One of the legs of a right triangle measures 8 cm and its hypotenuse measures 14 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
about 11.5 cm.
Step-by-step explanation:
I know the measurement of the other leg is about 11.5 cm. I know because I used the Pythagorean theorem.
a^2+b^2=c^2.
"a" and "b" are the values of the legs of the triangle, while "c" is the measure of the hypotenuse. We know that 8cm is the measure of one of the legs, and 14 cm is a measure of the hypotenuse.
8^2+b^2=14^2 simplified: 64+b^2=196
Then, I subtracted 64 on both sides, so I would have "b" by itself.
b^2=132
Next, I found the square root of both b^2 and 132, so I would find the true value of "b."
b=11.4891252931
So, the measure of the other leg rounded to the nearest tenth is about 11.5.
Related Questions
Simplify the expression 5 + (15 + x).
A. 5x + 20
B. x + 20
C. x + 5
D. x+ 15
Answers
Answer:
the answer is B
I hope you a good day!
Answer:
B
Step-by-step explanation:
You can't do anything in the parentheses because you can't add x to 15 yet since x is unknown. Thus, you add 5 to 15 and get 20 + x or B, x + 20
5.The employees of Xitrex, Inc., are paid each Friday. The company’s fiscal year-end is June 30, which falls on a Wednesday for the current year. Salaries and wages are earned evenly throughout the five-day work week, and $13,000 will be paid on Friday, July 2.
Required:
1. Prepare an adjusting entry to record the accrued salaries and wages as of June 30, a reversing entry on July 1, and an entry to record the payment of salaries and wages on July 2.
2. Prepare journal entries to record the accrued salaries and wages as of June 30 and the payment of salaries and wages on July 2 assuming a reversing entry is not recorded.
Answers
The entry to record the payment of salaries and wages on July 2 is a debit to Salaries and Wages Payable and a credit to Cash.
1. The adjusting entry on June 30 is necessary to recognize the expense for salaries and wages earned but not yet paid. It increases the Salaries and Wages Expense account and creates a liability in the Salaries and Wages Payable account.
The reversing entry on July 1 is made to simplify the subsequent accounting process and ensure accurate financial reporting. On July 2, when the payment is made, the Salaries and Wages Payable account is reduced, and Cash is decreased by the same amount.
2. Without a reversing entry, the journal entry on June 30 still recognizes the expense for salaries and wages earned but unpaid. The Salaries and Wages Expense account is debited, reflecting the expense, and the Salaries and Wages Payable account is credited, indicating the liability.
On July 2, when the payment is made, the Salaries and Wages Payable account is reduced, and Cash is decreased by the same amount. The absence of a reversing entry means that the Salaries and Wages Expense account will continue to reflect the total expense accrued throughout the fiscal year, rather than resetting to zero at the beginning of the new period.
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A triangular prism has a triangular face with a base of 13.5 feet and a height of 18 feet. Its volume is 2,187 cubic feet. What is the length of the triangular prism?
Answers
Answer:
The prism has a length x and a width x. Since it is a square at the base both length and width are the same amount x. The height is "half the length of one edge of the base". Since the base is x, this makes it 1/2x.
The volume's prism is found using V = l*w*h. Substitute and simplify.
13.5 = x*x*1/2x
13.5 = 1/2 x^3
27 = x^3
3 = x
The prism is 3 by 3 by 1.5.
Step-by-step explanation:
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1 A very small takeaway cafe with 2 baristas has customers arriving at it as a Poisson process of rate 60 per hour. It takes each customer 3 min- utes, on average, to be served, and the service times are exponentially distributed. Interarrival times and service times are all independent of each other. There is room for at most 5 customers in the cafe, includ- ing those in service. Whenever the cafe is full (i.e. has 5 customers in it) arriving customers don't go in and are turned away. Customers leave the cafe immediately upon getting their coffee. Let N(t) be the number of customers in the cafe at time t, including any in service. N(t) is a birth and death process with state-space S = {0, 1, 2, 3, 4, 5}. (a) Draw the transition diagram and give the transition rates, An and Un, for the process N(t). (b) If there is one customer already in the cafe, what is the probability that the current customer gets her coffee before another customer joins the queue?
Answers
The probability that the current customer gets their coffee before another customer joins the queue, given that there is one customer already in the cafe, is 0.5.
(a) The transition diagram for the birth and death process N(t) with state-space S = {0, 1, 2, 3, 4, 5} is as follows:
rust
Copy code
----> 0 ----> 1 ----> 2 ----> 3 ----> 4 ----> 5 ---->
Un=60 An=0 Un=60 An=0 Un=60 An=0 Un=0
In this diagram, the transitions from state i to i+1 represent the arrival of a customer, denoted by An, with a rate of 60 per hour. The transitions from state i to i-1 represent the departure of a customer, denoted by Un, with a rate of 60 per hour when the cafe is not empty (i.e., i > 0). The transition from state 5 to state 4 has a rate of 0 since no customer can enter the cafe when it is full.
(b) If there is one customer already in the cafe (state 1), the probability that the current customer gets their coffee before another customer joins the queue can be calculated using the concept of first-passage time. The probability can be obtained by calculating the probability that the process reaches state 0 before reaching state 2.
Let P(i) denote the probability of reaching state 0 before reaching state 2, starting from state i. We have:
P(1) = An / (An + Un)
In this case, An = 60 and Un = 60, so:
P(1) = 60 / (60 + 60) = 0.5
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below there was a daily rental cost for ski equipment at benton mountin ski resort radall rents one set of skis two set of poles and two pairs of boots the sales tax for the rental was 7.69 and he paid with a 100 bill how much chang should randall recive frome the 100 dollar bill
Answers
Answer:
hi
Step-by-step explanation:
Proving parallel lines. Find the value of x so that l // m. State the converse worksheet due tomorrow help please.
Answers
Answer:
x = 17Step-by-step explanation:
Find the diagram attached
The sum of the two adjacent angles is 180 degrees. Hence;
8x-9 + 53 = 180
8x + 44 = 180
Subtract 44 from both sides of the equation
8x + 44 - 44 = 180 - 44
8x = 136
Divide both sides by 8
8x/8 = 136/8
x = 17
Hence the value of x is 17
Pls help ASAP find the slope !!
Answers
Answer:
4,-4 I think
Step-by-step explanation:
My brain is off right now so might be wrong
Please awnser correctly! I will mark you Brainliest!
Answers
B. 120
Explanation:
Volume (of rect. prism) = W • L • H
Volume = 3 • 5 • 8
Volume = 120
A machine press has 51 yards of steel for making 4-inch nails. How many nails can be pressed from the steel?
Answers
51 yards of steel x 3 feet/yard = 153 feet of steel
153 feet x 12 inches/foot = 1836 inches of steel.
1836/4 inches per nail = 459 nails
Consider the following IVP: y' = ty + t², 0≤ t ≤ 2, y(0) = 1 The exact solution of this IVP is y(t) = y = -t² − 2(t+1) + 3et a. Use Euler's method with step size h = 0.1 to approximate y(1) (you can use Matlab and set a table of values)
Answers
The value of y(1) is found to be approximately 2.6742 based on the approximate values obtained using Euler's method.
First, we divide the interval [0, 1] into 10 subintervals (h = 0.1), resulting in 11 points including the initial point.
Using the Euler's method, we start with the initial condition y(0) = 1 and iterate the following formula for each step:
y_(i+1) = y_i + h * (t_i * y_i + t_i^2)
Calculating the values iteratively, we obtain a table of values for t and y as follows:
t | y
0.0 | 1.0000
0.1 | 1.1000
0.2 | 1.2110
0.3 | 1.3343
0.4 | 1.4708
0.5 | 1.6228
0.6 | 1.7920
0.7 | 1.9802
0.8 | 2.1892
0.9 | 2.4202
1.0 | 2.6742
Therefore, using Euler's method with a step size of h = 0.1, the approximate value of y(1) is 2.6742.
Euler's method is a numerical method used to approximate the solution of ordinary differential equations (ODEs). It uses small steps to approximate the derivative and iteratively updates the solution at each step. In this case, we applied Euler's method with a step size of h = 0.1 to approximate the solution y(1) for the given initial value problem. By calculating the values iteratively using the formula y_(i+1) = y_i + h * (t_i * y_i + t_i^2), we obtained a table of values that approximate the solution. The value of y(1) is found to be approximately 2.6742 based on the approximate values obtained using Euler's method.
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To test Hou= 103 versus Hy #103 a simple random sample of size n = 35 is obtained. Does the population have to be normally distributed to test this hypothesis? Why? O A. Yes, because the sample is random
OB. No, because n >=30. OC. No, because the test is two-tailed OD. Yes, because n>=30.
Answers
No, the population does not have to be normally distributed to test the hypothesis in this scenario. The correct answer is OB. No, because n >= 30.
In hypothesis testing, the assumption of normality is primarily related to the sampling distribution of the test statistic rather than the population distribution itself.
The Central Limit Theorem states that for a sufficiently large sample size (typically n >= 30), the sampling distribution of the sample mean or proportion tends to follow a normal distribution, regardless of the shape of the population distribution.
In this case, the sample size is given as n = 35, which satisfies the condition of having a sufficiently large sample size (n >= 30).
Therefore, we can rely on the Central Limit Theorem, which implies that the sampling distribution of the test statistic (such as the sample mean) will be approximately normal, even if the population distribution is not.
The choice of a two-tailed test or the fact that the sample is random does not determine whether the population needs to be normally distributed.
It is the sample size that plays a key role in allowing us to make inferences about the population based on the Central Limit Theorem.
Hence, the correct answer is OB. No, because n >= 30. The assumption of normality is not required in this scenario due to the sufficiently large sample size.
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A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 3 ft and the deep end, 9 ft.
Suppose the pool is full of water, and assume that the weight density of water is62.5\,lb/ft^3.
(a) Find the hydrostatic force (in lb) on the shallow end. (include units)
Hydrostatic force = (b) Find the hydrostatic force (in lb) on the deep end. (include units)
Hydrostatic force = (c) Find the hydrostatic force (in lb) on one of the sides that extends from the shallow end to the deep end. (include units)
Hydrostatic force = (d) Find the hydrostatic force (in lb) on the bottom of the pool. (include units)
Hydrostatic force =
Answers
The pool's hydrostatic force is 1,500 pounds at the shallow end, 4,500 pounds at the deep end, 1,500 pounds on each side from shallow to deep, and 0 pounds at the bottom.
(a) To compute the pressure the water exerts at that depth and multiply it by the shallow end's surface area, we must first measure the hydrostatic force on the shallow end. The equation P = gh, pressure is P, is the fluid's density, acceleration from gravity is g, the depth is h, determines the pressure that a fluid exerts at a given depth.
In this case, the depth of the shallow end is 3 ft. The weight density of water is given as 62.5 lb/ft³.
Plugging in these values, we have,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft)
P = 1,500 lb/ft².
To find the hydrostatic force, we multiply this pressure by the surface area of the shallow end, which is the width times the length,
Hydrostatic force = 1,500 lb/ft² * (20 ft * 40 ft)
Hydrostatic force = 1,500 lb. Therefore, the hydrostatic force on the shallow end is 1,500 lb.
(b) Using the same method as in part (a), we find that the pressure exerted by the water at the depth of the deep end, which is 9 ft, is ,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (9 ft)
P = 4,500 lb/ft².
Multiplying this pressure by the surface area of the deep end (20 ft * 40 ft), we get the hydrostatic force on the deep end,
Hydrostatic force = 4,500 lb/ft² * (20 ft * 40 ft)
Hydrostatic force = 4,500 lb.
Therefore, the hydrostatic force on the deep end is 4,500 lb.
(c) The depth of the side is varying linearly from 3 ft to 9 ft. Taking the average depth, we have (3 ft + 9 ft) / 2 = 6 ft.
Using the formula,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (6 ft),
We find that the pressure is 3,000 lb/ft².
Multiplying this pressure by the surface area of the side (20 ft * 6 ft), we get the hydrostatic force,
Hydrostatic force = 3,000 lb/ft² * (20 ft * 6 ft)
Hydrostatic force = 1,500 lb.
(d) Since the bottom of the pool is horizontal, the depth remains constant throughout, which is 3 ft. Plugging this value into the formul,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft),
p = 1,500 lb/ft², we find that the pressure is 1,500 lb/ft². However, since the bottom is horizontal, the surface area facing upward cancels out the surface area facing downward, resulting in a net force of 0 lb.
Therefore, the hydrostatic force on the bottom of the pool is 0 lb.
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Find the surface area of the prism.
Answers
Answer:
30 i think
Step-by-step explanation:
HELP PLEASE 50 POINTS
expression with its simplified form.
Answers
What is the area, in square centimeters, of the shaded part of the rectangle below?
Answers
Answer:
Step-by-step explanation:
17*8= the entire rectangle which is 136
Area of triangle=(base*height)divided by 2
The base of the white triangle is 4 because 8-4=4 and the height is 17
17*4=68
68/2=34
34= the area of the triangle
Area of the rectangle-area of the triangle=102
102 is your answer.
hopefully i did this right:)
18. In the photograph of a father and his daughter, the daughter's height is 2 cm and the father's height is 5 cm. If the father's height is actually 185 cm, how tall is the daughter?
Answers
Answer:
114cm
Step-by-step explanation:
When you're in a situation like this, you use ratios!
If the father's height is 5cm, and actually 185cm, the ratio of photo height and actual height is 1:57.
When we use this, the father is 57 times taller than him inside the photo, so since the daughter (in photo) is 2 cm, her height should be 2*57 cm.
2*57 = 114, which concludes to 114 cm.
:)
Mary has 12 boards. She cuts the boards into pieces that are each 1/3 of a board long. How many pieces will she have?
Answers
Answer:
36
Step-by-step explanation:
if you have one board and divde it by 3 you get 3 equally sized boards
and if you cut all 12 of them you get 36 equally sized boards.
In figure find the value of x triangle PQR
Answers
Answer:
x = 35
m<PQR = 70
Step-by-step explanation:
This is an isoceles triangle so the base angles are the same and they all add up to 180 so:
2x + 2x + 40 = 180
4x + 40 = 180
4x = 140
x = 35
m<PQR:
2x
2(35)
70
80% of grade 8 students, that is, 60 students want a new ice-cream shop in the
cafeteria. The total number of grade 8 students are?
Answers
Answer:
48
Step-by-step explanation:
60 students X 80%=48
20% is 12 students
40% is 24 students
60% is 36 students
so on and so forth.
Answer:
48.
Step-by-step explanation:
.80 x 60 = 48
The estimated regression equation for a model involving two independent variables and 10 observations follows. Here SST = 6,724.125, SSE = 507.75, S_b_1 = 0.0813, and s_b_2 = 0.0567.
ŷ = 29.1270 +0.5906x_1 + 0.4980x_2
a. Interpret the regression coefficients in this estimated regression equation
A one-unit increase in x_1 will lead to a 0.5906 unit decrease in y, when x_2 is held constant. A one-unit increase in x_2 will lead to a 0.498 unit increase in y, when x_1 is held constant.
A one-unit increase in x_1 will lead to a 0.5906 unit increase in y, when x_2 is held constant. A one-unit increase in x_2 will lead to a 0.498 unit decrease in y, when x_1 is held constant.
A one-unit increase in x_1 will lead to a 0.5906 unit increase in y, when x_2 is held constant. A one-unit increase in x_2 will lead to a 0.498 unit increase in y, when x_1 is held constant.
A one-unit increase in x_1 will lead to a 0.5906 unit increase in y. A one-unit increase in x_2 will lead to a 0.498 unit increase in y.
Answers
Option C is correct: A one-unit increase in x1 will lead to a 0.5906 unit increase in y, when x2 is held constant. A one-unit increase in x2 will lead to a 0.498 unit increase in y, when x1 is held constant.
The estimated regression equation for a model involving two independent variables and 10 observations follows. Here SST = 6,724.125,
SSE = 507.75,
Sb1 = 0.0813, and
Sb2 = 0.0567.
ŷ = 29.1270 +0.5906x1 + 0.4980x2
Interpretation of Regression Coefficients:
Below are the explanations of the regression coefficients in the estimated regression equation:
1. The regression coefficient for x1 is 0.5906. A one-unit increase in x1 will lead to a 0.5906 unit increase in y, when x2 is held constant.
2. The regression coefficient for x2 is 0.4980. A one-unit increase in x2 will lead to a 0.498 unit increase in y, when x1 is held constant.
Therefore, Option C is correct: A one-unit increase in x1 will lead to a 0.5906 unit increase in y, when x2 is held constant. A one-unit increase in x2 will lead to a 0.498 unit increase in y, when x1 is held constant.
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I need steps for this (need answers asap)
Answers
Answer:
(2x-7)(x+12)
Step-by-step explanation:
2x²+17x-84
(2x )(x )
We were told to use 7 and 12 to equal 84. Let's try 12 in the first bracket and 7 in the second:
(2x 12)(x 7): (2x)(7) and (12)(x) = 14x and 12x, which we cant make 17x from
Now let's try 7 in the first bracket and 12 in the second:
(2x 7)(x 12): (2x)(12) and (7)(x) = 24x and 7x, which we CAN use to make 17x if the 7x is negative, ie place a '+' before the twelve in the second bracket and a '-' before the seven in the first bracket.
(2x-7)(x+12)
Double check: (2x-7)(x+12)=2x(x+12)-7(x+12)=2x²+24x-7x-84=2x²+17x-84
Natalie made blueberry muffins for a bake sale. Each muffin cost her about $0.25 to make. She spent $8.75 to make all of the muffins. Natalie sold each muffin for $0.50 more than it cost her to make.
What is the total amount of money that Natalie received from selling her muffins?
Answers
Answer:
$17.5
Step-by-step explanation:
Answer:
26.25
Step-by-step explanation:
I took the test
PLEASE HELP ASAP !!
Which graph represents a solution to 6x + 4 = 31?
Answers
Answer:
A.
Step-by-step explanation:
If a translation of the figure above is plotted 7 units to the right and 2 units up, where will point A' be located on the new figure?
A. (7,2)
B. (-12,3)
C. (12,3)
D. (2,7)
Answers
If a translation of the figure above is plotted 7 units to the right and 2 units up, the (12,3) point A' will be located on the new figure.
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation. Here the image is translated as;
The given coordinate of the point is:- (7, 2)
Then it is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x because we just count 7 units to the right and then 2 units up.
Hence If a translation of the figure above is plotted 7 units to the right and 2 units up, the (12,3) point A' will be located on the new figure.
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A line has a slope of 2/3 and y-intercept of (0,3). Which of the following represents the equation of the line?
Answers
Answer:
just believe and ask for forgiveness
Step-by-step explanation:
god lovesyou amen you shall pass
Jane needs 6 1/2 of fabric to make a dress. She has one piece of fabric that is 1 1/2 yards and another piece of fabric that is 3 1/4 yards. How many more yards of fabric does Jane need to make the dress?
Answers
Answer:
1 1/2
Step-by-step explanation:
1 1/2 + 3 1/2 = 5
6 1/2 - 5 =1 1/2
A rectangle has a length of 3 units and a width of
y units. Write an expression for the area of this
rectangle.
Answers
Answer:
An expression for this would be 3y as length * breadth is the area of a rectangle.
which is the other end point of a line segment with one end point at (-2, -5) and midpoint at (3,2)
Answers
Answer:
(8,9)
Step-by-step explanation:
<|--------------------|--------------------------|>
(-2,-5) (3,2)
-2-3 = -5 = | -5 | = 5
-5-2=-7 = | -7 | = 7
3+5=8
2+7=9
(8,9)
Can someone please help me with this questions please help me I really need help please.
Answers
Answer:
C) Line A does not intersect Line B.
Step-by-step explanation:
Line A passes through (6 ,-30) & (-2 , 10)
Line B passes through (-4 , 28) & (2 , -2)
Find the slopes for each line. To find the slope, use the slope formula:
slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Line 1:
Let:
[tex](x_1 , y_1) = (6 , -30) \\(x_2 , y_2) = (-2 , 10)[/tex]
Plug in the corresponding numbers to the corresponding variables:
m = [tex]\frac{10 - (-30)}{-2 - 6} = \frac{10 + 30}{-8} = \frac{40}{-8} = \frac{-5}{1}[/tex]
Line 2:
Let:
[tex](x_1 , y_1) = (2 , -2)\\(x_2 , y_2) = (-4 , 28)[/tex]
Plug in the corresponding numbers to the corresponding variables:
m = [tex]\frac{28 - (-2)}{-4 - (2)} = \frac{28 + 2}{-4 - 2} = \frac{30}{-6} = \frac{-5}{1}[/tex]
The two lines share the same slope, therefore, they are parallel to each other. This means that they do not intersect at any given point.
Plz help, will give brainliest.
Answers
Answer:
1) X = 10 Therefore, 10 + 2 + 10 = 22.
2) B = 2 Therefore, 15 = 8(2) - 5 + 2(2)
3) B = -0.9 Therefore, -10 + 4(3(-0.9) + 10) = 19.