The lengths of the pieces are 1ft and 9ft
How to determine the length of sides
From the information given, we have that;
The shorter side = x
The longer side of the board = 6 +3x
The total length = 10
Substitute the values, we have;
x + 6 + 3x = 10
collect the like terms
x + 3x = 10 -6
Add or substract the like terms, we have;
4x = 4
Now, make 'x' the subject of formula by dividing by 4, we get;
4x/4 = 4/4
x = 1 ft
The longer side = 9ft
Hence, the values are 1 and 9
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Please help <3 I’d really appreciate it!! Algebra ll
a. The vertex form of its equation is, y = a(x-1)² + 16
b. The value of x is, 7
c. The equation of the axis of symmetry is, x = 1
d. The domain and range are respectively, all real values of x and y ≤ 16
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
a. The vertex form of a quadratic equation is given by y = a(x-h)²+ k, where (h, k) is the vertex of the parabola.
From the given information, we know that the vertex is at (1, 16), so the equation in vertex form is y = a(x-1)² + 16.
b. We are given that the parabola has one root at (-5, 0) and another root at (x, 0). Since the parabola is symmetric about the axis of symmetry, the x-coordinate of the vertex must be the midpoint of -5 and x. Using the midpoint formula, we get:
(-5 + x)/2 = 1
Solving for x, we get x = 7.
c. The axis of symmetry of a parabola is the vertical line that passes through the vertex. In this case, the vertex is at (1, 16), so the equation of the axis of symmetry is x = 1.
d. The domain of a quadratic function is all real numbers, since the function is defined for all values of x. The range of this function is y ≤ 16, since the vertex is at (1, 16) and the parabola opens downward.
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Hi I need help.
An education reform lobby is compiling data on the state of education in the United States. In their research they looked at the percent of people who graduate high school in 10 different states. The data are provided below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and the sample variance.
Round your answers to one decimal place.
High School Graduation Rate (%)
77.1
82.9
90
91.3
81.9
83.3
84.9
82.5
84.6
The sample variance and standard deviation are given as follows:
Variance = 87.22 %.
Standard deviation = 9.34%.
To obtain the variance and the standard deviation first, we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:
Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10
Mean = 75.85.
Then we must obtain the sum of the differences squared between each observation and the mean, as follows:
(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825
The sample variance is given by the above sum divided by one less than the sample size, hence:
Variance = 784.9825/9
Variance = 87.22 %.
The standard deviation is the square root of the variance, hence:
Standard deviation = sqrt(87.22)
Standard deviation = 9.34%.
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If $10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years? Round to the nearest dollar.
Please help!! Thank you!
Using angle relationships, the missing measures are:
m<3 = 138 degrees.
m<5 = 42 degrees.
m<8 = 138 degrees.
How to Find the Missing Angles?Using angle relationships, each of the measure of the angles can be calculated as follows:
Given that, m<1 = 138 degrees.
m<3 = m<1 [vertical angles are congruent]
Substitute:
m<3 = 138 degrees.
m<5 + m<3 = 180
Substitute:
m<5 + 138 = 180
m<5 = 180 - 138
m<5 = 42 degrees.
m<8 = m<3 [alternate interior angles are congruent]
m<8 = 138 degrees.
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2 brothers are to share $2600 in the following ratio 9:6 how much will each brother get ?
Answers
9x+6x=2600
15x=2600
x=520/3
9x=9×520/3=1560
6x=6×520/3=1040
The ratio of domestic cars to imported cars in the lot at Al’s Auto Shop is 3 : 2. There are 42 domestic cars in the shop. How many cars are there altogether?
There are 70 cars altogether in the lot.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of domestic cars to imported cars = 3 : 2,
Domestic cars = 42
Since, the number of domestic cars in the shop is 42,
Therefore,
3x = 42
x = 14
Therefore, the number of total cars = 14×5 = 70
Hence, there are 70 cars altogether in the lot.
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A disc is rolled thrice what is the probability
Probability of an event = (number of favorable event) / (total number of event).
P(B) = (Event B) / (total number of event).
Probability of getting 1 = 1/6.
Rolling dice is an independent event, it is not dependent on how many times it’s been rolled.
Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time.
Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.
Hence, the probability of getting 1 three times in a row is 0.463%.
Wesley has three different rectangular stickers. The red sticker is V2 cm
long and 1.5 cm wide. The green sticker is v12 cm long and 0.5 cm wide.
The yellow sticker is 3 cm long and 1.25 cm wide. Order the side lengths of
the stickers from greatest to least. Which sticker has the greatest area?
The order of the rectangular area from greatest to least is green sticker > yellow sticker > red sticker
What is the area of a rectangleThe area of a rectangle is calculated by multiplying its length by its width. So if the length of a rectangle is l and the width is w, then its area A is given by the formula A = l x w.
To solve this problem, we can find the area of each sticker one after the other.
Area = length * width
1. red sticker = 2 * 1.5 = 3cm²
2. green sticker = 12 * 0.5 = 6cm²
3. yellow sticker = 3 * 1.25 = 3.75cm²
The order is green sticker > yellow sticker > red sticker
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The smiths took out a $130,000, 30 year mortgage at an APR of 3.4%. The monthly payment was $576.53. What will be their total interest charges after 30 years?
The total interest charges after 30 years with an APR of 3.4 % is given by the equation A = $ 77,550.80
What is Annual Percentage Yield?The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.
Given data ,
Let the total interest charges after 30 years be represented as A
Now , the equation will be
The APR percentage = 3.4 %
The amount taken as loan = $ 130,000
The number of years = 30 years
The monthly payment = $ 576.53
The number of payments n = 30 x 12 = 360 payments
So , the total amount paid in 30 years = monthly payment x number of payments
Substituting the values in the equation , we get
The total amount paid in 30 years = 360 x 576.53
The total amount paid in 30 years = $ 207,550.80
Now , the total interest charges after 30 years A = total amount paid in 30 years - amount taken as loan
Substituting the values in the equation , we get
The total interest charges after 30 years A = $ 207,550.80 - $ 130,000
On simplifying the equation , we get
The total interest charges after 30 years A = $ 77,550.80
Hence , the interest charges after 30 years is $ 77,550.80
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The length of a rectangle is 4 in longer than its width. If the perimeter of the rectangle is 36 in, find its area.
A rectangle's length is 4 inches greater than its breadth.. If the perimeter of the rectangle is 36. Area will be 77[tex]cm^{2}[/tex].
Why isn't a rectangle a square?A quadrilateral with in all four of its angles being right angles is a rectangle. A quadrilateral with four right angles and four equal-length sides is called a square. As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides.As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides. Because a square is indeed a quadrilateral with in all four angles at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.
Finding the Area , we obtain:
Let the rectangle's breadth be x cm.
Its length is then x+4 cm.
According to the problem,
2{x+x+4}=36
or, 2x+4=18
or, x=7.
So, breadth is 7 cm and length is 11 cm.
So, the area is 7×11=77 [tex]cm^{2}[/tex].
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2x = 32 in y= mx +b form
The store you are buying the item down offers you an installment plan.
The terms of the contract for the plan are:
• $50 down
• 12 payments
• Finance charge of $100
Interest = Finance Charge = ________________
Total Payment = Cost of item + Finance charge = _____________
Monthly Payment = (Total Payment – Down payment / 12 = __________
1) Based on the percentage of the downpayment, the total payment made for the store item is $1,100, which includes a finance charge or interest of $100.
2) The monthly payment for 12 installments is $87.50.
How the total payment is computed:The total cost of the item is based on the downpayment's equivalent percentage (proportion).
A proportion is the equation of two or more ratios.
Finance Charge (Interest) = $100
Downpayment = $50 or 5%
Installment period = 12 months
Cost of item = $1,000 ($50/5%)
Total payment = $1,100 ($1,000 + $100)
Monthly payment = $87.50 ($1,100 - $50)/12
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Question Completion:The downpayment is 5% of the total cost of the item.
what is the least common denominator for 5/8, 7/20, and 7/13
Distance formula is D=~^ (X2-X1)*2 + (Y2- Y1)*2
pls help!
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad P2(\stackrel{x_2}{-3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~-3 - 6~~)^2 + (~~5 - 3~~)^2} \implies P1P2=\sqrt{( -9 )^2 + ( 2 )^2} \\\\\\ P1P2=\sqrt{ 81 + 4 } \implies P1P2=\sqrt{ 85 }[/tex]
BC is tangent to circle A at B and to circle D at C
AB=9, BC=26, DC=8
Find AD
The value of AD is 26.
How to solve thisThere are two circles with centers A and D.
The tangent line touches both points B and C.
The given measurements are enough to solve for the missing value and the solution is shown below:
AB=9BC=26DC=8Solve for the measurement of AC which the hypotenuse of legs AB and BC by Pythagorean theorem:
c²=a²+b²c²=9²+26²c=AC=27.51Solve for angle of A
sin A=26/27.51
A=70.93°
Finally, we solve for the length of AD using SOH
sin 70.93°=AD/27.51
AD=26
The answer is 26.
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Help me with this question…….
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets solve ~
[tex]\qquad \sf \dashrightarrow \: {x}^{2} = 10[/tex]
[ taking square root on both sides ]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} } = \sqrt{10} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \pm \sqrt{10} [/tex]
Both the values are appropriate here, as the square of both negative or positive value is same [positive value]
[tex] \huge\bold \large \bf{Solution }[/tex]
[tex] \rightarrow \large \displaystyle \sf \: {x}^{2} = 10 \: [/tex]
Transposing square on RHS , We get
[tex]\rightarrow \large \displaystyle \sf \: x \: = \sqrt{10} [/tex]
We know that,
10 does not even have a square root , so,
[tex]\rightarrow \large \displaystyle{\bf{ \pink{x \: = \pm \: \sqrt{10} }}}[/tex]
We know that the value of root is both negative and positive.
Option b is correct answer[tex] \purple {\rule{190pt}{4pt}}[/tex]
Statesvilles population in 2010 was about 24800 and was growing about 1.2% each year. If this continues, what will statesvilles population be in 2015?
yearly multiplication growth factor is (1+0.011) = 1.011. the year 2017, seven years after 2010, the population will be [tex]24800*2A1.011^7 = 26,774[/tex]
what is multiply ?
Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.
yearly multiplication growth factor is (1+0.011) = 1.011.
the year 2017, seven years after 2010, the population will be [tex]24800*2A1.011^7 = 26,774[/tex]
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A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited students to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of 10 words that were on the original list. Students were also asked to provide their Verbal SAT scores.
Consider the following (incomplete) grouped frequency distribution table that summarizes the data on five Verbal SAT score intervals collected from students who volunteered in 2009.
Grouped Frequency Distribution Table for Verbal SAT Score
Verbal SAT Score
f
cf
c%
700–800 17 60 100
600–699 22
500–599 15
400–499 4 6 10
300–399 2 2 3
What is the total number of scores in the data set?
Use the dropdown menus to complete the table by filling in the missing cumulative frequencies (cf) and cumulative percentages (c%).
On solving the provided question, we can say that The percentage (P) = 34%
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviations "pct.," "pct," and "pc" are alsο οccasionally used. It is frequently denoted using the percent symbοl "%," though. The amount of percentages has nο dimensions. With a denominatοr of 100, percentages are basically fractiοns.
To shοw that a number is a percentage, place a percent symbοl (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To cοmpute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
the total frequency:
Total = 29+53+50+22+1
Total = 155
The proportion (p)
p = f/total
The percentage (P)
P = p × 100
P =0.34 × 100 = 34%
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A man is considering two companies from which to rent a truck. Triangle Truck Rental charges $35 per day and 50 cents a mile. Circle Rent-A-Truck charges $55 a day
and 30 cents a mile. How far would he need to drive in one day for the both companies to have the same total cost?
How many miles would he need to drive in the day?
____ miles
Answer:
10 miles
Step-by-step explanation:
Let's call the number of miles driven in a day "x". The total cost for Triangle Truck Rental can be expressed as:
Cost (Triangle) = $35 + 0.5x
The total cost for Circle Rent-A-Truck can be expressed as:
Cost (Circle) = $55 + 0.3x
We want to find the value of x such that Cost (Triangle) = Cost (Circle). So we can set the two expressions equal to each other and solve for x:
$35 + 0.5x = $55 + 0.3x
0.2x = $20
x = 100 miles
So the man would need to drive 100 miles in one day for both companies to have the same total cost.
Find the center and radius! In standard form! ( Type an ordered pair)
Step-by-step explanation:
The center of the circle is (-2,-3)
The radius is 2 since the distance from the center to the point on the circle is 2
Therefore the standard equation is
[tex](x + 2) {}^{2} + (y + 3) {}^{2} = 4[/tex]
What is the driving time for a 1800-mile trip if you drive at an average speed of 45 miles per hour? What is the driving time at 69 miles per hour?
Answer:
40 hours
26.09 hours
Step-by-step explanation:
What is the driving time for a 1800-mile trip if you drive at an average speed of 45 miles per hour?
1800 / 45 = 40 hours
What is the driving time at 69 miles per hour?
1800 / 69 = 26.09 hours
Step-by-step explanation:
The driving time for a 1800-mile trip at an average speed of 45 miles per hour can be calculated as
Driving time = Total distance / Average speed
Driving time = 1800 miles / 45 miles per hour = 40 hours
Similarly, the driving time at an average speed of 69 miles per hour can be calculated as:
Driving time = 1800 miles / 69 miles per hour = 26 hours
So if you drive at an average speed of 45 miles per hour, the driving time for a 1800-mile trip would be 40 hours, and if you drive at an average speed of 69 miles per hour, the driving time would be 26 hours.
Eleven times the sum of a number and ten is 242. What is the number?
Point V is somewhere on the line segment . If UV = 8, then find the length of .
Answer:
it is 3
Step-by-step explanation:
just subtract
Decide which of the two given prices is better and explain why. Storage locker A rents for $33/yd^2 per month. Storage locker B rents for $1.49/ft^2 per week. (Assume 1 month=4 weeks.)
B is significantly more affordable and better than A, renting for $1.62 per square foot.
Yard and feet conversion:Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.
To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.
1 yard² = 9 feet²
A rents for $33 per yard squared
hence A rents $33 for 9 feet squared
hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared
Thus, as B is more economical, it is better.
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Figure ABCD is a kite. Find the
value of x.
A
B
D
x = [?]
AB = 4x
AD = x + 15
C
Answer:
x=5
Step-by-step explanation
4x=x+15
x=5
Answer:
Since ABCD is a kite, AB=AD and BC=CD
Given:
AB = 4x
AD = x + 15
equating both sides;
4x = x + 15
4x - x = 15
3x = 15
x = 15/3
x = 5
Select the correct definition of the standard error of the sample mean from the choices below. The standard error of the sample mean is Select O the standard deviation of the means of randomly drawn samples from the population. O the range of values above and belowO The sample statistic in a confidence interval. O the random and systematic errors that occur during data collection and analysis. O the probability distribution of the sample means. O rejecting the null hypothesis when it is true.
The standard error of a statistic or an estimate of a parameter is the standard deviation of its sampling distribution.
The standard deviation of the sample distribution is referred to as the standard error in statistics. In most cases, the sample mean of a data set differs from the actual population mean. SE is used to denote it. It is used to gauge how well a sample of a population represents that population. Data, samples and populations, means, medians and modes, dependent and independent variables, standard deviations, variance, and other concepts are all covered in the large field of statistics.
The standard error is one of the mathematical tools used in statistics to estimate variability. It is abbreviated as SE. The standard error of a statistic or an estimate of a parameter is the standard deviation of its sampling distribution. We can define it as an estimate of that standard deviation.
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Help me with this question
Answer
D. 4.2794....
Step-by-step explanation:
A, B, and C all have repeating decimal numbers, meaning they are rational. D's decimals are not repeating but infinite, meaning it is an irrational number.
Together, Steve and Tom sold 125 raffle tickets for their school. Steve sold 17 more than three times as many raffle tickets as Tom. How many raffle tickets did each boy sell?
Tom sold 27 raffle tickets and Steve sold 98 raffle tickets.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
Together, Steve and Tom sold 125 raffle tickets for their school.
Steve sold 17 more than three times as many raffle tickets as Tom.
Let s be the number of raffle tickets sold by Steve and t be the raffle tickets sold by Tom.
So,
3t + 17 + t = 125
4t = 108
t = 27
And s = 98
Therefore, Steve sold 98 and Tom sold 27 tickets.
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Find an equation for the line that passes through the points (-1, 4) and (-5, 6).
The equation of line is y = ( -1/2 )x + 7/2 , where the slope is m = -1/2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -1 , 4 )
Let the second point be Q ( -5 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - 4 ) / ( -5 - ( - 1 ) )
Slope m = 2 / ( -5 + 1 )
Slope m = -2/4 = -1/2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 4 = ( -1/2 ) ( x + 1 )
On simplifying the equation , we get
y - 4 = ( -1/2 )x - 1/2
Adding 4 on both sides of the equation , we get
y = ( -1/2 )x + 7/2
Hence , the equation of line is y = ( -1/2 )x + 7/2
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Bodmas sums
2.4of4.5-5.6/1.4+3.8*2
On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4
what is BODMAS ?The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.
By BODMAS
2.4of4.5-5.6/1.4+3.8*2
10.8-5.6/1.4+3.8*2
10.8-4+3.8*2
10.8-4+7.6
14.4
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