Solve the right triangle, ΔABC, for the missing side and angles to the nearest tenth given sides a = 14.9 and b = 17.5.
A. A = 31.6 , B = 58.4 , c = 9.2
B. A = 49.6 , B = 40.4 , c = 23
C. A = 40.4 , B = 49.6 , c = 23
D. A = 40.4 , B = 49.6 , c = 9.2
Answers
Answer:
C. A = 40.4 , B = 49.6 , c = 23
Step-by-step explanation:
First, we need to get the c using the pythagoras theorem;
c² = a²+b²
c² = 14.9²+17.5²
c² = 222.01 + 306.25
c² = 528.26
c = 22.98
c ≈ 23
Using the sin rule;
a/Sin<A = c/sin<C
14.9/sin<A = 23/sin90
14.9/sin<A = 23
sin<A = 14.9/23
sin <A = 0.6478
<A = arcsin(0.6478)
<A = 40.4degrees
Also, <A + <B + <C = 180
40.4 + <B + 90 = 180
<B = 180 - 130.4
<B = 49.6degrees
Related Questions
The quadratic equation [tex]x^2+3x+50 = 0[/tex] has roots r and s. Find a quadratic question whose roots are r^2 and s^2.
Answers
According to the question, our quadratic equation is :
\begin{gathered} \bf {x}^{2} - ( {r}^{2} + {s}^{2} )x + {r}^{2} {s}^{2} = 0 \\ \bf \implies \: {x}^{2} - ( - 91)x + {(rs)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + {(50)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + 2500 = 0\end{gathered}
x
2
−(r
2
+s
2
)x+r
2
s
2
=0
⟹x
2
−(−91)x+(rs)
2
=0
⟹x
2
+91x+(50)
2
=0
⟹x
2
+91x+2500=0
A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is
Answers
Answer:
24.4185<x<25.5815
Step-by-step explanation:
Given the following:
n = 64
mean x = 25
s = 2
z is the z score at 98% CI = 2.326
Get the Confidence Interval:
CI = x±z*s/√n
CI = 25±2.326*2/√64
CI = 25±2.326*2/8
CI = 25±0.5815
CI = (25-0.5815, 25+0.5815)
CI = (24.4185, 25.5815)
CI = 24.4185<x<25.5815
Hence the 98% confidence interval for the true average age of all students in the university is 24.4185<x<25.5815
help help me please!!!!!!!
Answers
9514 1404 393
Answer:
a) 3092.5 (rounded to tenths)
b) 39,600
c) ₹28,755
Step-by-step explanation:
These are all simple calculator problems. The arithmetic involved is something you learned in 2nd or 3rd grade.
__
a) Since we divide using the division algorithm, it isn't clear what "check your answer by division algorithm" is intended to mean. The result of the division (stopping at 1 decimal place) is 3092.5.
The usual method of checking a division problem is to multiply the quotient by the divisor to see if the dividend value is the result. Here, we have ...
13×3092.5 = 40202.5
This differs by from the dividend of 40203 by 0.5, which is the remainder showing in our long division. In short, the answer checks OK.
__
b) The value of each 4 is found by setting other digits to 0.
Most significant 4: 40,000
Least significant 4: 400
Difference in place value: 40,000 -400 = 39,600
__
c) The balance in the account is found by subtracting withdrawals from deposits:
₹35000 -6245 = ₹28,755
When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?
Answers
Answer:
55000×100/90
61,111.111
Solve 8x + c = k for x
Answers
Answer:
x = 1/8(k-c)
Step-by-step explanation:
8x + c = k
Subtract c from each side
8x +c-c = k-c
8x = k-c
Divide each side by 8
8x/8 = (k-c)/8
x = 1/8(k-c)
Answer:
x-1/8(k-c)
Step-by-step explanation:
Help solve problem please
Answers
Answer:
1 / 13
Step-by-step explanation:
The total number of cards in a deck = 52
The total number of aces in a deck = 4
Since selection is drawn with replacement, then probability of drawing a certiaj number of card from the deck will be the same each time a selection is made :
Probability = required outcome / Total possible outcomes
The required outcome = number of aces = 4
Total possible outcomes = total number of cards = 52
P(drawing an ace) = 4 / 52 = 1 /13
write your answer in simplest radical form
Answers
Step-by-step explanation:
5ft hight this ancle 90°so
answer is 5ft
Please help on this initial amount problem
Answers
Growth
Value of car change 28% each year
Solve the equation
P=100x-0.1x^2
Answers
Answer:
100x - 0.01x
Step-by-step explanation:
100x-0.1x^2
100x - 0.01x
Ethan buys a video game on sale. If the video game usually costs $60, and it was on sale for 20% off, how much did Ethan pay? Round to the nearest whole dollar.
Answers
Ethan will pay $31.99 with the discount.
How? This is the answer because:
If 39.99 is 100%, and you are trying to find 20%...
1. you need to set it up as a ratio (of course, you do not need to do this, but it is easier for me to do it this way)
2. the ratio will look like this: 39.99/100% x/20%
3. all we need to do from here is to cross multiply!
4 39.99 x
---------- = ----------
100 20
-price is on the top and percent on the bottom
-you would now do 39.99 times 20
-then divide by 100
5. once you have 20% of 39.99, you need to subtract that answer from the total
6. 39.99 - 7.998 = 31.992 (you need to round to the nearest hundredth)
Hope this helps <3
The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
Answers
Answer:
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 10 minutes and a standard deviation of 3 minutes
This means that [tex]\mu = 10, \sigma = 3[/tex]
Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
This is 1 subtracted by the p-value of Z when X = 15, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 10}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
13) What is 4 1/2 subtracted from 5.33?
A. 0.43
B. 0.53
C. 0.83
D. 1.08
Answers
Given:
[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33.
To find:
The value for the given statement.
Solution:
[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33 can be written as:
[tex]5.33-4\dfrac{1}{2}[/tex]
On simplification, we get
[tex]=5.33-\dfrac{8+1}{2}[/tex]
[tex]=5.33-\dfrac{9}{2}[/tex]
[tex]=5.33-4.5[/tex]
[tex]=0.83[/tex]
Therefore, the correct option is C.
Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Rounding each number to 4 significant figures and expressing in standard notation :
(a) 102.53070,
Since the number starts with a non-zero, the 4 digits are counted from the left ;
102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2
(b) 656.980,
Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.
656.980 = 657.0 (4 significant figures) = 6.57 * 10^2
(c) 0.008543210,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3
(d) 0.000257870,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4
(e) -0.0357202,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2
29 and one-fifth divided by 4 and StartFraction 6 over 7 EndFraction
Answers
Answer:
6 1/85
Step-by-step explanation:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
146/5÷34/7
Applying the fractions formula for division,
146/5*7/34=1022/170
Simplifying 1022/170, the answer is
6 1/85
A researcher surveyed 8 people to see if there is a
relationship between years of education and starting
salaries. The data points are shown on the graph.
Which best represents the equation of the trend line
shown on the graph? (Note that the graph has a break
on the x-axis.)
O y = 0.25x + 15
O y = 0.25x + 17.5
* y = 1.25x - 10
O y = 1.25x + 7.5
Answers
Answer:
[tex]y=1.25x+7.5[/tex]
Step-by-step explanation:
We can see that the trend line is the line of best fit to the data points.
The equation of a straight line is given by:
y = mx + b:
where y, x are variables, m is the slope of the line and b is the y intercept.
From the graph, we can see that the line passes through the points (10, 20) and (14, 25). Therefore the equation of the line is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-20=\frac{25-20}{14-10}(x-10)\\\\y-20=1.25(x -10)\\\\y-20=1.25x-12.5\\\\y=1.25x+7.5[/tex]
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 47 states. What is the probability that she selects the route of three specific capitals?
Answers
Answer:
1 / 97290
Step-by-step explanation:
The number of ways of selecting 3 specific route capitals from 47 states can be obtained thus :
Probability = required outcome / Total possible outcomes
Total possible outcomes = 47P3
Recall :
nPr = n! / (n-r)!
47P3 = 47! / (47-3)! = 47! / 44! = 97290
Hence, probability of selecting route if 3 specific capitals is = 1 / 97290
Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.
Answers
Answer:
4 e
Step-by-step explanation:
dz6dxrx xrrx6 xz33x4xr4x xrx
Bill invested $4000 at 6%
compounded annually. Find the
accumulated amount at the end of
12 years.
Answers
Answer:
$ 8048.79Step-by-step explanation:
P = $4000t = 12 yearsr = 6% = 0.06Formula:
A = P(1 + r)^tThe total amount:
A = 4000*(1 + 0.06)^12 = 8048.79We have to find the,
Accumulated amount at end of 12 years.
The formula we use,
→ A = P(1+r)^t
It is given that,
→ P = $4000
→ t = 12 years
Then r will be,
→ 6%
→ 6/100
→ 0.06
Then the total amount is,
→ P(1+r)^t
→ 4000 × (1 + 0.06)^12
→ 8048.79
Thus, $ 8048.79 is the amount.
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 10 in-state applicants results in a SAT scoring mean of 1173 with a standard deviation of 38. A random sample of 15 out-of-state applicants results in a SAT scoring mean of 1076 with a standard deviation of 57. Using this data, find the 95% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Find the margin of error to be used in constructing the confidence interva.
Answers
Answer:
jebtucky
Step-by-step explanation:
yes yee yee yee eyetegevw
An item costs $20 and sells for $50.
a. Find the rate of markup based on cost.
b. Find the rate of markup based on selling price.
Answers
Step-by-step explanation:
50-20=30 rate of markup
Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%
Answers
Answer:
x = 50
y = 50
Step-by-step explanation:
[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]
.12(100-y) + .38y = 25
x = 50
y = 50
After the booster club sold 40 hotdogs at a football game, it had $90 in profit.
After the next game, it had sold a total of 80 hotdogs and had a total of $210
profit. Which equation models the total profit, y, based on the number of
hotdogs sold, X?
Answers
Step-by-step explanation:
x = goods y = $
x Sold = 40, Y = $90
x Sold = 80, Y = $210
sum of xHotdogs = 40+80 = 120 Hotdogs
Sum of Y$ = $90 + 210 = 300
so
X = 2A & Y = 3 its mean one hotdogs can sold for one each = $2.25 and we round it to $3
So = XY = 2A + 3
sorry if i wrong
Which expression is equivalent to 9+y+y+3
Answers
Answer:
b
Step-by-step explanation:
You only need to add the real numbers and the ys.
Answer:
12 + 2y
Step-by-step explanation:
9+y+y+3
Combine like terms
9+3 + y+y
12 + 2y
The stem-and-leaf plot above shows house sale prices over the last week in Tacoma. What was the most
expensive house sold? Give your answer in dollars
$
Answers
Answer:
the answer is 2
Step-by-step explanation:
this khan academy problem confuses me... (5/3)^3= can anyone help me solve it?
Answers
Answer:
4.629
Step-by-step explanation:
(5/3)³5×5×5/3×3×3125/274.629.Hope it is helpful to you
which of the following is not an asymptote of the hyperbola xy = -42? y = 0 x = 0 y = x
Answers
Given:
The equation of the hyperbola is:
[tex]xy=-42[/tex]
To find:
The the equation which is not an asymptote of the hyperbola.
Solution:
We have,
[tex]xy=-42[/tex]
It can be written as:
[tex]y=\dfrac{-42}{x}[/tex]
Equating denominator and 0, we get
[tex]x=0[/tex]
So, the vertical asymptotic is [tex]x=0[/tex].
The degree of numerator is 0 and the degree of denominator is 1.
Since the degree of numerator is greater that the degree of denominator, therefore the horizontal asymptote is [tex]y=0[/tex] and there is no oblique asymptote.
Therefore, [tex]y=x[/tex] is not an asymptote of the given hyperbola and the correct option is C.
Hshejoffpeowhwbwbwhjskfofofoekwwoksnfnf Helppp
Answers
Answer:
Step-by-step explanation:
3. ZW ≅ WX
use the function to find f(-2) f(x)=[tex]3^{x}[/tex]
Answers
Answer:
[tex] \frac{1}{9} [/tex]
Step-by-step explanation:
[tex]f( - 2) = {3}^{ - 2} [/tex]
[tex]1 \div 9 = .111[/tex]
Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3? in a test plese help fast
Answers
Answer:
Graph (a)
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x+ 6} -3[/tex]
Required
The graph
First, calculate y, when x = 0
[tex]y = \sqrt[3]{0+ 6} -3[/tex]
[tex]y = \sqrt[3]{6} -3[/tex]
[tex]y = -1.183[/tex]
The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin
Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct
Answer:
the answer is A
Step-by-step explanation:
How would yo expand ln (1/49k)?
Answers
Answer:
Step-by-step explanation:
It depends on whether you mean ln(1/49k) or ln(1/(49k)).
