Find the length of side AB.
Give your answer to 1 decimal place.
Answers
Answer:
The answer is below
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, scalene, equilateral, acute, obtuse and right angled triangle. A right angle triangle is a triangle with one angle being 90°.
Trigonometric ratios is used to show the relationship between the angles and sides of a right angled triangle. Examples are:
sinΘ = opposite/hypotenuse; cosΘ = adjacent/hypotenuse; tanΘ = opposite/adjacent
From the question:
cos(62) = AB/12
AB = 12 * cos(62)
AB = 5.6 cm
Related Questions
Explain why the following function is not piecewise continuous
Answers
9514 1404 393
Answer:
the function has no finite limit at the left end of the interval (5, ∞)
Step-by-step explanation:
In order for the function to be piecewise continuous, it must have finite limits at the endpoints of each of the subintervals. Here, the function goes to infinity as x → 5+, so has no finite limit there.
What is the simplified value of the exponential expression 27 1/3 ?
O1/3
O1/9
O3
O9
Answers
Answer:
the correct answer is 3
hope it helps
have a nice day
The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x19.4, with standard deviation s1-2.5. For the mean was X2-6.5, with standard deviation S2-2.4. Based on these data, can we conclude that the yellow paint has less visibility after 1 year?
Use a 10% level What are we testing in this problem?
a. difference of means
b. single proportion
c. difference of proportions
d. single mean
e. paired difference
Answers
Answer:
a. difference of means
Step-by-step explanation:
Given that :
Mean , x = 9.4
Standard deviation, [tex]s.d_1[/tex] = 2.5
Number, [tex]n_1[/tex] = 12
Mean, y = 6.5
standard deviation, [tex]s.d_2[/tex] = 2.4
Number, [tex]n_2[/tex] = 12
The null hypothesis is : [tex]$H_0: \mu_1=\mu_2$[/tex]
The alternate hypothesis is : [tex]$H_1: \mu_1>\mu_2$[/tex]
Level of significance, [tex]\alpha[/tex] = 0.1
From the [tex]\text{standard normal table, right tailed,}[/tex] [tex]$t_{1/2}$[/tex] = 1.363
Since out test is right tailed.
Reject [tex]H_0[/tex], if [tex]$T_0>1.363$[/tex]
We use the test statics,
[tex]$t_0=\frac{(x-y)}{\sqrt{\frac{s.d_1}{n_1}+\frac{s.d_2}{n_2}}}$[/tex]
[tex]$t_0=\frac{(9.4-6.5)}{\sqrt{\frac{6.25}{12}+\frac{5.76}{12}}}$[/tex]
[tex]$t_0=2.899$[/tex]
[tex]$|t_0|=2.899$[/tex]
[tex]\text{Critical value}[/tex]
The value of [tex]$|t_{1/2}|$[/tex] with minimum [tex]$\left(n_1-1,n_2-1)$[/tex] that is 11 df is 1.363
We go [tex]$|t_0|=2.899$[/tex] and [tex]$|t_{1/2}|$[/tex] = 1.363
Decision making:
Since the value of [tex]|t_0|>|t_{1/2}|$[/tex] and we reject the [tex]H_0[/tex]
The p-value : right tail [tex]H_a:(p>2.8988)[/tex]
= 0.00724
Therefore the value of [tex]$p_{0.1} > 0.00724$[/tex], and so we reject the [tex]H_0[/tex]
Thus we are testing 'the difference of means" in this problem.
Recall the creative calligraphy case we discussed in class. Suppose you have received a rush order of 55 invitations that have to be created in the next (four hour) work session. What is the most time You (i.e. not Susie) can spend writing on the card and envelope for each invitation and still fill the order
Answers
Answer:
About 4 minutes and 3 seconds
Step-by-step explanation:
If I have 55 invitations to be created in four hours.
4 hours × 60 =240 minutes
240/55= 4.36 minutes
So if I spend 4 minutes and 3 seconds on an invitation, I should be able to fill the order.
Jeremy bought 3 pairs of pants that cost
The same amount of money. He had a
$10 off coupon for the pants. Using the
coupon, Jeremy spent $35. Write an
equation that can be used to find the cost
of the pants before the coupon was
applied
(use p as your variable)
Help fasttt
Answers
Answer:
3p - 10 =35
Step-by-step explanation
You want to cancel out everything, besides the p, on the left side.
then add the ten to 35 to cancel it out
divide 3 by 45 to cancel it out
p equals 15
The answer is 15
In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.
Answers
9514 1404 393
Answer:
x = 19
A = 30°
B = C = 75°
Step-by-step explanation:
In an isosceles triangle, the angles opposite the congruent sides have the same measures.
A = B
3x +18 = 7x -58
76 = 4x . . . . . . . . add 58-4x
19 = x . . . . . . . . . divide by 4
Then the equal angles measure ...
A = B = 3(19) +18 = 75
C = 2(19) -8 = 30
Angles A, B, C measure 75°, 75°, 30°, respectively.
_____
Alternate solution
The sum of angles in a triangle is 180°, so you could write ...
(3x +18) +(7x -58) +(2x -8) = 180
12x = 228 . . . . . add 48
x = 19 . . . . . divide by 12
1. In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major health-care concerns. The survey results showed that 574 of the respondents lack confidence they will be able to afford health insurance in the future. Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future.
Answers
Answer:
The correct answer is "1668". A further solution is provided below.
Step-by-step explanation:
According to the question,
Estimated proportion,
[tex]\hat{p} = \frac{574}{1007}[/tex]
[tex]=0.57[/tex]
Margin of error,
E = 0.02
Level of confidence,
= 90%
= 0.90
Critical value,
[tex]Z_{0.10}=1.65[/tex]
Now,
⇒ [tex]0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }[/tex]
[tex]0.0004=2.7225\times \frac{0.2451}{n}[/tex]
[tex]n=\frac{2.7225\times 0.2451}{0.0004}[/tex]
[tex]=1668.21[/tex]
or,
[tex]n \simeq 1668[/tex]
Find all the roots of the equation
[tex] {x}^{6} - 64 = 0[/tex]
Answers
X^2 -64=0
Factorization:
(x+8)(x-8)=0
Solution:
X+8=0 x^1=-8
X-7=0. X^2=8
Answer:
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
Step-by-step explanation:
[tex]x^{6} -64 = 0\\(x^{3} -8)(x^{3} + 8) = 0\\ \\( x - 2) (x^{2} + 2x + 4)( x + 2) (x^{2} -2x + 4) = 0\\[/tex]
x = 2
x =-2
x =1 +√3i
x =1 -√3i
x =-1 +√3i
x =-1 -√3i
PLESE HELP WITH ANSWER. rewrite the function in the given form
Answers
s hard and too long I'm only of class 13
There are 4 contestants in a beauty pageant. How many results are possible for the first, second, and third place?
Answers
Explanation:
There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.
What was the original price of the car? Show all work
Answers
Answer:
I got u, it is litearly 16540/83.8 = $19737.5
Step-by-step explanation:
its very simple sincen 100-16.2=83.8
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 27 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?
Answers
Answer:
9.5833333333 yd³
9 7/12 yd³
Step-by-step explanation:
23 * 27 * 5/12 = 258.75 ft³
1 yd³ = 3ft * 3ft * 3ft
1 yd³ = 27 ft³
258.75 ft³ * 1 yd³/27 ft³ = 9.5833333333 yd³
9.5833333333 yd³
9 7/12 yd³
An item is regularly priced at $84. Ashley bought it on sale for 70% off the regular price.
Use the ALEKS calculator to find how much Ashley paid
Answers
Answer:
58.80
Step-by-step explanation:
84 x .7(70%) =58.80
x = log e square root e
x=
Answers
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
By definition, we have [tex]\log_a b=c\implies c^a=b[/tex].
Therefore, given [tex]\log_e \sqrt{e}=x[/tex], we have:
[tex]e^x=\sqrt{x}[/tex]
Solving, we have:
[tex]x=\boxed{\frac{1}{2}}[/tex]
(Recall that [tex]a^{(\frac{b}{c})}=\sqrt[c]{a^b}[/tex]).
Answer:
1/2
Step-by-step explanation:
Given :-
log e √e log e e ^½ 1/2 log e e 1/2 * 11/2Does the equation 3x-6y=0 represent a direct variation? *
Answers
Answer:
yes
Step-by-step explanation:
if you change it to standard form, it would be
y=1/2x
because it's in the format of y=ax then it is direct variation
Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount
Answers
Answer:
25
Step-by-step explanation:
divide 48 by 4 which is 25%
Steve has 12 biscuits in a tin.
There are 7 digestive and 5 chocolate biscuits.
Steve takes two biscuits at random from the tin.
Work out the probability that he chooses two different types of biscuits.
Answers
Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question.
A number line going from negative 9 to positive 1.
–3
0
2
Answers
Answer:
-5 it is
Step-by-step explanation:
Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming pool with an area of 1,000 square feet can be installed for $50,000, whereas the installation of an 800 square foot swimming pool costs $35,000. Select the correct graph that models the given relationship.
Answers
Answer:
$35,000
Step-by-step explanation:
if $50,000 is to install an area of 1,000 square feet swimming pool and $35,000 can be used to install an 800 square foot swimming pool I think the best graph model is 800 square feet for $35,000 for a cost cut of $15,000 is a good bargain
Please help solve
-5<14-4x≤3
Answers
Answer:
Interval notation (-5,3]
The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x. Find the average value of the cost function over the interval [0, 700).
Answers
Answer:
The average value of the cost function over the interval is of $23,500.
Step-by-step explanation:
Average value of a function:
The average value of a function, over an inteval [a,b], is given by:
[tex]A = \frac{1}{b-a} \int_{a}^{b} f(x) dx[/tex]
In this case:
Function [tex]C(x) = 20000 - 10x[/tex], interval with [tex]a = 0,b = 700[/tex]
So
[tex]A = \frac{1}{700} \int_{0}^{700} 20000+10x dx[/tex]
[tex]A = \frac{1}{700} (20000x+5x^2)|_{0}^{700}[/tex]
So
[tex]A = \frac{20000(700)+5(700)^2}{700} = 23500[/tex]
The average value of the cost function over the interval is of $23,500.
what can you infer about angles x and y based on the information in the other triangles?
Answers
As we can tell x and y add up to 180 as angles on a line are equal to 180 and we know the value of x as angles in a triangle add up to 180
A bank gives you a loan of 1,500,000 Baht to buy a house. The interest rate of the loan is 0.01% per day (Using 1 year = 365 days) How much interest you pay after 10 years
Answers
Answer:
547 500
Step-by-step explanation:
Interest for 1 year:
0.01%×365=3.65 a year
3.65×10=36.5% for 10 years
36.5×1,500,000÷100=547 500
The interest paid after 10 years is 547 ,500 Baht.
What is Interest ?Interest is the amount paid or earned when a loan is taken or an investment is done respectively.
It is given that
Principal = 1,500,000 Baht
Rate = 0.01 % per day
Time period = 10 years
Interest = ?
Interest = P *R *T/100
Interest = 1500000 * 0.01 *365* 10 / 100
Interest = 547,500 Baht
Therefore the interest paid after 10 years is 547 ,500 Baht.
To know more about Interest
https://brainly.com/question/13324776
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Translate the sentence into an inequality. The product of w and 2 is less than 23.
Answers
Answer:
2w<23
Step-by-step explanation:
The product of w and 2 mean that w multiplied by 2
Suppose 49% of the doctors in America are dentists. If a random sample of size 689 is selected, what is the probability that the proportion of doctors who are dentists will be less than 47%
Answers
Answer:
[tex]P(<47\%)=0.1468[/tex]
Step-by-step explanation:
From the question we are told that:
Percentage of Dentist Doctors P(D)=49\%
Sample size n=689
Generally the equation for probability that the proportion of doctors who are dentists will be less than [tex]P(<47\%)[/tex] is mathematically given by
[tex]P(<47\%)=Z>(\frac{\=x-P(D)}{\sqrt{\frac{P(D)*1-P(D)}{n}}})[/tex]
[tex]P(<47\%)=Z>(\frac{0.47-0.49}{\sqrt{\frac{0.49*0.51}{689}}})[/tex]
[tex]P(<47\%)=Z>(1.05)[/tex]
Therefore from table
[tex]P(<47\%)=0.1468[/tex]
Find the distance between the two points.(-7,4/19) and (7,4/9)
Answers
Answer:
d=(14,0)Step-by-step explanation:
√(7-(-7))^+(4/19-4/19)^√(7+7)^+(0)^√(14)^+0= 14A public opinion survey is administered to determine how different age groups feel about an increase in the minimum wage. Some of the results are shown in the table below.
For Against No Opinion
21-40 years 20 5
41-60 years 20 20
Over 60 years 55 15 5
The survey showed that 40% of the 21 - 40 year-olds surveyed are against an increase, and 15% of the entire sample surveyed has no opinion. How many 21 - 40 year-olds surveyed are for an increase? How many 41 - 60 year-olds are against an increase?
Answers
Answer:
25 ; 35
Step-by-step explanation:
Given :
____________For __ Against __ No Opinion
21-40 years _________20 _______5
41-60 years ___20 ______________20
Over 60 years _55____ 15________ 5
Given that :
40% of 21-40 are against
Then :
40% = 20
To a obtain 100% of 21 - 40
40% = 20
100% = x
Cross multiply
0.4x = 20
x = 20/0.4
x = 50
100% of 21 - 40 = 50 people
For = 50 - (20 + 5)
= 50 - 25
= 25
2.)
Total who have no opinion :
(5 + 20 + 5) = 30
30 = 15%
Total number surveyed will be , x :
30 = 15%
x = 100%
Cross multiply :
0.15x = 30
x = 30/0.15
x = 200
Number of 41 - 60 against an increase, y:
(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200
165 + y = 200
y = 200 - 165
y = 35
A radio transmission tower is 180 feet high. How long should a guy wire be if it is to be attached to the tower 11 feet from the top and is to make an angle of 45° with the ground?
Answers
Answer:
Step-by-step explanation:
A right rectangular prism has a length of 214 cm, width of 8 cm, and height of 2012 cm.
What is the volume of the prism?
Enter the answer in the box.
cm³
Answers
Answer:
(using the numbers youve prpvided) 3444544
Step-by-step explanation:
214 x 8 x 2012 = 3444544
Find the square root of 1225 by Division method.
Answers
Answer:
35
Step-by-step explanation:
square root of 1225 is 35
Answer:
Write 1225 as 5 x 5 x 7 x 7
So, 52 x 72 = 1225
So (5 x 7)2 = 1225
So √1225 = 5 x 7 = 35
