Given statement solution is :- The average hotel room cost in 2012 would be $199.97, none of the provided options are correct.
To calculate the average hotel room cost in 2012, we can use the formula:
y = a(1 + r)^t
where:
y = future value (cost in 2012)
a = initial value (cost in 1980)
r = annual growth rate (5.1% or 0.051)
t = number of years (2012 - 1980 = 32)
Substituting the given values into the formula, we have:
y = $48.00(1 + 0.051)^32
Calculating the value:
y ≈ $48.00(1.051)^32
y ≈ $48.00(2.718282)^0.051(32)
y ≈ $48.00(2.718282)^1.632
y ≈ $48.00 * 4.171331
y ≈ $199.97
Rounding to the nearest cent, the average hotel room cost in 2012 would be $199.97.
Therefore, none of the provided options are correct.
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Use mid segment formula to find
a) x=
b) EF=
c) BC=
A
E
B
لی
3
D
4x+6
9x+4
F
Answer:
x = 5EF = 26BC = 49Step-by-step explanation:
Given midsegment EF = (4x+6) and base segment BC = (9x+4) of a trapezoid with base AD = 3, you want the value of x and the lengths of the two segments EF and BC.
MidsegmentThe midsegment parallel to the base segment is the average of the lengths of the parallel bases.
4x +6 = 1/2((9x +4) +3))
8x +12 = 9x +7 . . . . . . . . . multiply by 2 and simplify
5 = x . . . . . . . . . . . . subtract 8x+7
SegmentsUsing this value of x, we find the lengths of the segments to be ...
EF = 4·5 +6 = 26
BC = 9·5 +4 = 49
Check(BC +AD)/2 = EF
(49 +3)/2 = 52/2 = 26 . . . . as required
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HELP! Can someone please help with the picture question below?
The probability that either event A or B will occur is 11/17.
We have,
The Addition Rule for Probability:
P(A U B) = P(A) + P(B) - P(A ∩ B),
where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.
Now,
P(A) = 9/17
P(B) = 2/17
There is no intersection of Q and B so,
P(A ∩ B) = 0
Now,
P(A U B) = P(A) + P(B) - P(A ∩ B),
Substituting the values.
P(A U B) = The probability that either event A or B will occur.
So,
P(A U B)
= 9/17 + 2/17 - 0
= 11/17
Thus,
The probability that either event A or B will occur is 11/17.
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Factor 6a² - 12a - 5a + 10 by grouping.
O (6a - 5)(a + 2)
(6a - 5)(a - 2)
(6a + 5)(a + 2)
-
O (6a + 5)(a − 2)
Answer: Therefore, the correct factorization by grouping is (a - 2)(6a - 5).
Step-by-step explanation:
To factor 6a² - 12a - 5a + 10 by grouping, we can group the terms in pairs:
6a² - 12a - 5a + 10
Taking common factors from the first two terms and the last two terms separately:
6a(a - 2) - 5(a - 2)
Now, we can see that (a - 2) is common in both terms, so we can factor it out:
(a - 2)(6a - 5)
Hello!
6a² - 12a - 5a + 10
= 6a² - 17a + 10
= 6a² - 5a - 12a + 10
= (6a² - 5a) + (-12a + 10)
= a(6a - 5) - 2(6a - 5)
= (6a - 5)(a - 2)
In a sample of 560 adults, 336 had children. Construct a 95% confidence interval for the true population proportion of adults with children.
Give your answers as decimals, to three places
< p <
What is the expected value of �?
The confidence interval is 0.559 < p < 0.641 and expected value is 0.600
Confidence IntervalTo construct a confidence interval for the true population proportion, we can use the formula:
p ± Z * √((p × (1 - p)) / n)
Where:
p = sample proportion (336/560)
Z = critical value for the desired confidence level
95% confidence = Z-value of approximately 1.96
n = 560
Let's calculate the confidence interval:
p = 336/560 ≈ 0.600
Z ≈ 1.96 (for a 95% confidence level)
n = 560
Plugging these values into the formula:
p ± Z × √((p × (1 - p)) / n)
0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)
0.600 ± 1.96 × √((0.240) / 560)
0.600 ± 1.96 × √(0.0004285714)
0.600 ± 1.96 × 0.020709611
0.600 ± 0.040564459
The confidence interval is:
0.559 < p < 0.641
Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.
The expected valueFor proportions, the expected value is simply the sample proportion, which is approximately 0.600.
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Multiply: (Hint - use one of the formulas)
(5m² - 3)²
The simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.
Given is an expression (5m² - 3)², we need to simplify the expression,
To multiply the expression (5m² - 3)², we can use the formula for squaring a binomial:
(a - b)² = a² - 2ab + b²
In this case, a = 5m² and b = 3.
Substituting these values into the formula, we get:
(5m² - 3)² = (5m²)² - 2(5m²)(3) + (3)²
= 25m⁴ - 30m² + 9
Therefore, the simplified form of (5m² - 3)² is 25m⁴ - 30m² + 9.
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What is the answer pls
Last year, 5 friends went to the beach. They each drank the same number of canned drinks and had 2 drinks left over. 2 friends could not come to the beach this year. The others brought the same number of drinks as last year and each drank equally as much as the year prior, this time ending with 8 drinks left over. How many beverages did each friend drink?
Each friend drank a total of 3 beverages during their visit to the beach.
Numerical calculationTo find the number of beverages each friend drank, let's assume the number of drinks they brought and consumed this year is represented by 'x'.
From the given information, we can set up the following equations:
Last year:
5x + 2 = Total number of drinks (equation 1)
This year:
3x + 8 = Total number of drinks (equation 2)
Since the total number of drinks should be the same in both years, we can set equation 1 equal to equation 2:
5x + 2 = 3x + 8
Now, let's solve this equation to find the value of 'x':
5x - 3x = 8 - 2
2x = 6
x = 3
So, each friend drank 3 canned drinks both last year and this year.
Therefore, each friend drank 3 beverages.
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factored form of 12a-b
The factored form of the expression 12a - b is simply 12a - b.
We have,
The concept used in the expression 12a - b is that of combining like terms. When we have an algebraic expression like this, the goal is typically to simplify or rewrite it in a more concise form.
In this case, 12a and -b are two terms in the expression.
The concept of combining like terms allows us to combine these terms together if they have the same variable(s) raised to the same power(s).
The expression 12a - b cannot be factored further using simple algebraic techniques.
Factoring typically involves breaking down an expression into its constituent factors, such as common factors or binomial factors.
However, in the case of 12a - b,
There are no common factors or binomial factors that can be extracted.
Therefore,
The factored form of the expression 12a - b is simply 12a - b.
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4(-2)² + 8(-2) + 3(-2) + 6 = ? Can you break down how you solved it
Answer:
Step-by-step explanation:
To solve the expression 4(-2)² + 8(-2) + 3(-2) + 6, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
First, we will simplify any calculations within parentheses:
4(-2)² + 8(-2) + 3(-2) + 6
(-2)² is equal to (-2) * (-2), which is 4:
4 * 4 + 8(-2) + 3(-2) + 6
Next, we perform the multiplication:
4 * 4 = 16
Now, we have:
16 + 8(-2) + 3(-2) + 6
Next, we continue with the multiplication:
8(-2) = -16
3(-2) = -6
Now, we have:
16 + (-16) + (-6) + 6
Finally, we simplify the addition and subtraction from left to right:
16 + (-16) = 0
0 + (-6) = -6
-6 + 6 = 0
Therefore, the expression 4(-2)² + 8(-2) + 3(-2) + 6 simplifies to 0.
PLEASE HELP ME ANSWER THIS QUESTION I REALLY NEED IT
The radius 5cm, of a sphere increases at the rate of 0.4 cm/s. At what rate will the area be increasing?
a) 40 pi cm^2/s b) 24 pi cm^s/ s c) 16 pi cm^2/ s d) 10 pi cm^2/ s
The rate at which the surface area of the sphere is increasing is 16π cm^2/s.(option-c)
To find the rate at which the area of a sphere increases when its radius is increasing at a given rate, we can use the formula for the surface area of a sphere, which is A =[tex]4πr^2[/tex], where r is the radius of the sphere and A is its surface area. We can then differentiate this with respect to time t to find the rate of change of area with respect to time, which is given as dA/dt.
Given that the radius of the sphere increases at the rate of 0.4 cm/s, we can find the rate of change of area as follows:
- Differentiate the surface area formula with respect to time t:
dA/dt = d/dt [tex](4πr^2)[/tex]
- Use the chain rule to differentiate[tex]r^2[/tex]with respect to time t:
d/dt (r^2) = 2r (dr/dt)
- Substitute the value of dr/dt given as 0.4 cm/s, and the radius value as 5 cm:
dA/dt = 4π(5)^2 (2 × 0.4)
- Simplify the expression to get the rate of change of area with respect to time:
dA/dt = 16π [tex]cm^2/s[/tex]
(option-c)
Find the difference by subtracting the second polynomial from the first.(11m^(2)n^(5)-3m^(2)n^(3)+5mn-n ) and (-6m^(2)n^(5)+3m^(2)n^(5)+m+2n )
The difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
To subtract the second polynomial from the first polynomial, we need to perform term-wise subtraction. Let's break down the process step by step:
The first polynomial is: 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n.
The second polynomial is: -6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n.
To subtract the second polynomial from the first, we need to change the signs of all terms in the second polynomial and then combine like terms.
First, let's change the signs of the terms in the second polynomial:
-(-6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n) = 6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n.
Now, we can combine like terms by adding or subtracting coefficients of similar monomials:
(11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n) - (6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n)
= 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n - 6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n
= (11m^(2)n^(5) - 6m^(2)n^(5)) + (-3m^(2)n^(3) + 3m^(2)n^(5)) + (5mn + m) + (-n + 2n)
= 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
Therefore, the difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
In summary, to find the difference, we changed the signs of all terms in the second polynomial and then combined like terms with the first polynomial. The resulting polynomial is the difference between the two original polynomials.
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HELP WTH IS THIS PLSSS HAVE FIND K
[tex]-16=k\cdot2^2\\4k=-16\\k=-4[/tex]
2. The area of a figure is 207 m². If the
dimensions are multiplied by what will
be the area of the new figure?
PLEASE HELP REALLY IMPORTANT The price of a container of laundry detergent (in dollars)
varies with the size (x) of the container (in pounds). The
variables have a strong linear correlation and the equation
for the least squares regression line is y^= 0.86x + 0.52
Based on the regression equation, which is the best
prediction for the price of a 70-pound container of detergent?
$70
$86
$65
$60
Answer:
$60
Step-by-step explanation:
Based on the regression equation, the best prediction for the price of a 70-pound container of detergent can be found by substituting x = 70 into the equation:
y^ = 0.86x + 0.52
y^ = 0.86(70) + 0.52
y^ = 60.2 + 0.52
y^ ≈ $60.72
Therefore, the best prediction for the price of a 70-pound container of detergent is approximately $60.72. However, since we are dealing with prices, it is reasonable to round this value to the nearest dollar, which would be $61. But since none of the answers are 61 it would be $60.
3.2 The line drawn from the midpoint of the one side of a triangle, parallel to the second side, ... ACS is a triangle. P is a point on AS and R is a point on AC such that PSRQ is a parallelogram. PQ intersects AC at B such that B is the midpoint of AR. QC is joined. Also, CR-PS, C, -50° and BP- 60 mm. C 2 R 3 2 B/3 2 3.2.1 Calculate the size of A 3.2.2 Determine the length of QP. 2 1 P 2 (5) (3) [9]
The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).
To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using this formula, we can find the coordinates of P and Q as follows:
Coordinates of midpoint P:
P = ((2 + (-3)) / 2, (-1 + 4) / 2)
= (-1/2, 3/2)
Therefore, the coordinates of midpoint P are P(-1/2, 3/2).
Coordinates of midpoint Q:
Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)
= (-3/2, -4)
Therefore, the coordinates of midpoint Q are Q(-3/2, -4).
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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)
What is a cash cycle? explain. calculate using the following information. (assume 360 days in a year). opening balances raw material 1,00,000 wip 45,000 finishes goods 1,35,000 debtors 6,00,000 creditors 8,60,000 closing balances raw material 2,00,000 wip 65,000 finishes goods 1,25,000 debtors 5,45,000 creditors 9,75,000 costs incurred during the year manufacturing costs 11,60,000 excise duty 18,80,000 selling and distribution expenses 6,20,000 admin. overheads 2,00,000 total sales 2,01,96,800 total purchases 1,46,00,000 40% of sales are on credit and 70% of purchases are on credit
The cash cycle, also known as the operating cycle or cash conversion cycle, is a financial metric that measures the time it takes for a company to convert its investments in inventory and other resources into cash flow from sales. It provides insight into the efficiency of a company's working capital management.
The cash cycle can be calculated using the following formula:
Cash Cycle = Inventory Conversion Period + Receivables Conversion Period - Payables Conversion Period
1. Inventory Conversion Period (ICP):
ICP measures the average number of days it takes for the company to convert its raw materials into finished goods. It is calculated as:
ICP = (Average Inventory / Cost of Goods Sold) x Number of Days in a Year
Average Inventory = (Opening Inventory + Closing Inventory) / 2
Cost of Goods Sold = Total Sales - Closing Inventory
2. Receivables Conversion Period (RCP):
RCP measures the average number of days it takes for the company to collect payment from its customers. It is calculated as:
RCP = (Average Receivables / Total Sales) x Number of Days in a Year
Average Receivables = (Opening Receivables + Closing Receivables) / 2
Opening Receivables = Total Sales x Percentage of Sales on Credit
Closing Receivables = Total Sales x Percentage of Sales on Credit - Collections
3. Payables Conversion Period (PCP):
PCP measures the average number of days it takes for the company to pay its suppliers. It is calculated as:
PCP = (Average Payables / Total Purchases) x Number of Days in a Year
Average Payables = (Opening Payables + Closing Payables) / 2
Opening Payables = Total Purchases x Percentage of Purchases on Credit
Closing Payables = Total Purchases x Percentage of Purchases on Credit - Payments
Now, let's calculate the cash cycle using the provided information:
Given data:
Opening balances:
Raw material: ₹1,00,000
WIP: ₹45,000
Finished goods: ₹1,35,000
Debtors: ₹6,00,000
Creditors: ₹8,60,000
Closing balances:
Raw material: ₹2,00,000
WIP: ₹65,000
Finished goods: ₹1,25,000
Debtors: ₹5,45,000
Creditors: ₹9,75,000
Costs incurred during the year:
Manufacturing costs: ₹11,60,000
Excise duty: ₹18,80,000
Selling and distribution expenses: ₹6,20,000
Admin. overheads: ₹2,00,000
Total sales: ₹2,01,96,800
Total purchases: ₹1,46,00,000
Percentage of sales on credit: 40%
Percentage of purchases on credit: 70%
1. Calculate the Inventory Conversion Period (ICP):
Average Inventory = (Opening Inventory + Closing Inventory) / 2
Opening Inventory = Raw Material + WIP + Finished Goods
Closing Inventory = Raw Material + WIP + Finished Goods
Opening Inventory = ₹1,00,000 + ₹45,000 + ₹1,35,000 = ₹2,80,000
Closing Inventory = ₹2,00,000 + ₹65,000 + ₹1,25,000 = ₹3,90,000
Average Inventory = (₹2,80,000 + ₹3,90,000) / 2 = ₹3,35,000
Cost of Goods Sold = Total Sales - Closing Inventory
Cost of Goods Sold = ₹2,01,96,800 -
Austin, Texas has a statue of Stevie Ray Vaughn that is 12 feet tall. It cast an 8 ft shadow. Doug stops to admire the statue. Doug's shadow is 3.5 ft. How tall is Doug?
Answer:
5.25 feet tall
Step-by-step explanation:
Doug's height / Doug's shadow = Statue's height / Statue's shadow
x / 3.5 = 12 / 8
Cross-multiplying:
8x = 3.5 * 12
8x = 42
Dividing both sides by 8:
x = 42 / 8
x ≈ 5.25
if the percentage difference was 34.846% and the number of voters were 3066649 in 2016, calculate the number of registered voters (A) in 2011
Answer:
Step-by-step explanation:
A shop has jars of strawberry jam and raspberry jam in the ratio 3:1
Two customers come into the shop and randomly select a jar of jam
to purchase.
The probability that both customers select strawberry jam is 11/20
a) How many jars of jam does the shop have initially?
b) Given that the customers both chose the same type of jam, work
out the probability that they both chose strawberry.
The shop initially has 0.884 jars of jam
The probability that both customers chose strawberry jam, is 0.25.
a) Let's assume the number of jars of strawberry jam is 3x and the number of jars of raspberry jam is x.
So, the total number of jars of jam in the shop is 3x + x = 4x.
According to the given information, the probability that both customers select strawberry jam is 11/20.
So, the probability of the first customer selecting a jar of strawberry jam = (3x/4x) = 3/4,
and the probability of the second customer
= ((3x-1)/(4x-1)).
Now, (3/4) ((3x-1)/(4x-1)) = 11/20
(3/4) ((3x-1)/(4x-1)) = 11/20
20(3/4) ((3x-1)/(4x-1)) = 11
15 (3x-1) = 44 (4x-1)
45x - 15 = 176x - 44
176x - 45x = 44 - 15
131x = 29
x ≈ 29/131
Therefore, the value of x is 0.221
To find the initial number of jars of jam in the shop, we can substitute this value of x into the equation:
4x = 0.884
b) The probability of the first customer selecting strawberry jam is
= (3x)/(4x)
= 3/4.
Therefore, the probability that both customers chose strawberry jam is:
= (3/4) x ((3x-1)/(4x-1))
= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))
= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))
≈ 0.25
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La ganancia obtenida después de t años de
haber realizado una inversión inicial de
$1.000.000 está dada por la expresión:
1.000.000 × 2t
¿Qué representa el número 2 en la
expresión anterior?
A)las ganancias obtenidas en el segundo año
B)las ganancias obtenidas en el último año
C) que cada nuevo año las ganancias se reducen a la mitad
D) que cada nuevo año las ganancias se duplican con respecto al año anterior
In the given expression, "2" represents that each new year the profits double with respect to the previous year. So the correct answer is D) that each new year the profits double with respect to the previous year.
How to explain the expressionIn the given expression, the variable "t" represents the number of years that have passed since the initial investment was made. The expression 1,000,000 × 2t calculates the profit obtained after "t" years.
Therefore, the correct answer is D) that each new year the profits double with respect to the previous year.
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The profit obtained after t years of
have made an initial investment of
$1,000,000 is given by the expression:
1,000,000 × 2t
What does the number 2 represent in the
previous expression?
A) the profits obtained in the second year
B) the profits obtained in the last year
C) that every new year the profits are cut in half
D) that each new year the profits double with respect to the previous year
Mis disculpas por la respuesta anterior, cometí un error en la explicación. La respuesta correcta es la opción D. La expresión 1.000.000 × 2t indica que cada nuevo año las ganancias se duplican con respecto al año anterior.
En la expresión, el número 2 indica que las ganancias se duplican cada año con respecto al año anterior. La expresión 1.000.000 × 2t significa que la inversión inicial de un millón de dólares se multiplica por 2 elevado a la potencia de t, donde t es el número de años que han pasado.Cuando t=1, se refiere al primer año después de la inversión, y la ganancia sería 1.000.000 dividido por 2=1, es decir, dos millones. Esto significa que las ganancias del segundo año (opción A) serían de 2.000.000 de dólares.En general, las ganancias del año anterior se duplican cada año subsiguiente. Por lo tanto, la D es la opción correcta porque significa que las ganancias se duplican cada año con respecto al año anterior.
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Calculate the 2022 Horizontal Analysis variance of “Sales Revenue” in %. Fill in the equations using the financial statements provided (no symbols or commas) and the % should be in a XX.XX format:
Step 1: Blank 1; – Blank 2; = Blank 3;
Step 2: Blank 4; ÷ Blank 5; = Blank 6 %
Blank 1
Add your answer
Blank 2
Add your answer
Blank 3
Add your answer
Blank 4
Add your answer
Blank 5
Add your answer
Blank 6
The horizontal variance of sales between 2021 and 2022 is 340
How did we arrive at this?
By removing the sales figure of 2021 from that of 2022, we are able to arrive at the above figure.
That is Amount of 2022 – Amount of 2021 = Absolute Change.
Figure for 2022 = 3800
Less
Figure for 2021 = 3,460
Variance 340
Excel formula : = Cell no. of amount of 2022 - Cell no of amount of 2021
Note that a negative amount means decrease and positive amount means increase.
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Please help!
flynn is playing with a toy that is tied to his hand by a string. the toy falls toward the floor then risee back towards flynns hand, and repeats this motion, following the path illustrated by the given graph. (see pic)
use the graph to complete the function h(t) that models the toys height, in feet, above the floor t seconds after it has left flynns hand.
h(t)=____ (poss. answers- 2, 1.75, 3.5, 4) cos=(____pi^t) poss. answers- 6, 1/6, 1/3, 3)
+_____ (poss. answers- 1.75, 0.25, 2, 2.25)
Answer:
h(t) = 1.75 cos (π/6) + 2.25
Step-by-step explanation:
the amplitude of a regular cos graph is 1 (it alternates between +1 and -1 on the y-axis). that is, amplitude = (1 - -1)/2 = 2/2 = 1.
this graph has amplitude (4 - 0.5)/2 = 3.5/2 = 1.75.
the graph repeats for every sixth value on the x-axis (time axis).
in the x-axis direction, a cos graph that becomes 6 times larger is cos (π/6). a cos graph that becomes 6 times smaller is cos (6π).
so for our graph, it is cos (π/6).
what about the y-shift?
the graph has already been enlarged 1.75 times parallel to the y-axis.
it crosses the y-axis at 4. so the y-shift is 4 - 1.75 = 2.25.
so our graph is given by h(t) = 1.75 cos (π/6) + 2.25
Answer: got it right
h(t)=1.75, cos(1/3), + 2.25
Step-by-step explanation:
Simplify the following expression:
(8t − 6t2) + 14(3t + 4)
After simplifying, what number is multiplied by the t?
We can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.
To simplify the given expression (8t - 6t^2) + 14(3t + 4), we first need to apply the distributive property by multiplying 14 with both terms inside the parentheses. This gives us:
8t - 6t^2 + 42t + 56
Now, we can combine like terms by adding the coefficients of the t and t^2 terms. The t^2 term has a coefficient of -6, and there are no other t^2 terms in the expression, so we can just bring it down as it is. The t term has a coefficient of 8 + 42 = 50, so we can simplify the expression further as:
-6t^2 + 50t + 56
From this expression, we can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.
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What are the exact solutions of x2 - 5x-7= 0, where
Ox=
O
x=
X
H
-5± √3
2
5+√3
2
-5± √53
2
5± √53
2
X=
-b± √b²-4ac7
2a
Hello!
it's a quadratic equation
x = (-b ± √(b² - 4ac))/2a
= (-(-5) ± √((-5)² - 4*1*(-7)))/(2*1)
= (5 ± √(25 + 28))/2
= (5 ± √53)/2
Hello !
Answer:
[tex]\large \boxed{\sf x= \dfrac{5\pm\pl\sqrt{53}}{2} }[/tex]
Step-by-step explanation:
This equation is a quadratic equation in the form ax²+bx+c=0
The solution of this equation is given by the quadratic formula :
[tex]\sf x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here we have :
a = 1b = +5c = -7Let's replace a, b and c with their values in the quadratic formula :
[tex]\sf x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\times1\times(-7)}}{2\times 1} \\\sf x= \dfrac{5\pm\pl\sqrt{25+28}}{2} \\\boxed{\sf x= \dfrac{5\pm\pl\sqrt{53}}{2} }[/tex]
Have a nice day ;)
Solve the system with elimination.
-2x + 7y =10
x - 3y = -3
Answer:
x = 9 and y = 4
Step-by-step explanation:
-2x + 7y = 10 (call this equation '1')
x - 3y = -3 (call this '2')
multiply '2' by 2:
2x - 6y = -6 (call this '3')
add '1' and '3':
(-2x + 7y = 10) + (2x - 6y = -6)
0x + y = 4
y = 4
sub that back into '1':
-2x + 7y = 10
-2x + 7(4) = 10
-2x + 28 = 10
-2x = 10 - 28 = -18
x = -18/-2 = 9
sub both y = 4 and x =9 into '2' to check if everything adds up:
x - 3y = -3
9 - 3(4) = 9 - 12 = -3
so x = 9 and y = 4
NO LINKS!! URGENT HELP PLEASE!!!!
4. Use the theorems for interior and exterior angles of a polygon to find:
d. The interior angle of a regular 44-gon.
e. The number of sides in a regular polygon with an interior angle is 175°.
f. The exterior angle in a regular hexagon.
Answer:
d) 171.8°
e) 72
f) 60°
Step-by-step explanation:
Part dThe Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.
The number of sides of a 44-gon is n = 44. Therefore, the measure of its interior angle is:
[tex]\begin{aligned}\textsf{Interior angles of a 44-agon}&=\dfrac{(44-2) \cdot 180^{\circ}}{44}\\\\&=\dfrac{42\cdot 180^{\circ}}{44}\\\\&=\dfrac{7560^{\circ}}{44}\\\\&=171.8^{\circ}\;\sf(nearest\;tenth)\end{aligned}[/tex]
Therefore, the interior angle of a 44-gon is 171.8°.
[tex]\hrulefill[/tex]
Part eThe Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.
Given the interior angle of a regular polygon is 175°, then:
[tex]\begin{aligned} \textsf{Interior angle}&=175^{\circ}\\\\\implies \dfrac{(n-2) \cdot 180^{\circ}}{n}&=175^{\circ}\\\\(n-2)\cdot 180^{\circ}&=175^{\circ}n\\\\180^{\circ}n-360^{\circ}&=175^{\circ}n\\\\5^{\circ}n&=360^{\circ}\\\\n&=72\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 72.
[tex]\hrulefill[/tex]
Part fAccording the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.
Therefore, to find exterior angle of a regular hexagon, divide 360° by the number of sides:
[tex]\begin{aligned}\sf Exterior\;angle&=\dfrac{360^{\circ}}{\sf Number\;of\;sides}\\\\&=\dfrac{360^{\circ}}{6}\\\\&=60^{\circ}\end{aligned}[/tex]
Therefore, the exterior angle of a regular hexagon is 60°.
Answer:
4. a. 171.818°
b. 72 sides
c. 60°
Step-by-step explanation:
d. The interior angle of a regular polygon with n sides can be calculated using the formula:
[tex]\bold{Interior Angle =\frac{ (n-2) * 180\°}{n}}[/tex]
For a regular 44-gon, the interior angle would be:
[tex]\bold{Interior Angle =\frac{ (44-2) * 180\°}{44}=171.818^o}[/tex]
[tex]\hrulefill[/tex]
e. The number of sides in a regular polygon with an interior angle of 175° can be found using the formula:
[tex]\bold{n = \frac{360\° }{180\° - Interior \:Angle}}[/tex]
For an interior angle of 175°, the number of sides would be:
substituting Value,
[tex]\bold{n =\frac{ 360\° }{ 180\° - 175\°} = \frac{360\° }{ 5\° }= 72 \:sides}[/tex]
[tex]\hrulefill[/tex]
f.
The sum of the exterior angles of any polygon is always 360°.
Since a regular hexagon has six sides,
n=6
exterior angle would be [tex]\bold{\frac{360\° }{ n}}[/tex]
substituting value,
exterior angle=[tex]\bold{\frac{360\° }{ 6}=60\°}[/tex]
[tex]\hrulefill[/tex]
Tom buys 5 shirts for $10 total. He also buys shorts for
$4.50 each. What inequality represents the situation?
He only has $50 to spend/
A. 5x + 10 < 50
B. 4.50x + 5 < 10
c. 10+ 4.5x ≤ 50
d. 5x +4.5x < 50
Answer:
c
Step-by-step explanation:
we know he spends 10$ on shirts but not how much he spends on shorts. Since we know he has $50 to spend, we can buy shorts up to the $50 limit including $50. The only inequality that includes $50 is c
C, 10+ 4.5x ≤ 50
Happy to help, have a great day! :)
Apply the square root principle to solve (x – 2)^2 + 20 = 0.
Question 1 options:
A)
x = 2 + 2i , x = 2 – 2i
B)
x = –2 + 2i , x = –2 – 2i
C)
x = 2 + 2 , x = 2 – 2
D)
x = –2 + 2, x = –2 – 2
Answer:
швлалалаось.чллслслслсб вщлалс
A group of ten students recorded the number of minutes they spent on one math homework problem. The
mean amount of time was 9 minutes, but the MAD was 7 minutes.
Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label
your axis.
1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."
2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.
3. Plot a dot for each student's data point along the horizontal axis.
4. Arrange the dots in order from smallest to largest time spent on the problem.
5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."
6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)
To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:
The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.
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If the reliability is
r = 0.25,
the equation becomes
R(n) =
0.25n
0.75 + 0.25n
.
What percent improvement is there in the reliability when the test length is doubled?
The percentage improvement in reliability when test length is doubled is 15%
R(n) = 0.25n / (0.75 + 0.25n)
For a test length of 1substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(1) = 0.25(1) / (0.75 + 0.25(1))
R(1) = 0.25 / 1
R(1) = 0.25
For a test length of 2when test length is doubled , n = 2
substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(2) = 0.25(2) / (0.75 + 0.25(2))
R(2) = 0.5 / 1.25
R(2) = 0.4
Percentage improvement can be calculated thus ;
R(2)-R(1)/R(1) × 100%
(0.4-0.25)/0.25 × 100%
0.15 × 100%
=15%
Therefore, percentage improvement in reliability is 15%
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