Answer:
Step-by-step explanation:
The unit rate is 400 square feet per gallon.
What is unitary method ?
Unitary method is a mathematical way of deriving a single unit and then finding the required unit by multiplying.
A graph is shown in the diagram and two points are given x co-ordinate represents paint used per gallon and y co-ordinate represents wall painted in square feet.
Given (1/4,100) implies 1/4th of a gallon paint is needed to pain 100 square feet of wall.
∴ In 1 gallon (100)÷1/4 square feet of wall can be painted which is 400 square feet.
And the unit rate is 400 square feet per gallon.
The choices below are data sets. In the choices, w is a constant. Each choice has the same mean.
Which choice has the greatest standard deviation?
A.)
w-2, w-1, w, w + 1, w+ 2
B.)
w-2, w-2, w, w + 2,w+2
C.)
w-3, w-1, w, w + 1, w+3
D.)
w-3, w, w, w, w +3
Answer:
C)w-3, w-1, w, w + 1, w+3
Step-by-step explanation:
I'm not great with standard deviation, but I know that the greater the standard deviation, the more spread out the data is.
C) is the correct answer, the data points do not repeat and are spread out more than A.
You can check this by calculated each standard deviation (but only if you are crazy ;] )
Hope this helps,
:]
The formula K=1/2mv² is used to find the kinetic energy of an object in
motion using its mass, m, and its velocity (speed), v. Solve the equation
for the mass, m.
What is the Equation?
Is it: m = K/2v²
Answer:
m = 2k/v²
Step-by-step explanation:
K = ½mv²
multiply both sides by 2
2 × k = ² × ½mv²
2k = mv²
divide both sides by (v²)
m = 2k/v²
i hope this helped
4. The Johnsons' bill at a restaurant is $124.00. How much money should the Johnsons leave if they plan to tip their waiter 15%?
Answer:
142.6
Step-by-step explanation:
100% + 15% = 115%
115÷100 = 1.15
1.15 x 124 = 142.6
Hope that helped
3(2x+4) = 6x + 8
3(2x + 4) = 6x + 8
6x + 12 = 6x + 8
-6x -6x
12 = 8
no solution??
Answer: no solution
Step-by-step explanation:
Correct, there is no solution as any values of x and y will make the equation false
Prove that tan(A+B)
cot(A−B)
=
2−2
2−2�
Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
tan(A+B)/cot(A-B)
tan(A+B)/1/tan(A-B)
(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)
tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB
We know algebraic identity
(a+b)(a-b)=a²-b²
(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)
tan²A-tan²B/1-tan²Atan²B
Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
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Rick bought 5 yogurt bars at a snack shop. Each yogurt bar cost $1.80. Complete the table to show the price of 2, 3, 4, and 5 yogurt bars.
By using multiplication, it can be calculated that
The complete table is
Number of yogurt bars Cost of yogurt bars ($)
1 1.80
2 3.60
3 5.40
4 7.20
5 9.00
What is multiplication?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
This is a word problem on multiplication
Cost of 2 yogurt bars = $1.80 [tex]\times[/tex] 2 = $3.60
Cost of 3 yogurt bars = $1.80 [tex]\times[/tex] 3 = $5.40
Cost of 4 yogurt bars = $1.80 [tex]\times[/tex] 4 = $7.20
Cost of 5 yogurt bars = $1.80 [tex]\times[/tex] 4 = $9.00
So the table is
Number of yogurt bars Cost of yogurt bars ($)
1 1.80
2 3.60
3 5.40
4 7.20
5 9.00
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0=x2+18x+45
I need help with this place
The factorise quadratic equation x² + 18x + 45 = 0 is (x + 3)(x + 15)
How to factorise quadratic equation?A quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.
Therefore, quadratic equation can be represented as follows:
ax² + bx + c
where
a, b and c are constantHence, let's factorise x² + 18x + 45 = 0
x² + 18x + 45 = 0
Let's find the two numbers to add to get 18 and multiply to get 45
Therefore, the numbers are 3 and 15
x² + 18x + 45 = 0
x² + 3x + 15x + 45 = 0
x(x + 3) + 15(x + 3) = 0
(x + 3)(x + 15) = 0
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PLEASE HELP!!!!!! It’s algebra
When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
What is a annual inflation rate?
A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.
Here, we have
Given
The cost of the gallon of milk earlier was $2.81
The cost of a gallon of milk now is $3.48.
The total time period is 10 years.
r = (F/P)ⁿ⁻¹ - 1
r = {(3.48/2.81)^(1/10) - 1}×100
r = {(1.238)^(1/10) - 1}×100
r = 0.0215 ×100
r = 2.15
Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
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Four boards were given to Sam to build a triangular picture frame for a large painting.
32 feet
21 feet
8 feet
12 feet
Which of these boards could be used for his project?
The sum of any two sides of a triangle must be greater than the other thus 32 feet,21 feet, and 12 feet will be the correct so options (A),(B), and (D) are correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
As per the given,
To be a triangle of three side polygon the sum of any two sides must be greater than the third side.
If we take 32 feet,21 feet, and 8 feet.
21 + 8 = 29 < 32 so it will not form any triangle.
Thus, 8 cannot be taken. now let's take 32,21 and 12 here 21 + 12 = 33 > 32 so it will form a triangle this will be used for the project.
Hence "The right answer will be 32 feet, 21 feet, and 12 feet because the sum of any two sides of a triangle must be bigger than the other".
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Write the
equation
of the line In
Slope-Intercept
Form.
Type your
answer here.
Answer:y=2x+3
Step-by-step explanation:
The slope intercept form is y=mx+b
m equals to slope
b equals the y-intercept
the slop of this equation is 2
The y-intercept is at (0, 3)
y=2x+3
What is the value of x?
Enter your answer in the box.
The value of x in the intersecting line is 54.
How to find angles in intersected lines?When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles angles on a straight lines.
Therefore, angle 2x + 2 is vertically opposite to the angle 3x - 52 .
Vertically opposite angles are congruent to each other.
Vertical Angles are the angles opposite each other when two lines cross. in other words, vertical angles are formed when two lines meet each other at a point.
Hence,
2x + 2 = 3x - 52
2x - 3x = -52 - 2
- x = -54
Therefore,
x = 54
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What is the term to term rule for this sequence ? 625,125,25,5,1
The required expression for the term of the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
How to know whether a given sequence is geometric?In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.
The given sequence is as follows,
625, 125, 25, 5, 1
The first term is given as a₁ = 625
And, the ratio of the consecutive terms are,
125/625 = 1/5
25/125 = 1/5
Since the ratio of two consecutive terms are equal, the given sequence is a geometric sequence.
The nth term of a geometric sequence is given as aₙ = a₁rⁿ⁻¹.
Thus, the expression for the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
Hence, the term for the given sequence can be written in general form as aₙ = 625 × (1/5)ⁿ⁻¹.
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Diego is also training for the tournament. The graph shows the relationship between the time in the distant he rows how many meters does Diego Roper minute
Diego rows 300 meters per minute
How to determine the the number of rows per minuteInformation given in the question include
The graph shows the relationship between the time in the distant, Diego rows
The data is plotted as a linear function
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
the slope, m calculating using the points on the graph (1, 300) and (2, 600)
m = (y₀ - y₁) / (x₀ - x₁)
m = (600 - 300) / (2 - 1)
m = 300 / (1)
m = 300
The number of meters Diego rows per minute is solved to be 300
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Let g(x) be a horizontal compression of f(x) = -x + 4 by a factor of 0.5. Write the
rule for g(x).
g(x) = 4x+4
g(x)=x-4
g(x)=0.5x-4
g(x)=-2x+4
1 pts
There is no correct answer given.
Horizontal compression of f(x) = -x + 4 by a factor of 0.5 will be -2x + 4.
What is a horizontal function?A horizontal line that a function's graph looks to coincide with but does not really do so is said to be its horizontal asymptote. The final behavior of the function is determined using the horizontal asymptote.
Given, g(x) is a horizontal compression of function f(x) = - x + 4 by a factor of 0.5. Hence,
g(x) = -x / 0.5 + 4
g(x) = -2x + 4
Therefore, By a factor of 0.5, the horizontal compression of the function (f(x)) is -x + 4 will result in -2x + 4.
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explain the process of the square root of 80n3
The square root of 80 is 4√5 ≅ 8.92.
What is a square root of a number?
In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. The positive number, when multiplied by itself, represents the square of the number. Thus, the square root of the square of a positive number gives the original number.
Using Prime Factorization:
The first step in this method is to find the prime factors of 80.
80 = 2 × 2 × 2 × 2 × 5
To find the root from here, we can simplify this to
√80 = √(2 × 2 × 2 × 2 × 5)
√80 = 4√5
We can either leave it at this or find the root of 5 which is 2.23 and simplify further.
Hence, Square Root of 80 = 4√5 ≅ 8.92.
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Herb and Marci Jordan obtained an installment loan that has a 10% APR to purchase a dishwasher that sells for $699. 95. They agree to make a down payment of 20% and to make 12 monthly payments. What is the finance charge?
$699.95×20%=$139.99, is the finance charge.
What is finance charge?A finance charge is any fee that reflects the cost of credit or borrowing under American law.
Some forms of credit have fees and interest that accrue over time. [1] In addition to interest, it also includes additional costs, like those for financial transactions.
The Truth-in-Lending Act and Regulation Z, which were issued by the Statutory Reserve Board, contain information about the federal definition of a finance charge.
A financing charge in personal finance is just the cash amount paid to borrow money, whereas interest is the amount paid as a percentage, such as the annual percentage rate (APR).
Compared to standard dictionary definitions or accounting definitions, these definitions are more specific.
Lenders and creditors both calculate finance charges in different ways. a majority.
Hence, $699.95×20%=$139.99, is the finance charge.
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A company manufactures water bottles. The list below describes the number of water bottles manufactured in three months.
• February: 4, 100 water bottles
• March: 7% more water bottles in February
• April: 500 more water bottles in March
What is the percent change, to the nearest percent, in the number water bottles the company manufactured from February to April. show your work
Answer:
19%
Step-by-step explanation:
You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.
ChangeThe change from February to March is given as 7%.
The change from March to April is 500 bottles. In terms of the February quantity, this is ...
500/4100 × 100% ≈ 12.2%
Then the total of changes from February to April is ...
change = 7% +12.2% = 19.2% ≈ 19%.
The number of bottles manufactured increased by about 19% from February to April.
__
Additional comment
When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.
Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.
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Karima made 9 pairs of earrings in 9 hours. At this rate: How long will it take Karima to make 12 pairs of earrings?
Answer:
12 hours
Step-by-step explanation:
1 pair per hour ?
1) Is the pattern linear? If yes, state the initial value and constant rate
2) Is the pattern discrete or continuous? How can you tell
1. It can be piecewise linear; from x = 1 to x = 4, the y-value increases by the same amount each time. From x = 0 to x = 1, the y-value stays the same.
However, if it is supposed to be a single function, it would be non-linear because it changes slope.
2. It is discrete because there is no data between the points.
would somebody be nice enough to help me with this? i’m confused
The triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
What is the Angle-Angle similarity theorem of triangles?
The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In the given figure,
In ΔPQR and ΔPXY
∠P ≅ ∠P ----- Common Angle
∠PQR ≅ ∠PXY ----Corresponding angles.
So, ΔPQR ~ ΔPXY -----(AA test)
Hence, the triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 3. If there were 4296 total votes, how many no votes were there?
Answer: 1611 no votes
Explanation:
4296/8=537
537*3=1611
Which of the following is a point on the line defined by the parametric equations below?
[x(t)=t+7
y(t) = 5-2t
○ (3,10)
○ (7,0)
O (8,3)
O (2,1)
The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.
What is an example of a parametric equation?Well, a parametric equation is an equation where the variables (usually x and y) are expressed in terms of a third parameter, usually expressed as t. For example: Consider the equation of a circle with radius r and center at (0,0) : x2+y2=r2 x 2 + y 2 = r 2 .parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable. More than one parameter can be employed when necessary.If there are m free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors: x = s1v1 + s2v2 + ··· + smvm. This is called a parametric equation or a parametric vector form of the solution.Types of Parametric test–
Two-sample t-test.Paired t-test.Analysis of variance (ANOVA)Pearson coefficient of correlation.To learn more about parametric refer to:
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a test consists of 10 true/false questions. if a student guesses on each question, what is the probability that thestudent will answer at least7questions correctly.
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
A test consists of 10 true/false questions.
If a student guesses on each question
The probability that the student will answer at least7questions correctly.
The probability that the student answers each question correctly is 1/2, and
The probability that the student answers each question correctly is also 1/2
{Bernoalli trail}
Bernoalli trail for at least 7 times,
Probability P = [tex]C7_{10} (\frac{1}{2}) ^{7} (\frac{1}{2}) ^{7}[/tex]
Using the formula nCr = n!(n−r)!r!
= 10!(10−7)!7!
Subtract 7 from 10.
= 10!(3)!7!
Simplify 10!(3)!7!.
Rewrite 10! as (10⋅9⋅8⋅7!)
= (10⋅9⋅8⋅7! / (3)!7!)
Cancel the common factor of 7!.
Cancel the common factor.
= 10⋅9⋅8⋅7! / (3)!7!
Rewrite the expression.
= 10⋅9⋅8 / (3)!
Multiply 10 by 9.
= 90⋅8 / (3)!
Multiply 90 by 8.
= 720 / (3)!
Expand (3)! to 3⋅2⋅1.
= 720 / 3⋅2⋅1
Multiply 3 by 2.
= 720 / 6⋅1
= 720 / 6
Divide 720 by 6
= 120
So,
We can write,
P = [tex]\frac{120}{2^{7} }[/tex]
P = [tex]\frac{120}{128}[/tex]
Therefore,
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
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There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer: x=5
Step-by-step explanation:
Answer:
(x - 1)² = 16
Step-by-step explanation:
x² - 2x - 15 = 0
x² - 2x + 1 = 15 + 1
(x - 1)² = 16
Find the 56th term of the following arithmetic sequence 7,10,13,16
The 56th term of the following arithmetic sequence 7,10,13,16 is 172.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given
Arithmetic sequence 7,10,13,16.
We have to find the 56th term.
The common difference between terms: 10 - 7 = 3
Using the arithmetic progression formula:
nth term = first term + (n-1)* common difference
56th term = 7 +(56-1) 3
56th term = 7 + 55×3
56th term = 7 + 165
56th term = 172
Hence, the 56th term of the following arithmetic sequence 7,10,13,16 is 172.
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Which table of values represents the equation y = 7x - 3?
The table of values which represent the equation y = 7x - 3 is: table D.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;
For ordered pair (-2, -1), we have:
y = 7x - 3
-1 = 7(-2) - 3
-1 = -14 - 3
-1 = -17 (False).
For ordered pair (-2, -19), we have:
y = 7x - 3
-19 = 7(-2) - 3
-19 = -14 - 3
-19 = -17 (False).
For ordered pair (-2, -15), we have:
y = 7x - 3
-15 = 7(-2) - 3
-15 = -14 - 3
-15 = -17 (False).
For ordered pair (-2, -17), we have:
y = 7x - 3
-17 = 7(-2) - 3
-17 = -14 - 3
-17 = -17 (True).
In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.
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Punch recipe. Orange juice, 3, 1/3. Grape juice six and 1/2. Cherry juice. 4 and 1/8. Club soda, one and 1/4. About how much fruit juice,(orange, grape, and cherry) is used in the punch.
answers.
11 cups
12 cups
13 cups
14 cups
Answer:
14 cups
Step-by-step explanation:
3 + 6 = 9
9 + 4 = 13
13 + 1 = 14
14 plus fraction
149 cars are waiting to take a ferry across the channel. Each ferry can only hold 18 cars. How many trips will it take to get all the cars across?
5
8
6
9
Answer: the answer is 8
Step-by-step explanation:
The Answer is: 8
Simply divide 149 by the numbers you see,
A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in: 8 ft. How tall is the model of the lighthouse in inches?
Answer:
The Answer is 20 inches tall
Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday. He also has a part-time job that pays $8 per hour. How many hours will he need to work to have $250 in his bank account?
Choose the equation that correctly models the situation. The letter h represents the hours Ike will need to work.
(250−126)h=20+8
126+20+8+250=h
126+20+8h=250
250+126+20=8h
Answer:
126+20+8h=250
Step-by-step explanation: