Dominic took a 20-question online quiz. He received 5 points for every correct answer. For every question he answered
incorrectly, he lost 2 points. The quiz also had a 20-point bonus for finishing in one hour or less. Since Dominic finished
the quiz in less than one hour, his score S is determined by x, the number of questions answered correctly.
Drag and drop expressions into the function to correctly define S(a).
The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20
How to determine the function that correctly defines S(x)We have the following definitions in the question
Correct answers = xTotal questions = 20Points for correct answers = 5Points for incorrect answers = -2Bonus for finishing in one hour or less = 20If the total questions is 20, then
Incorrect answers = 20 - x
So, the points gained/lost are
Gained = 5 * x = 5x
Lost = -2 * (20 - x) = -2(20 - x)
Bonus = 20
Add the above points to get the function S(x)
S(x) = 5x - 2(20 - x) + 20
Hence, the definition is S(x) = 5x - 2(20 - x) + 20
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Suppose that So, S1, S2,... is a sequence of subsets of N. Which one of the following sets is guaranteed to be different from all sets in the sequence? (a) S = {n | n & Sn²} (b) S = {n | n² & Sn²} (c) S = {n²| n & Sn²} (d) S = {n² | n² & Sn} (e) S = {n² | n & Sn} Explain why your chosen set is guaranteed not to be in the sequence So, S1, S2, ...
Suppose that So, S1, S2,... is a sequence of subsets of N the following sets is guaranteed to be different from all sets in the sequence is S = {n² | n² & Sn}.
Subsets are a part of the mathematical concept of sets. A set is anything that is wrapped in curly braces, such as "a,b,c,d." If set A is a collection of even integers and set B is composed of the numbers 2, 4, and 6, then set A is the superset of set B and set B is said to be a subset of set A. Review Sets Subset and Superset for further details.
Set A is referred to as a subset of Set B if each element of Set A is also present in Set B. In other words, Set B includes Set A.
As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
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Students at two high schools were asked about their plans after graduation. The table displays the results for 300 students at Henderson High School. The bar graph displays the results for 300 students at Johnson High School. Which Statement about the results from Henderson High School and johnson high school must be true?
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
Options F and G are the correct answer.
We have,
The number of students in Henderson High School.
Work = 96
College = 114
Armed forced = 48
Other = 42
The number of students in Johnson High School.
Work = 30
College = 40
Armed forced = 15
Other = 15
From the information,
The number of students in Work for Henderson High School is greater than Johnson High School.
Now,
Henderson High School:
Armed force and other = 48 + 42 = 90
Mode = college
Johnson High School.
Armed force and other = 15 + 15 = 30
Mode = college
Thus,
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
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A data set contains three points, and two of the residuals are -10 and 20.
What is the third residual?
If a data set contains three points, and two of the residuals are -10 and 20, the third residual is 10 (option B).
What is a residual?A residual is the difference between the observed value and the estimated value of the quantity of interest.
The residual of a data points should normally sum up to zero (0). This means the following applies:
-10 + 20 + x = 0
x = 10
Therefore, if data set contains three points, and two of the residuals are -10 and 20, the third residual is 10.
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CHECK YOUR UNDERSTANDING
The Wacky Widget Company sells widgets for
$4.00 each wholesale. A local store has a
markup of $1.20.
A. What is the retail price?
B. What percent is the markup price?
Answer:
Retail price = $5.20
Percentage of mark up price = 30%
Step-by-step explanation:
Company sells $4.00 each wholesale.
Now the local store which is the retailer has a markup of $1.20.
This means that the retail price is;
Retail price = wholesale price + mark up = $4.00 + $1.20
Retail price = $5.20
To find the percentage of the markup, it is the fraction of the wholesale price multiplied by 100%.
Thus;
Percentage of Markup is;
1.2/4 × 100% = 30%
4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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Select the graph that correctly represents ƒ(x) = –2(x + 4)2 – 1.
The graph that correctly represents f(x) = –2(x + 4)² is graph (B).
What is a graph?A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph. In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to connected and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other types of graphs.So, graph of: f(x) = –2(x + 4)²
Then,
f(x) = -2(x + 4)² f(x) = (-2x - 8)²Now, plot (-2x - 8)² on the graph.
(Refer to the graph attached below)
Therefore, the graph that correctly represents f(x) = –2(x + 4)² is graph (B).
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Suppose that we are testing H0: µ = µ0 versus H1: µ > µ0. Calculate the P -value for the following observed values of the test statistic (round all answers to 4 decimal places.
(a)z0 = 2.35,
(b)z0 = 1.53,
(c)z0 = 2.00,
(d)z0 = 1.85,
(e)z0 = -0.15.
Please show steps will rate Life Saver
The p-values for the observed values of the test statistic are 0.0094, 0.0628, 0.0228, 0.032 and 0.4404.
To calculate the p-value for each observed value of the test statistic, we need to find the area under the standard normal distribution curve to the right of each z-score. This is because the alternative hypothesis is one-tailed, with the inequality sign pointing to the right (i.e., H1: µ > µ0). Here are the steps to calculate the p-value for each observed value:
For z0 = 2.35, the area to the right of the z-score can be found using a standard normal distribution table or calculator. The area is 0.0094, which is the p-value.
For z0 = 1.53, the area to the right of the z-score is 0.0628, which is the p-value.
For z0 = 2.00, the area to the right of the z-score is 0.0228, which is the p-value.
For z0 = 1.85, the area to the right of the z-score is 0.0322, which is the p-value.
For z0 = -0.15, the area to the right of the z-score is 0.5596. However, since the alternative hypothesis is one-tailed with the inequality sign pointing to the right, we need to subtract this area from 1 to get the p-value. Therefore, the p-value is 1 - 0.5596 = 0.4404.
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Maya’s unpaid balance is $205.16. Her APR is 14.4% and she has $82.10 in new transactions. What is her new balance? Responses $289.72 $289.72 $290.71 $290.71 $316.80 $316.80 $533.45
Based on the information given the new balance is $289.72.
New balanceFirst step is to calculate the finance charge
\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)
\(\text{Finance charge}=205.16\times0.012\)
\(\text{Finance charge}=2.46\)
Second step is to calculate the New balance
\(\text{New balance}=205.16+2.46+82.10\)
\(\text{New balance}=\bold{\$289.72}\)
In conclusion, the new balance is $289.72.
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Plz help on this question
Answer:
B
Step-by-step explanation:
Because it'll be 1²+2×1-3=0
And -3²+2(-3)-3=9-6-3=0
So it's impossible
Lots of people use breakfast cereal as a daily source of fiber, and these cereals also contain the mineral potassium. Suppose a linear model was made to predict a cereal's potassium content using its fiber content, and suppose the model had intercept 37 and slope 25. For a cereal having 255 milligrams of potassium and 9 grams of fiber, what is the residual (in mg)?
Answer:
The residual is of 7 mg.
Step-by-step explanation:
Linear model:
A linear model has the following format:
\(y = mx + b\)
In which m is the slope and b is the intercept.
Suppose the model had intercept 37 and slope 25.
This means that \(b = 37, m = 25\)
So
\(y = 25x + 37\)
9 grams of fiber
This means that \(x = 9\). So
\(y = 25(9) + 37 = 262\)
255 milligrams of potassium. What is the residual (in mg)?
Expected subtracted by actual. So
262 - 255 = 7
The residual is of 7 mg.
Gavyn, Richard and Stephen share some sweets in the ratio 4:2:3. Gavyn gets 10 more sweets
than Stephen. How many sweets does Richard get?
Answer:
13 is richard
Step-by-step explanation:
Answer:
10 sweets.
Step-by-step explanation:
So all of them share the sweets in a ratio of 4:2:3. Since Gavyn gets 10 more sweets than Stephen, and the ratio of Gavyn's sweets to Stephens sweets is 4:3, which means that x=10. To clarify, a ratio can be written as 4x:3x, so x=10. So now you do Richards ratio (2x) and you just plug in x and you get 20. So Richard gets 20 sweets.
-2a-6a-9=-9-6a-2a
help please g
Answer:
the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).
Step-by-step explanation:
To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:
Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.
Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.
Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).
In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).
PLSSSSSSSSSSS HELPPPPPPPPPP OMG PLSSSSSSSS HELPPPPPP
Answer:
A
Step-by-step explanation:
You can see they are multiplying x by 3 every time.
Answer:
A) y=3x
Step-by-step explanation:
find the pattern between x and y. if we try using the equation y=3x, plug in the values to check if its correct.
input(x) = 2
output(y)=6
6=3(2)
6=6
The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine
the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Find the
location of the earthquake's epicenter if it is 4 miles away from A (5,2), 3 miles away from B (-2,2), and 5 miles away from C (1, -3).
Answer:
The coordinates of the epicenter are (1,2) ie x=1, y =2
Step-by-step explanation:
We use the fact that the distance d between 2 points, (C y₁) and (x₂, y₂) is computed by the Pythagorean formula:
(x₁ - x₂)² + (y₁ - y₂) = d²
Let the epicenter be located at (x, y)
Distance dA from point A(5,2) is known to be 4 and is given by the equation:
(x-5)² + (y - 2)² = dA² = 4² = 16 ==>
(x-5)² + (y-2)² = 16 (1)
Similarly, the distance from point B(-2,2) is given as 3. Therefore,
(x - (-2))² + (y-2)² = 3² = 9 or
(x + 2)² + (y-2)² = 9 (2)
Distance from point C(1,-3) ==>
(x-1)² + (y-(-3))² ==> (x-1)² + (y +3)² = 25 ...(3)
(1) - (2) cancels out the y terms and gives us
(x-5)² - (x+2)² = 7 (4)
This simplifies to
x² + -10x + 25 - (x² +4x + 4) = 7
or
x² + -10x + 25 -x² -4x - 4 = 7
-10x -4x = 7 - 21 = -14
Therefore, -14x = -14 giving us x = 1
Substituting for x = 1 in equation (3) gives us
(1-1)² + (y+3)² = 25 or
y + 3 = √25 = 5 giving y = 2
So we get the epicenter coordinates as x=1, y =2
Crosscheck in each of the equations (1), (2) and (3) for consistency
Equation 1 : (1-5)² + (2-2)² = -4² = 16 Check!
Equation 2: (1-(-2))² + (2-2)² = (1+2)² = 3² = 9 Check!
Equation 3: (1-1)² + 2-(-3))² = (2+3)² = 5² Check!
What is 46856+564??? Please help!
Answer:
47420
Step-by-step explanation:
Answer is : 47420 aaaa
name the decimal number for 0.5
Answer:
zero point five
Step-by-step explanation:
zero point five
15. Many people swimming in a pool experience pain in their ears if they dive to the
bottom. Why is this?
A. Pressure increases as the depth of the water column above them increases.
B. The area of the pool is wider where it's deeper.
C. Pressure decreases as the depth of the water column above them increases.
D. The vapor pressure at the surface is removed.
Answer:
The answer is Ahope this helps
Nolan has 4 sets of water colors. Each set has 8 colors. How
many total colors would he have if he bought 2 more sets?
Answer:
He would have 48
Step-by-step explanation:
1 set: 8
2 sets: 16
3 sets: 24
4 sets: 32
5 sets: 40
5 sets: 48
OR
{4(8)} + 2(8)
32 + 2(8)
32 + 16
48
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!
Answers
48
Steps
4+2=6
8 times 6= 48
Winona has two jobs; one pays $10.00 per hour and the other pays $9.25 per hour plus an average of 70% of the hourly pay in tips and bonuses. Each pay
period, 20% of her total pay goes to taxes.
Part 1 of 2
(a) Write and simplify an equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the
number of hours, y, worked at the second.
The total take-home pay from Winona's two jobs can be found using the equation
P=
Part 2 of 2
X
3
(b) If Winona is committed to work 30 hours per week at the first job, how many hours per week would she need to work at the second job if she needs
her biweekly take-home pay to be $800? Round the answer to one decimal place.
In order for her biweekly take-home pay to be $800, Winona needs to work
hours per week at her second job.
Answer:
76.5 hours
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
Step-by-step explanation:
Part 1 of 2:
(a) The equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the number of hours, y, worked at the second job can be written as:
P = (10x) + (9.25y + 0.7 * 9.25y) - 0.2[(10x) + (9.25y + 0.7 * 9.25y)]
Simplifying the equation:
P = 10x + 9.25y + 0.7 * 9.25y - 0.2(10x + 9.25y + 0.7 * 9.25y)
Part 2 of 2:
(b) If Winona is committed to working 30 hours per week at the first job, let's assume x = 30. We need to find the number of hours per week, y, she would need to work at the second job to reach a biweekly take-home pay of $800.
Using the simplified equation from part (a), we substitute x = 30 and solve for y:
800 = (10 * 30) + (9.25y + 0.7 * 9.25y) - 0.2[(10 * 30) + (9.25y + 0.7 * 9.25y)]
800 = 300 + (9.25y + 0.7 * 9.25y) - 0.2(300 + (9.25y + 0.7 * 9.25y))
Now, we can solve for y:
800 = 300 + 9.25y + 0.7 * 9.25y - 0.2(300 + 9.25y + 0.7 * 9.25y)
Simplify the equation:
800 = 300 + 9.25y + 0.7 * 9.25y - 0.2 * 300 - 0.2 * 9.25y - 0.2 * 0.7 * 9.25y
Combine like terms:
800 = 300 - 60 + 9.25y - 1.85y - 0.1295y
800 = 240 + 7.32y
Subtract 240 from both sides:
560 = 7.32y
Divide both sides by 7.32:
y ≈ 76.5
Therefore, Winona would need to work approximately 76.5 hours per week at her second job to reach a biweekly take-home pay of $800.
find the volume of the figure
Answer:
Step-by-step explanation:
base area=41.57 in²
height=9 in
volume=41.57×9=374.13 in³
Write the equation of the scenario.
Tony's father is thinking of buying his son a six-month movie pass for $40. With the
pass, movies cost $3.00 each.
A y = 30+4x
B y = 40+ 3x
C y= 3 + 40x
D y=4 + 30x
IM IN A HURRY
Factor 21x^2 - 14x - 56
Answer:
7((x-2)(3x+4))
Step-by-step explanation:
Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product. You get 7((x-2)(3x+4))
Directions - name the scale factor for the following dilation:
When a dilation is performed, the scale factor can be found as the quotient between the lengths of two corresponding parts of the scaled figure and the original figure.
In this case, notice that the side AB in the original figure corresponds to the side A'B' in the scaled figure.
Then, the scale factor is the quotient of the length A'B' over the length AB.
Since A'B' = 3 and AB = 1, then the scale factor is equal to:
\(\frac{A^{\prime}B^{\prime}}{AB}=\frac{3}{1}=3\)Therefore, the scale factor is equal to 3.
x^2 + y^2 +2x+6y=26
what is the center
what is the radius
please show calculations/steps
Answer:
centre = (- 1, - 3 ) , radius = 6
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² + 2x + 6y = 26 ( collect x and y terms )
x² + 2x + y² + 6y = 26
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(3)y + 9 = 26 + 1 + 9
(x + 1)² + (y + 3)² = 36 ← in standard form
with centre = (- 1, - 3 ) and r = \(\sqrt{36}\) = 6
\((x {}^{2} + 2x + 1) - 1 = (x + 1) {}^{2} - 1\)
\((y {}^{2} + 6y + 9) - 9 = (y + 3) {}^{2} - 9\)
\((x + 1) {}^{2} - 1 + (y + 3) {}^{2} - 9 = 26\)
\((x + 1) {}^{2} + (y + 3) {}^{2} = 26 + 10\)
\((x + 1) {}^{2} + (y + 3) {}^{2} = 36\)
General form:\((x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} \)
Center coordinates: I ( a , b ) I ( -1 , -3 )Radius:\(r {}^{2} = 36\)
\(r = \sqrt{36} = 6\)
there's 20 points for both problems if you could please solve this
which is equal to (sinx+cosx)^2+(sinx-cosx)^2 using identities?
The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to
4 + 2sinxcosx.How to simplify the identityTo simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.
Expanding the squared terms
(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)
Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:
(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)
Simplifying the expression, we have:
2 + 2sinxcosx + 2
Combining like terms, we get:
4 + 2sinxcosx
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Mental math33.23 divided by 1,000
Answer:
0.03323
BRAINLIEST, PLEASE!
Step-by-step explanation:
Move the decimal place 3 places to the left.
33.23 becomes 0.03323.
given cos theta=4/5 and theta is in the 1st quadrant. find the angle equivalent to theta between 0 and 360 degrees. (give answer to 2. dp)
The angle equivalent to θ between 0 and 360 degrees is approximately 36.87 degrees.
We have,
To find the angle equivalent to θ between 0 and 360 degrees, we can use the inverse cosine function \((cos^{-1}).\)
The given value of cos θ = 4/5 represents the cosine of an angle in the first quadrant. In the first quadrant, all trigonometric functions are positive, including cosine.
Taking the inverse cosine \((cos^{-1})\) of both sides of the equation, we get:
θ =\(cos^{-1}(4/5)\)
The inverse cosine function returns the angle whose cosine is equal to the given value.
Evaluating \(cos^{-1}(4/5)\) using a calculator or trigonometric tables, we find the value to be approximately 36.87 degrees.
Therefore,
The angle equivalent to θ between 0 and 360 degrees is approximately 36.87 degrees.
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any of the 2 questions would help please! thank you so much
Answer:
3) False, should be divided by z²
4) True
Step-by-step explanation:
3) 18(\(\frac{1}{9}\)x⁴y)(x²y⁴z⁻²) ⇒ 2x⁶y⁵/z²