refuse to take part in a study, or who drop out before the study can be completed, are systematically different from those who participate.
What is sampling?A statistical technique called sampling uses a small portion of a larger population to represent the entire population. Sampling is a topic that takes into account the many approaches that might be used to survey a segment of the population and looks for a sample that is most representative of the entire population. The ability of a particular subset of a population's members to be generalized to the entire population is referred to as a sample's "generalizability," or "representativeness." For a highly generalizable outcome,Sampling is a key tool in the scientific method, allowing researchers to provide evidence that generalizable theories are true simply from a sample of specific facts.Hence,Non-response bias can occur when subjects who refuse to take part in a study, or who drop out before the study can be completed, are systematically different from those who participate.
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four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. find the probability of the given event. (round your answer to four decimal places.) four cards of the same suit are drawn.
The probability of selecting four cards of the same suit is 0.0106.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Given that, four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards
No. of cards for each suit = 13
Total types of four suits = 4(hearts, spades, diamond, clubs)
Probability = (conditional case)/(total case)
So, total number of conditional case = No. of case of selecting all 4 cards of hearts suit + no. of case of selecting all 4 cards of spades suit + no. of case of selecting all 4 cards of clubs suit + no. of case of selecting all 4 cards of diamonds suit
= 13C4 + 13C4 + 13C4 + 13C4
= 4*13C4 = 4*13!/9!4! = 4*13*12*11*10*9!/9!*4*3*2*1 = 2860
Total number of cases = 52C4 = 52!/48!4! = 270725
So, probability of getting all 4 cards of the same suit =
2860/270725
= 0.0106.
Hence, The probability of selecting four cards of the same suit is 0.0106.
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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
h=56.5
h=37.3
h=33.6
h=9
PLEASE HELP
The value of h in a regular polygon of 16 sides is 37.3.
According to the question,
We have the following information:
A regular polygon has 16 sides. And one of its angles measures (5h − 29)°.
We know that following formula is used to find the sum of interior angles of a polygon:
(n-2)*180 where n is the number of sides of a polygon
(16-2)180
14*180
2520°
Now, in this polygon, there are 16 sides. So, there will be 16 angles.
Now, to find the measurement of one angle, we will divide total sum by number of angles.
One angle = 2520/16
One angle = 157.5°
Now, we have the following expression:
5h-29 = 157.5
5h = 157.5+29
5h = 186.5
h = 186.5/5
h = 37.3
Hence, the correct option is B (the second one).
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2B math need help with this problem have a math test tomorrow
Answer:
∴ x = 113
Step-by-step explanation:
5-sided polygon: pentagon
total interior angles of a pentagon
= (5-2) × 180°
= 540°
x + x + x + 14 = 540° - 90° - (180 - 83)°
3x + 14 = 540 - 90 - 97
3x = 353 - 14
3x = 339
∴ x = 113
Convert the equation y = 3x - 5 from slope-intercept form to standard form.
Given that x is a nonnegative number, a student conjectured that x+4
The value of x is a counter example to the student's conjecture (x = 2).
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that x is a non-negative number, a student conjectured that x + 4 < x².
Since x is a non-negative number, A and B are eliminated.
This leaves C and D at the value of x = 2,
2 + 4 < 2²
6 < 4 is false.
Therefore, the value of x is a counterexample to the student's conjecture (x = 2).
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how to solve peggy is preparing a colored frosting for a cure. for the right shade of purple, she needs 25 milliliters of a 44% concentration food coloring. the store has a 25% red and a 50% blue concentration of food coloring. how many milliliters each of blue food coloring and red food coloring should be mixed to make the necessary amount of purple food coloring?
Answer:
25% red and 28% blue.
Step-by-step explanation:
Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of
15 1/2 m
Gabriel wants it to be 7- m long.
4
How wide does the planter box need to be?
Answer:
2m Wide
Step-by-step explanation:
In a direct variation, y=80 when x=5. Write a direct variation equation that shows the relationship between x and y.
As per the concept of direct variation, y = 80 when x = 5, then the direct variation equation shows the relationship between x and y will be y = 16x
Equation
Basically, the equation is a statement that two expressions, which include variables and/or numbers, are equal. And in essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given,
In a direct variation, y=80 when x=5.
Here we have to write a direct variation equation that shows the relationship between x and y.
Here we have given that,
The value of y = 80 when x = 5
Therefore, there are often two different sorts of variables in analytics.
And we have obtained that independent variables will have an impact on dependent variables.
Now, what occurs as a result of the independent variable is referred to as a dependent variable.
Here we have given equation x is the independent variable while y is the dependent variable.
So, it can be written as,
=> 80 = 16(5)
Therefore, the resulting equation is y = 16x
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PLEASE HELP THIS IS OVERDO
What is the product of 2p + q and –3q – 6p + 1?
–12p2 – 6pq – 4p – 3q + 1
–12p2– 12pq + 2p – 3q2 + q
–9p2q2 + 12pq – 2p + q
12p2 + 12pq +2p + 3q2 + q
The product of the algebraic expression as the product of (2p + q) and (-3q - 6p + 1) is; - 12p² - 12pq + 2p - 3q²+ q
How to multiply algebraic expressions?
We want to find the product of (2p + q) and (-3q - 6p + 1) and this gives;
(2p + q) * (-3q - 6p + 1)
Now, this can be broken down further using distributive property of algebra into;
2p(-3q - 6p + 1) + q(-3q - 6p + 1)
= -6pq - 12p² + 2p - 3q² - 6pq + q
= - 12p² - 3q² - 12pq + 2p + q
Rearranging gives us;
- 12p² - 12pq + 2p - 3q²+ q
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Paul has to put shingles on a roof. A brand new construction worker takes 12 hours to do it alone. When Paul asks the new worker to help him, they can do the job in 2 hours less than it takes Paul to do it alone. How many hours does it take Paul to do the job alone? Workingtogetherformula1a+1b=1T
The number of hours that it takes for Paul to do the job alone is of:
6 hours.
How to obtain the time it takes for Paul do to the job alone?The time that it takes for Paul to do the job alone is given by the together rate, which is obtained as the sum of the separate rates.
The rates in the context of this problem are given as follows:
Construction worker: 1/12.Paul: 1/x.Together rate: 1/(x - 2) -> 2 hours less than Paul's alone.Hence the value of x is obtained applying the together rate, and it gives the number of hours that it takes for Paul to do the job alone.
Hence:
1/(x - 2) = 1/x + 1/12
1/(x - 2) = (12 + x)/(12x)
Applying cross multiplication, we have that:
(12 + x)(x - 2) = 12x
x² + 10x - 24 = 12x
x² - 2x - 24 = 0
(x + 4)(x - 6).
Applying the Factor Theorem, the solutions are given as follows:
x + 4 = 0 -> x = -4 -> extraneous solution, as the number of hours cannot be negative.x - 6 = 0 -> x = 6 -> actual solution.More can be learned about the together rate at https://brainly.com/question/27859524
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Can you locate the school where sir isaac newton was once the lucasian professor of mathematics?.
Answer:
The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.
Step-by-step explanation:
Find the equation of the linear function represented
by the table below in slope-intercept form.
X
1
2
3
4
y
0
-5
-10
-15
The equation of the linear function in slope-intercept form is [tex]y=-5x+5[/tex]
What is slope-intercept form of linear function?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
Different values of x and y are given.
Find the slope using any two points from the given points.
[tex]m=\frac{-5-0}{2-1}\\ =-5[/tex]
Use the point-slope form of line to obtain the equation.
[tex]y-0=-5(x-1)\\[/tex]
Arrange the equation in slope- intercept form.
[tex]y=-5x+5[/tex]
So, the equation of the linear function in slope-intercept form is [tex]y=-5x+5[/tex].
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If someone uses 400 liters of orange juice, how much strawberry juice would they need?
Answer:
you need to post the rest of the problem for us to figure it out. if someone walked up to you and asked you this you'd think they're out of their mind
also confused about this
Graph (B) represents the base function f (x)=√x and the stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex].
What is graph?Graphs are used to map functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis, vertical y-axis.
The graph of this function can be obtained by putting different values of x.
x = 0 gives f (x) = 0
x = 1 gives f (x) = 1
x = 2 gives f (x) = 1.414
x = 3 gives f (x) = 1.732
Drawing these points in the graph and connecting we get a curve(black) which can be seen in all given diagram (A), (B), (C), (D).
Now, we have stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex]
The graph of this function can be obtained by putting different values of x.
x = 0 gives g (x) = 0
x = 1 gives g (x) = -1.5
x = 2 gives g (x) = -2.121
x = 3 gives g (x) = -2.598
Drawing these points in the graph and connecting we get a curve(red) which can be seen in diagram (D).
By combining these two graphs we get the graph of diagram (D).
Therefore, the base function f (x) and the stretched function g (x) together represents the diagram (D).
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Bella manages a cafe.She bought 15.625 pounds of oranges . She mutiplies the weigh of the oranges by 0.4 to find the weight of the oranges she will use in fruit salads
The weight of an object is the amount of gravitational force applied on the object by the earth. The weight of the oranges to be used is 6.25 pounds.
The level of influence of the earth's gravitational pull on an object determines its weight. This depends also on the size of the mass of the object.
Given that Bella bought 15.625 pounds of oranges.
Let the weight of the oranges required to prepare fruit salad be represented by W. Then the weight of the oranges required is 0.4 of the weight of oranges bought, so that;
W = 0.4 * 15.625
= 6.25
W = 6.25
Thus, the weight of the oranges required to be used for fruit salad is 6.25 pounds.
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Can someone please help me on this, I don't understand :)
The values of x and y are 23.3 and 106 as per given diagram.
What is Alternate Interior Angles?
The word "alternate" refers to the transversal's "alternating sides." The "location" of these angles is expressly described by this designation.The alternate interior angles are equal in size when the lines are parallel.The sides of the transversal are "alternated" by alternate interior angles, which are "internal" (between the parallel lines). They are not neighbouring angles, as you can see (next to one another sharing a vertex).The alternate interior angles are equivalent when a transversal cuts two parallel lines.Hence, (3x + 4)° = 74°
3x = 74° - 4°°
x = 70° / 3
x = 23.3
What is Interior Angles on the Same Side of the Transversal?
The name of these angles describes their "location."The measures are supplemental when the lines are parallel.These angles are situated precisely where their names suggests. They are on the same side of the transversal and are "interior" (between the parallel lines).Hence, (3x+4)° + y° = 180°
74° + y° = 180°
y = 106°
Hence, the values of x and y are 23.3 and 106 as per given diagram.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
By evaluating the exponential equation, we will see that the amount owed after 6 years is $8551.56
How to find the amount owed after 6 years?The formula we need to use is the exponential equation:
A = P*(1 + r/n)^(n*t)
Where:
P is the initial amount, here we know that it is $5,300
r is the rate, in this case is 8%, but it needs to be written as a decimal, so we have r = 0.08
t is the variable, this time is the time in years, we want to find the amount owed after 6 years, so t = 6
n is how many the the rate applies on one unit of t, in this case the rate is monthly, and there are 12 months on a year, so n = 12.
Replacing all that in the given formula we will get:
A = $5,300*(1 + 0.08/12)^(12*6) = $8551.56
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PLEASE HELP !!!! brainliest will be given to first answer
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has a $860 budget for food a month. How much can John spend on food for each cow per month?
Answer:
Approximately $15 per cow
Step-by-step explanation:
I Need help wit this one
The area of the shaded region is 422.16 cm sq.
Given,
In the question:
Radius of the circle is 12 cm.
The length of rectangle is 10cm
and, Breadth of the rectangle is 3cm.
A rectangle sits inside a circle.
To find the Area of the shaded region.
Now, According to the question;
we know that:
Area of a circle is = [tex]\pi r^2[/tex]
Radius = 12cm
Area of a circle is = 144[tex]\pi[/tex]
Using [tex]\pi[/tex] = 3.14
Area of a circle is = 144 x 3.14 = 452.16 cm sq.
The area of rectangle = 3 x 10 = 30cm sq.
So, The area of the shaded region:
452.16 - 30 = 422.16cm sq.
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help
If f(1) = 3 and f(n) = f(n − 1) – 3 then find the value of f(4).
If f(1) = 3 and f(n) = f(n − 1) – 3 then the value of f(4) is -6.
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Given,
Function:
f(1) = 3
f(n) = f(n - 1) -3
Let n = 2
f(2) = f(2-1) - 3
f(2) = 3 - 3
Relation:
f(2) = 0
Let n = 3
f(3) = f(3 -1) - 3
f(3) = 0 -3
f(3) = -3
Let n = 4
f(4) = f( 4 -1) - 3
f(4) = -3 -3
Value:
f(4) = -6
If f(1) = 3 and f(n) = f(n − 1) – 3 then the value of f(4) is -6.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 7.8
B. 9.8
Step-by-step explanation:
A. 2006 = 3 years
y = 7.1(1.03)ˣ
y = 7.1(1.03)⁽³⁾
y = 7.1(1.092727)
y = 7.7511907
y = 7.8
----------------------------------------------------------------------------------------------------------
B. 2014 = 11 years
y = 7.1(1.03)ˣ
y = 7.1(1.03)⁽¹¹⁾
y = 7.1(1.38423387)
y = 9.82806047
y = 9.8
If it says, "Round to the nearest tenth," the answer is 9.8. If the answer says, "Round to the nearest whole number," the answer is 10
I hope this helps!
Factorise the following 2x + 10
Answer:
2(x+5) I believe
Step-by-step explanation:
Suppose T: ℝ3→ℝ2 is a linear transformation. Let U, V and W be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(W).
U = 1, -3, 3 V = −1,3,−2 W = −3,9,−7 T(U) = 2,2 T(V) = 0,1
T(W) = ???
By using the concept of Linear Transformation, the value of T(W) obtained is T(W) = (2, 6)
What is Linear Transformation?
A function through one vector space to the next that respects this same underlying (linear) structure of the each vector space is called a linear transformation. A linear operator, or map, is another name for a linear transformation. The transformation is known as just an endomorphism as well as, if invertible, an automorphism when the range of a transformation matches the domain. The underlying field of the two vector spaces must be identical.
Let u, v be two element of a vector space V and let c be a scalar
T is said to be a Linear Transformation if
i) T(u + v) = T(u) + T(v)
ii) T(cu) = cT(u)
T: [tex]\mathbb{R}^{3} \rightarrow \mathbb{R}^2[/tex] is a linear transformation
U = (1, -3, 3), V = (−1,3,−2)
W = [tex]c_1[/tex] U + [tex]c_2[/tex] V
(-3, 9, -7) = [tex]c_1[/tex](1, -3, 3) + [tex]c_2[/tex](-1, 3, -2)
[tex]c_1 - c_2 = -3[/tex] ...... (1)
[tex]3c_1 - 2c_2 = -7[/tex] ..... (2)
Multiplying (1) by 2
[tex]2c_1 - 2c_2 = -6[/tex] .... (3)
Subtracting (2) from (3),
[tex]c_1 = 1[/tex]
Putting the value of [tex]c_1[/tex] in (1)
1 - [tex]c_2[/tex] = -3
[tex]c_2 = 3 + 1\\c_2 = 4[/tex]
T(W) = T(U) + 4T(V)
T(W) = (2, 2) + 4(0, 1)
T(W) = (2, 6)
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Maya is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random. What is the probability that maya's first guess is correct and her second guess is incorrect?.
Maya is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.
The probability that maya's first guess is correct and her second guess is incorrect is 0.24.
From the question given above, the following data were obtained:
Correct answer (C) = 222
Total answer = 555
Incorrect answer (I) = 555 – 222 = 333
Next, we shall determine the probability that her 1st guess is correct.
Correct answer, nC = 222
Total answer, nS= 555
Probability of correct answer, P(C) =?
P(C) = nC / nS
P(C) = 222 / 555
Next, we shall determine the probability that her 2nd guess is incorrect
Incorrect answer, nI = 333
Total answer, nS = 554
Probability of incorrect answer, P(I) =?
P(I) = nI / nS
P(I) = 333 / 554
Finally, we shall determine the probability that her first guess is correct and her second guess is incorrect.
Probability of correct answer, P(C) = 222 / 555
Probability of incorrect answer, P(I) = 333 / 554
Probability of 1st correct and 2nd incorrect, P(C n I) =?
P(C n I) = P(C) × P(I)
P(C n I) = (222 / 555) × (333 / 554)
P(C n I) = 0.24
Hence the answer is, The probability that maya's first guess is correct and her second guess is incorrect is 0.24.
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Answer:
0.3
Step-by-step explanation:
Khan Academy ;)
Challenge Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the
wire they need. Andy needs 25 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Cost of Wire
Length in
Inches (x)
110
125
160
185
Cost in
Dollars (y)
5.50
6.25
8.00
9.25
Andy will spend $15 for her wire. Emily will spend $27.25 for her wire.
1 = 12 ℎ
1 = 3 = 36 ℎ
=5.50/110 (⁄ℎ)
=6.25/125 (⁄ℎ)
=8.00/160 (⁄ℎ)
=9.25/185 (⁄ℎ)
Andy needs 25 feet of the wire
25(12 inches) = 300 inches
300(5.50 / 110) = 15(Dollars)
Andy will spend $15 for her wire.
Emily needs 15 yards of the wire
15(36 ℎ) = 540 ℎs
110a + 125b + 160c + 185d ≥ 540
6(110) = 660
4(110) + 125 = 565
3(110) + 2(125) = 580
110 + 3(125) = 485
2(125) + 2(160) = 570
110(5.50/110) + 3(145)6.25/125 = 27.25
540 (5.50/110) = 27
Emily will spend $27.25 for her wire.
If she can cut the wire, then Emily will spend $27 for her wire.
∴ Andy will spend $15 for her wire. Emily will spend $27.25 for her wire.
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What is 2+2 - 5 + 42 - 64 (5 x 5) - 32 x 1/2 + 6/5 * 2^5
Answer:
-1536.6 if not the answer den sorry
Step-by-step explanation:
Answer:
its -39363/25, -1574.32, and -1574 13/25 (hopefully this helps, sorry if its wrong)
A cyclist rode 5.83 miles in 0.4 hours.
How fast was she going in miles per hour?
At that rate, how long will it take her to go 5.5 miles?
Answer:
Its 12.5 miles per hour.
Step-by-step explanation:
Distance covered by cyclist=3.75 miles. Time =0.3 hours. Speed =3.75÷0.3=12.5
hope this helps
Answer:
0.4 miles per hour
Step-by-step explanation:
Distance covered= 5.83 miles
Time taken to cover the distance =0.4 hours
[tex] speed \: = \frac{distance}{time} [/tex]
[tex] = \frac{5.83}{0.4} [/tex]
=14.575 ~=14.5 miles per hour
If the rate (speed) = 14.575 miles per hour
Distance = 5.5 miles
[tex]time = \frac{distance}{speed} [/tex]
[tex] = \frac{5.5}{14.575} [/tex]
=0.337 ~= 0.4 hours
When collecting data, what is a sample?
Thank you for helping.
Answer:
Step-by-step explanation:
Artista , it's the 3rd answer, a random set from the group being studied
A veterinarian has been asked to prepare a diet, x ounces of Brand A and y ounces of Brand B, for a group of dogs to be used in a nutrition study at the School of Animal Science. It has been stipulated that each serving should be no larger than 8 oz and must contain at least 29 units of Nutrient I and 20 units of Nutrient II. The vet has decided that the diet may be prepared from two brands of dog food: Brand A and Brand B. Each ounce of Brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of Brand B contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 5 cents/ounce, and Brand B costs 7 cents/ounce. Determine how many ounces of each brand of dog food should be used per serving to meet the given requirements at a minimum cost. (x,y)=... What is the minimum cost? (Round your answer to the nearest cent.) ..... cents per serving
To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .
In the question ,
it is given that ,
the each serving should not be larger than 8oz .
let the number of Ounces of Brand A food = x , and
let the number of ounces of brand B = y ,
So , x + y ≤ 8
Brand A has 3 units of Nutrient 1 and 4 units of Nutrient 2 , and
Brand B has 5 units of Nutrient 1 and 2 units of Nutrient 2 ,
So , 3x + 5y ≥ 29 ,
and 4x + 2y ≥ 20,
and x , y ≥ 0 .
given, that
cost of Brand A = 5 cents/ounce
cost of Brand B = 7 cents/ounce
So , the cost equation is c(x) = 5x + 7y ,
drawing the given inequalities on the graph ,
From the graph given below , we find that the vertices of the feasible region are ,
(2,6) , (5.5,2.5) , (3,4)
Substituting the points in the cost equation , we get
For point (2,6) , C = 5(2) + 7(6) = 10 + 42 = 52
For point (3,4), C = 5(3) + 7(4) = 15 + 28 = 43
For point (5.5,2.5) , C = 5(5.5) + 7(2.5) = 45 ,
the minimum cost is at point (3,4) ,
So , 3 ounces of Brand A and 4 ounces of Brand B should be used .
Therefore , To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .
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Barabas received a mark of 50% on a recent test. Barabas answered 13 of the first 20 questions correctly. Barabas also answered 25% of the remaining questions on the test correctly. If each question on the test was worth one mark, how many questions in total were on the test?
Answer:
32
Step-by-step explanation:
You want the total number of questions on the test if the final score was 50%, and there were 13 correct out of the first 20, and 25% correct among the remainder.
SetupLet q represent the number of questions on the test. Then (q-20) is the number of remaining questions, and the number correct is ...
13 +0.25(q -20) = 0.5(q)
Solution8 +0.25q = 0.5q . . . . . . . simplify
8 = 0.25q . . . . . . . . . . . . subtract 0.25q
32 = q . . . . . . . . . . . . . . multiply by 4
There were 32 questions in total on the test.
