The length of the springboard, x is 28.2. The correct option is (4).
We can say that the length of the springboard (x) is the hypotenuse of a right triangle, where the opposite side is the height of the spring (8 inches) and the angle opposite the height is 16.5 degrees.
Using trigonometry, we can write:
sin(16.5) = 8 / x
Multiplying both sides by x, we get:
x * sin(16.5) = 8
Dividing both sides by sin(16.5), we get:
x = 8 / sin(16.5)
Using a calculator, we can evaluate this expression to the nearest tenth of an inch as:
x ≈ 28.2
Therefore, the length of the springboard to the nearest tenth of an inch is approximately 28.2 inches. The answer is option (4).
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Pre-study scores versus post-study scores for a class of 120 college freshman English students were considered. The residual plot for the least squares regression line showed no pattern. The least squares regression line was y = 0.2 +0.9x with a correlation coefficient r = 0.76. What percent of the variation of post- study scores can be explained by the variation in pre-study scores? a. We cannot determine the answer using the information given. b. 76.0% C. 87.2% od. 52.0% .e.57.8%
Option B is the correct answer that is 76%. The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is 0.76, which indicates a moderately strong positive linear relationship between pre-study scores and post-study scores.
The coefficient of determination (r^2) is the proportion of the variation in the dependent variable (post-study scores) that can be explained by the independent variable (pre-study scores). It is calculated by squaring the correlation coefficient (r^2 = r^2).
So, in this case, r^2 = 0.76^2 = 0.5776. This means that 57.76% of the variation in post-study scores can be explained by the variation in pre-study scores. However, the question asks for the percentage of variation that can be explained by the independent variable, not the coefficient of determination. Therefore, the answer is b. 76.0%.
Option B is the correct answer of this question.
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for the following questions, supposeu=h1,0,1iandv=h2,2,0i.(a) (5 points) evaluate 2u v
2u v = 4, where vector u = (1,0,1) and v = (2,2,0) when eu=h1,0,1iandv=h2,2,0i.
To evaluate 2u v, we first need to find the scalar product (dot product) of u and v vector:
u · v = (h1,0,1i) · (h2,2,0i) = 1(0) + 0(2) + 1(2) = 2
Then, we can multiply this result by 2:
2u v = 2(u · v) = 2(2) = 4
Therefore, 2u v = 4.
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the yellow cab company charges a flat fee of $3.50 and an additional $2.50 per mile. the relaxicab company charge $2.30 per mile and a $4.54 fee. at how many miles do the two companies charege the same amount? write a system of equations that computes the cost of the cabs. use for the miles, and for the cost.
Step-by-step explanation:
Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.
Let x = distance (mile)
let y = total charge (dollars)
Yellowcab company equation for cost calculation; 3.50 + 2.5x = y
laxicab company equation for cost calculation; 4.54+2.3x = z
the two companies charge the same amount when y = z
; 3.50 + 2.5x = 4.54+2.3x
x = 5.2 miles
COST CALCULATION
;3.50 + 2.5x = ?
if x = 5.2;
; 3.50 + 2.5(5.2) =$16.50
OR
; 4.54+2.3x = ?
; 4.54 + 2.3(5.2) = $16.50
10. A cone has a Volume of 94.25cm ^ 3 If the radius of the cone is 3 cm, what is the height of the cone?
Answer:
10 cm
Step-by-step explanation:
V =1/3 x π x r² x h
94.25 =1/3 x π x 3² x h
94.25 ÷ 3π =h
so, h= 10 cm
Help I will be marking brainliest!!!
A. 2270 feet
B. 2548 feet
C. 4455 feet
D. 9813 feet
If you can, show work. Thanks❤️
How do you write 50% as a fraction?
Answer:
\(\frac{1}{2}\)
Step-by-step explanation:
Answer:
50% as a fraction would be 1/2
A square floor has a side length of 8xcubedysquared units. a square tile has a side length of xy units. how many tiles will it take to cover the floor
To cover the square floor with a side length of 8xcubedysquared units using square tiles with a side length of xy units, it will take (64xy^2)/(8xcubedysquared) tiles.
The area of the floor can be calculated by squaring the side length of the floor:
Area of the floor = (8xcubedysquared)^2 = 64x^2(cubedysquared)^2 = 64x^2(cubedysquared)(cubedysquared)
The area of each tile is given by squaring the side length of the tile:
Area of each tile = (xy)^2 = x^2y^2
To determine the number of tiles required to cover the floor, we divide the area of the floor by the area of each tile:
Number of tiles = (Area of the floor) / (Area of each tile) = (64x^2(cubedysquared)(cubedysquared)) / (x^2y^2) = (64xy^2) / (8xcubedysquared)
Thus, it will take (64xy^2)/(8xcubedysquared) tiles to cover the square floor.
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3x + 3 = 4 + x + (-1)
Answer:
x=0
Step-by-step explanation:
Answer:
x = 0
Step-by-step explanation:
3x+3=4+x-1
3x+3=x+4-1
3x+3=x+3
3x+3-3=x+3-3
3x=x
3x-x=x-x
2x=0
\(\frac{2x}{2}=\frac{0}{2}\)
x = 0
how The Marine Discovery Aquarium sells ocean-themed cookies in their gift shop. Last month, they sold 65 shark cookies and 85 clown fish cookies. The cookies were so popular that they want to order more cookies this month. They plan to order 170 clown fish cookies this month.
If they keep the same ratio, how many shark cookies should they order this month?
There are 130 shark cookies should they order this month.
We have to given that;
Last month, they sold 65 shark cookies and 85 clown fish cookies.
Hence, If they plan to order 170 clown fish cookies this month.
Then, Number of shark cookies should they order this month is, x
Hence, We get;
65 / 85 = x / 170
x = 130
Thus, There are 130 shark cookies should they order this month.
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Find the ratio 45 sec to 1 min
Answer:
3:4
Step-by-step explanation:
Paper Company receives a $4,700, 3-month, 11% promissory note from Dame Company in settlement of an open accounts receivable. What entry will Paper Company make upon receiving the note?
Paper Company will make the following entry:
Debit: Notes Receivable - Dame Company $4,700
Credit: Accounts Receivable $4,700
What is an entry?
An "entry" in accounting refers to the recording of a financial transaction or event in the company's books or accounting system. It is the process of documenting the impact of a transaction on the financial statements.
1. Debit: Notes Receivable - Dame Company ($4,700) - This account represents the amount owed to Paper Company by Dame Company and is classified as a noncurrent asset since it will be settled in more than one year.
2. Credit: Accounts Receivable ($4,700) - This account represents the open accounts receivable from Dame Company, which is now being settled through the promissory note.
By making this entry, Paper Company acknowledges the receipt of the promissory note and removes the outstanding accounts receivable from their books, replacing it with a notes receivable asset.
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A right triangle has two legs that measure b=4 and a=
✓ 84 , how long is the hypotenuse?
Answer:
Sides: a = 9.165 b = 4 c = 10
Step-by-step explanation:
Is that check mark supposed to be square root?
Answer:
\((4^{2} +(\sqrt{84} ^{2} )\\=100\)
Step-by-step explanation:
If \(\rm \: x = log_{a}(bc)\), \(\rm \: y = log_{b}(ca)\), \(\rm \: z = log_{c}(ab)\) , the xyz is equal to :
(a) x + y + z
(b) x + y + z + 1
(c) x + y + z + 2
(d) x + y + z + 3
Use the change-of-basis identity,
\(\log_x(y) = \dfrac{\ln(y)}{\ln(x)}\)
to write
\(xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}\)
Use the product-to-sum identity,
\(\log_x(yz) = \log_x(y) + \log_x(z)\)
to write
\(xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}\)
Redistribute the factors on the left side as
\(xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}\)
and simplify to
\(xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)\)
Now expand the right side:
\(xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}\)
Simplify and rewrite using the logarithm properties mentioned earlier.
\(xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1\)
\(xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}\)
\(xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}\)
\(xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)\)
\(\implies \boxed{xyz = x + y + z + 2}\)
(C)
In a hand of 13 cards chosen at random from an ordinary deck of 52 cards, let X be
the number of spades. Find E(X) and V ar(X). (Note: In the 52 cards, 13 of them are
spades.)
The values of E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.
To find E(X) and Var(X) for the number of spades in a hand of 13 cards chosen at random from a 52-card deck, we will use the concepts of probability and statistics.
E(X), or the expected value, is the average number of spades you would expect to get in a hand of 13 cards. To find E(X), we can use the formula:
E(X) = (Number of spades in the deck / Total number of cards in the deck) * Number of cards drawn
E(X) = (13 spades / 52 cards) * 13 cards drawn
E(X) = (1/4) * 13
E(X) = 3.25
So, the expected number of spades in a 13-card hand is 3.25.
Next, let's find Var(X), or the variance, which is a measure of how much the number of spades can vary from the expected value. We can use the formula for variance of a hypergeometric distribution:
Var(X) = (Number of cards drawn * Number of spades * Number of non-spades) / ((Total number of cards in the deck)^2 * (Total number of cards in the deck - 1))
Var(X) = (13 cards drawn * 13 spades * 39 non-spades) / ((52 cards)^2 * (52 cards - 1))
Var(X) = (13 * 13 * 39) / (52 * 52 * 51)
Var(X) ≈ 2.238
So, the variance for the number of spades in a 13-card hand is approximately 2.238.
In summary, E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.
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FIN220 Q19
QUESTION 19 Based on the data below calculate the company's annual holding cost? Annual requirements = 7500 units Ordering cost = BD 12 Holding cost-BD 0.5 O 150 300 45000 O 12.5
To calculate the company's annual holding cost, we need to multiply the annual average inventory by the holding cost per unit.
First, we need to calculate the annual average inventory. The formula for the average inventory is (Q/2), where Q represents the order quantity.
Given:
Annual requirements (Demand) = 7500 units
Ordering cost = BD 12
Order quantity (Q) = 150, 300, 45000 (Assuming these are different order quantities)
Holding cost per unit = BD 0.5
For each order quantity, we can calculate the annual average inventory using the formula (Q/2). Then, we multiply the average inventory by the holding cost per unit.
For order quantity Q = 150:
Average Inventory = Q/2 = 150/2 = 75 units
Holding Cost = Average Inventory * Holding cost per unit = 75 * 0.5 = BD 37.5
For order quantity Q = 300:
Average Inventory = Q/2 = 300/2 = 150 units
Holding Cost = Average Inventory * Holding cost per unit = 150 * 0.5 = BD 75
For order quantity Q = 45000:
Average Inventory = Q/2 = 45000/2 = 22500 units
Holding Cost = Average Inventory * Holding cost per unit = 22500 * 0.5 = BD 11250. Now, we sum up the holding costs for each order quantity:
Annual Holding Cost = BD 37.5 + BD 75 + BD 11250 = BD 11362.5 Therefore, the company's annual holding cost is BD 11362.5.
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Kristen wrote a number that is equal to three times the difference of 65 and 48. Which
expression represents the number that Kristen wrote?
3 x 65 - 48
3 x 48 - 65
3 x(65 – 48)
(3 x 65) - 48
Help me
Answer:
3 x(65 – 48)
Step-by-step explanation:
n = 3(65-48)
2(b + 5) = 3(b - 2) + 23
Answer:
b = -7
Step-by-step explanation:
2(b + 5) = 3(b - 2) + 23
2b + 10 = 3b - 6 + 23
10 + 6 -23 = 3b - 2b
-7 = b
Answer:
b = -7
Step-by-step explanation:
\(2(b+5) = 3(b-2) + 23\)
for the left side of the equation: \(2*b + 2*5 = 2b + 10\)
for the right side of the equation: \(3*b + 3*-2 = 3b - 6 + 23 = 3b + 17\)
\(2b + 10 = 3b + 17\)
to isolate b, subtract 2b from both sides
\(10 = b + 17\)
subtract 17 from both sides
\(-7 = b\\b = -7\)
which of the following does NOT represent a function?
Answer:
Third graph does not represent a function.
Step-by-step explanation:
A function is a relation in which each element of the domain corresponds with exactly one element of the range. You could use the vertical line test to verify whether a given graph represents a function. The vertical-line test states if a vertical line passes through more than one point on the graph of a relation, then the relation is not a function. A relation is a set of pairs of input (x values) and output (y values).
Looking at the third graph and conducting the vertical line test, you'll see that the vertical line will pass through more than one point on the graph of a relation.
Below is a screen capture of the vertical line test I've done using the image you've provided. You'll see that given an x-value of 3, it has two corresponding y-values: 4 and -4.
Find the area of the shape shown below.
Answer:
The answer should be 4800
I Think There is ALLWAYZ a 50-50 CHANCE
Company b manufactures speakers used in cell phones. the critical component is imported from china. if they are
unable to sell their speakers in china, how will this affect the economy?
exports will outpace imports.
imports will outpace exports
domestically sold goods will cost less.
there will be no effect
If Company B is unable to sell their speakers in China, it will have a significant impact on the economy: Decreased exports, Imbalanced trade, Economic implications, Reduced revenue. Second option is correct.
1. Decreased exports:
Since the critical component for the speakers is imported from China, Company B's inability to sell in China means they won't be exporting their finished speakers to the Chinese market. This will result in a decrease in exports, as the speakers won't be reaching Chinese consumers.2. Imbalanced trade:
When exports are lower than imports, it creates an imbalance in trade. In this case, if Company B can't sell speakers in China, their imports from China will continue while their exports to China decrease. This can lead to an imbalance in trade, with imports outpacing exports.3. Economic implications:
Imbalanced trade can have various economic implications. For example, if imports outpace exports, it can lead to a trade deficit, which means the country is spending more on imports than it is earning from exports. This can affect the overall economic health of the country and potentially impact factors like employment and GDP.4. Reduced revenue:
If Company B is unable to sell their speakers in China, it will result in a decrease in revenue for the company. This can have a cascading effect on their operations, including potential job losses and reduced investment in research and development or expansion.In summary, if Company B cannot sell their speakers in China, it will lead to a decrease in exports, an imbalance in trade, potential economic implications, and reduced revenue for the company. These effects can have broader consequences on the economy as a whole. Therefore, the second option is correct answer.
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can someone please help me find the answer to the following?
1. Surface area:
We need to split trinagular prism into 5 different polygons. Then calculate the area for each of them, and finally add up the five results to find the total surface area.
We have 2 triangles and 3 rectangles.
Both triangles are equal, so, we only need to find the area for one of them:
- Triangle:
\(A_t\text{ = }\frac{b\cdot h}{2}\)We know h (h = 5 in), but we don't know b, and here is where the Pythagorean theorem comes in:
\(hypotenuse^2=side^2_1+side^2_2\)For our trinagle, we know the hypotenuse length (13 in) and one side length (5 in), so:
\(\begin{gathered} \text{missing}_{}\text{ side = }\sqrt[]{hypotenuse^2-side^2_1} \\ \text{missing}_{}\text{ side = }\sqrt[]{13^2-5^2} \\ \text{missing}_{}\text{ side = }\sqrt[]{169\text{ - 25}}\text{ = }\sqrt[]{144}\text{ = 12} \end{gathered}\)And so, going back to the triangle area, we have:
\(A_t\text{ = }\frac{b\cdot h}{2}\text{ = }\frac{12\cdot5}{2}=30in^2\)- "Front" rectangle area:
\(A_r\text{ = }length\cdot\text{ width = 13 }\cdot20=260in^2\)- "Right" rectangel area:
\(A_r\text{ = }length\cdot\text{ width = 20 }\cdot5=100in^2\)- "Left" rectangle area:
\(A_r\text{ = }length\cdot\text{ width = 20 }\cdot12=240in^2\text{ (12 comes from Pythagorean theorem result)}\)Finally, the surface area of the triangle prism is:
30 + 30 + 260 + 100 + 240 = 660 in^2
2. Volume
The volume is just the area of the base triangle times the height of the prism. So:
\(V=A_t\cdot\text{ h = 30 }\cdot20=600in^3\)HELP ME PLEASE AND THANKS :) <3
Answer:
D. Cost
It is cost because the y axis is the dependent variable because the cost depends on the weight and the dependent is the y axis.
Step-by-step explanation:
Please mark brainliest I hope this helps.
Answer:
D the cost
Step-by-step explanation:
cause the costs always go on the y axis
How do you convert millimeters to centimeters?
Millimeters can be converted into centimeters by dividing the value by 10. The solution has been obtained by using the unit conversion.
What is unit conversion?
A unit conversion is used to express the same property in a different unit of measurement. For instance, you could use minutes instead of hours to represent time or feet instead of miles to indicate distance. It commonly occurs when measurements are provided in one system of units, such as feet, but are required in a different system, such as chains.
We are required to convert millimeters to centimeters.
We know that 1 centimeter = 10 millimeters
So, for converting millimeters to centimeters, we need to divide the value by 10.
Hence, millimeters can be converted into centimeters by dividing the value by 10.
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the poster shows how many of its games the football team has won so far. express this information as a fraction, a percent and as a decimal
Answer:
12/15 is the fraction one
12% I think
12.0 I think
Step-by-step explanation:
what is wrong with the following statement: boolean y = 12.5;
Answer:
we can not assign a floating-point number to a boolean variable
Step-by-step explanation:
The statement "boolean y = 12.5;" is incorrect or "wrong" because it is attempting to assign a floating-point value (12.5) to a boolean data type, which is a type of data that can only represent two values: true or false.
A boolean data type is a fundamental data type in programming and is commonly used in logic and decision-making structures. It is used to represent conditions that are either true or false, and can be used to control program flow, make decisions, and perform logical operations.
In the statement "boolean y = 12.5;", the value 12.5 is a floating-point value, which is a type of data that represents a decimal number with a fractional component. However, a boolean data type is not capable of representing such values, and can only represent two states: true or false.
In programming, attempting to assign a value of the wrong data type to a variable is known as a "type error" or a "type mismatch." Type errors can cause programs to fail, produce unexpected results, or behave in unintended ways.
To fix the statement "boolean y = 12.5;", the data type of the variable "y" should be changed to a data type that can represent decimal values, such as a floating-point data type like "double" or "float." Alternatively, if the intent of the statement was to assign a boolean value to the variable, the value of 12.5 should be replaced with a boolean expression that evaluates to either true or false.
In summary, the statement "boolean y = 12.5;" is incorrect or "wrong" because it attempts to assign a floating-point value to a boolean data type, which is not a valid data type for the value being assigned. Type errors like this can cause programs to fail, produce unexpected results, or behave in unintended ways, and must be corrected to ensure proper program operation.
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Jenny wrote the following expression in her notebook:
2· 2· 2· x· x· x + 16· y· y· y· y
Show how Jenny can correctly rewrite this expression using exponents.
Answer:
2³ · x³ + 16 · y^4
Step-by-step explanation:
She just had it all spread out this is the easier way to write it.
Hope this helps.
Answer:
Step-by-step explanation:x°=1 yo = 1. 2x2yo - 34° y ². 2. - 3 correct. ¿ ... Check for a GCF. 6x2.2.3 xx ху ах у ay²:2 Y Y nothing in common. NO GCF ... -16. ^. ( x <. -2) graph the solution. : 13-2x = 37 +4%. -4x. - 4x. -13. 13-6x<37. -13 x < ...
URGENT!
find the value of x in each supplementary angle pair
\( \frac{x}{3° } + 49° = 180° \\ \)
Cross multiply
\(x + 147° = 180°\)
simplify
x = 180° - 147°
answer : x = 33°
PLS HELP ILL MARK AS BRAINLIEST PLSS
Answer:
10%
Step-by-step explanation:
I think it's right lol but I could be wrong I forgot a lot of this stuff
but out of all the data it goes from 22-42 so 20 points in total
there is only 2 of the data points behind 24, so it is 2/20 or 10%
The cost to a distributor for a product is $40. The distributor sells the product for $82 to his customers. What is the markup rate?
The markup rate will be 51.21 % when the cost of the product is $40 and sells for $82.
What is the markup rate?The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.
As per the question, we have
cost = $40
sale price = $82
markup = sale price - cost
markup = 82- 40 = 42
markup rate = markup/sale price × 100%
markup rate = 42/82 × 100%
markup rate = 0.5121 × 100%
markup rate = 51.21 %
Thus, the markup rate will be 51.21 % when the cost of the product is $40 and sells for $82.
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find all the expressions that are equal to 4*10^-3
Answer:
Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)