Answers
Answer:
m=[tex]7\sqrt3[/tex]
n=7
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14
We need to find the lengths of m and n
Firstly, let's find the measure of the other acute angle
The acute angles in a right triangle are complementary, meaning they add up to 90 degrees
Let's make the measure of the unknown acute angle x
So x+60°=90°
Subtract 60 from both sides
x=30°
So the measure of the other acute angle is 30 degrees
This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle
In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]
In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]
Now substitute the value of a into the formulas to find n and m to find the lengths of those sides
So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7
And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]
Hope this helps!
Related Questions
The hiking trail 2600 miles long and passes through fourteen states. Because it is their first time hiking the trail, Janet and kellen plan to start hiking in Georgia and hike 416 miles. What percent of the trail will they hike?
Answers
Answer:
They will hike 16% of the trail in Georgia.
Step-by-step explanation:
We have that:
The hiking trail is of 2600 miles.
416 of those miles are in Georgia?
What percent of the trail will they hike?
Georgia distance multiplied by 100% and divided by the total distance. So
416*100%/2600 = 16%
They will hike 16% of the trail in Georgia.
Write an absolute value equation to satisfy the given solution set shown on a number line.
Answers
Answer:
|x + 6| = 2
Step-by-step explanation:
For a general absolute value equation:
| f(x) | = b
We can rewrite it as:
f(x) = b
f(x) = -b
with b > 0.
Because in the number line we have only two points graphed, this means that our absolute value equation has two solutions.
And we can conclude that one solution comes from the equation:
f(x) = b
And the other solution comes from the equation:
f(x) = -b
And thus, f(x) is a linear equation, that we can simply write as:
x - c
Then our equations can be rewritten as:
x - c = b
x -c = -b
Now let's look at the graph, we can see that the two solutions are:
x = -8
and
x = -4
Let's input each one of these in one of our above equations (the order does not matter).
-4 - c = b
-8 - c = -b
The larger value of x, (x = -4) needs to be in the equation with the positive value of b.
From the first equation we can get:
b = -4 - c
now we can replace the variable "b" in the second equation by "-4 - c" to get:
-8 - c = -(-4 - c)
-8 - c = 4 + c
-8 - 4 = c + c
-12 = 2c
-12/2 =c
-6 = c
Now that we know the value of c, we can input it in the equation:
b = -4 - c
to find the value of b
b = -4 - (-6) = -4 + 6 = 2
b = 2
Then the absolute value equation is:
|x - (-6) | = 2
|x + 6| = 2
8 ^ 3 −9⋅2÷3 can someone please help me quickly
Answers
Answer:
506
Step-by-step explanation:
8³-9×2÷3
= 512 - 9 × 2 ÷3
= 512 - 9 × ⅔
= 512 - 3 × 2
= 512 - 6
= 506
PEDMAS rule
P: Parentheses
E: Exponent
D: Division
M: Multiplication
A: Addition
S: Substraction
9. Find the value of the trigonometric ratio tan C
Answers
Hi there!
[tex]\large\boxed{tanC = 40/9}[/tex]
tan = O / A, or the opposite side over the adjacent side.
From the diagram, we can see that the opposite side = 40 and the adjacent side = 9, so:
tan C = 40 / 9
Answer:
tan C = 40/9
Step-by-step explanation:
According to SOH - CAH - TOA, tan = opposite over adjacent.
In the picture, the opposite of tan C is 40 and the adjacent is 9.
So, tan C = 40/9
P.S. - Answer above is also correct.
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a significance level of ? can be found as follows. In the expression
E=z?p1(1?p1)n1+p2(1?p2)n2?????????????????????????
we replace both n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, and p2, by 0.5 (because their values are not known). Then we solve for n, and get
n=(z?)22E2.
Finally, increase the value of n to the next larger integer number.
Use the above formula and Table C to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 99% confidence level and that the error is smaller than 0.07.
n=______.
Answers
Answer:
n= (z)22E2
n=10× 99%÷ 0.07
What is the area of this figure?
Answers
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
the line parallel to 2x – 3y = 6 and containing (2,6)
what is the equation of the line ?
Answers
First, write out the equation in slope intercept form.
-3y= -2x+6
y= 2/3x -2
The slope of the equation is 2/3, m.
Substitute the slope and coordinate into y=mx+b. Since it’s parallel, the slope remains the same.
6= 2/3(2)+b
6= 4/3+b
14/3=b
y= 2/3x + 14/3
PLEASE HELP!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answers
Answer:
y = 4x - 1.5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x - 1.5
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The determinant of a triangular matrix is the sum of the entries on the main diagonal Choose the correct answer below.
A. The statement is true. Cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a determinant equal to the son of the tries to the radar
B. The statement is true. The determinant of A is the following finite series. n det A= (-1)* laj, det A1 J = 1 In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal.
C. The statement is false. The determinant of a matrix is the arithmetic mean of the entries along the main diagonal OD The statement is false. The determinant of a triangular matrix is the product of the entries along the main diagonal
Answers
To win at LOTTO in one state, one must correctly select numbers from a collection of numbers (1 through ). The order in which the selection is made does not matter. How many different selections are possible?
Answers
Answer: If order does not matter then we can use following formula to find different combinations of 6 numbers out of 46 numbers
Step-by-step explanation: Use following Combination formula
nCr = n! / r!(n-r)!
n=46
r=6
=46!/6!(46-6)!
=46!/[6!(40)!]
=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)
Cancel out 40!
=46*45*44*43*42*41/(6*5*4*3*2*1)
=6744109680/720
=9366819
A survey of several 8 to 9 year olds recorded the following amounts spent on a trip to the mall: $31.11,$25.01,$18.53,$14.37,$24.16,$21.91 Construct the 80% confidence interval for the average amount spent by 8 to 9 year olds on a trip to the mall. Assume the population is approximately normal. Step 1 of 4 : Calculate the sample mean for the given sample data. Round your answer to two decimal places.
Answers
Solution :
Amounts spent on a trip : $31.11, $25.01, $18.53, $14.37, $24.16, $21.91
Confidence interval = 80%
Average amount spent = 8 to 9 years old
One sample T confidence interval
μ : Mean of variance
80% of confidence interval results :
Using statistical software,
Variable : data
Sample mean : 22.515
Std. Err. = 2.3479945
DF = 5
L. limit : 19.049632
U. Limit : 25.980368
SD = 5.75
Critical value = 1.476
Form a union for the following sets.
M = {1, 2, 4, 8)
N = (2,5,8)
Answers
Answer:
Step-by-step explanation:
When you are asked to find the union of sets you find numbers that are present in both sets.
So a number that appears in both the sets of M and N are 2 and 8.
So M U N = { 2,8} where U is the symbol for union.
y = 95°, find the measure of x
Answers
9514 1404 393
Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
what’s the formula to find the shaded area?
Answers
shaded area = area of outer figure - area of inner figure........
Shaded area = 123.84
Step-by-step explanation:
Shaded area = 576 - 452.16
Shaded area = 123.84
Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. Use Exhibit 10.13. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three-sigma control limits. SAMPLE NUMBER READINGS (IN OHMS) 1 1027 994 977 994 2 975 1013 999 1017 3 988 1016 974 997 4 998 1024 1006 1010 5 990 1012 990 1000 6 1016 998 1001 1030 7 1000 983 979 971 8 973 982 975 1030 9 992 1028 991 998 10 997 1026 972 1021 11 990 1021 1028 992 12 1021 998 996 970 13 1027 993 996 996 14 1022 981 1014 983 15 977 993 986 983 a. Calculate the mean and range for the above samples.
Answers
Answer:
See explanation
Step-by-step explanation:
Given
See attachment for proper presentation of question
Required
Mean and Range
To do this, we simply calculate the mean and the range of each row.
[tex]\bar x = \frac{\sum x}{n}[/tex] ---- mean
Where:
[tex]n = 4[/tex] ---- number of rows
[tex]R = Highest - Lowest[/tex] --- range
So, we have:
Sample 1
[tex]\bar x_1 = \frac{1027+ 994 +977 +994 }{4}[/tex]
[tex]\bar x_1 = 998[/tex]
[tex]R_1 = 1027- 994[/tex]
[tex]R_1 = 33[/tex]
Sample 2
[tex]\bar x_2 = \frac{975 +1013 +999 +1017}{4}[/tex]
[tex]\bar x_2 = 1001[/tex]
[tex]R_2 = 1017 - 975[/tex]
[tex]R_2 = 42[/tex]
Sample 3
[tex]\bar x_3 = \frac{988 +1016 +974 +997}{4}[/tex]
[tex]\bar x_3 = 993.75[/tex]
[tex]R_3 = 1016-974[/tex]
[tex]R_3 = 42[/tex]
Sample 4
[tex]\bar x_4 = \frac{998 +1024 +1006 +1010}{4}[/tex]
[tex]\bar x_4 = 1009.5[/tex]
[tex]R_4 = 1024 -998[/tex]
[tex]R_4 = 26[/tex]
Sample 5
[tex]\bar x_5 = \frac{990 +1012 +990 +1000}{4}[/tex]
[tex]\bar x_5 = 998[/tex]
[tex]R_5 = 1012 -990[/tex]
[tex]R_5 = 22[/tex]
Sample 6
[tex]\bar x_6= \frac{1016 + 998 +1001 +1030}{4}[/tex]
[tex]\bar x_6= 1011.25[/tex]
[tex]R_6= 1030-998[/tex]
[tex]R_6= 32[/tex]
Sample 7
[tex]\bar x_7 = \frac{1000 +983 +979 +971}{4}[/tex]
[tex]\bar x_7 = 983.25[/tex]
[tex]R_7 = 1000-971[/tex]
[tex]R_7 = 29[/tex]
Sample 8
[tex]\bar x_8 = \frac{973 +982 +975 +1030}{4}[/tex]
[tex]\bar x_8 = 990[/tex]
[tex]R_8 = 1030-973[/tex]
[tex]R_8 = 57[/tex]
Sample 9
[tex]\bar x_9 = \frac{992 +1028 +991 +998}{4}[/tex]
[tex]\bar x_9 = 1002.25[/tex]
[tex]R_9 = 1028 -991[/tex]
[tex]R_9 = 37[/tex]
Sample 10
[tex]\bar x_{10} = \frac{997 +1026 +972 +1021}{4}[/tex]
[tex]\bar x_{10} = 1004[/tex]
[tex]R_{10} = 1026 -972[/tex]
[tex]R_{10} = 54[/tex]
Sample 11
[tex]\bar x_{11} = \frac{990 +1021 +1028 +992}{4}[/tex]
[tex]\bar x_{11} = 1007.75[/tex]
[tex]R_{11} = 1028 -990[/tex]
[tex]R_{11} = 38[/tex]
Sample 12
[tex]\bar x_{12} = \frac{1021 +998 +996 +970}{4}[/tex]
[tex]\bar x_{12} = 996.25[/tex]
[tex]R_{12} = 1021 -970[/tex]
[tex]R_{12} = 51[/tex]
Sample 13
[tex]\bar x_{13} = \frac{1027 +993 +996 +996}{4}[/tex]
[tex]\bar x_{13} = 1003[/tex]
[tex]R_{13} =1027 -993[/tex]
[tex]R_{13} =34[/tex]
Sample 14
[tex]\bar x_{14} = \frac{1022 +981 +1014 +983}{4}[/tex]
[tex]\bar x_{14} = 1000[/tex]
[tex]R_{14} = 1022 -981[/tex]
[tex]R_{14} = 41[/tex]
Sample 15
[tex]\bar x_{15} = \frac{977 +993 +986 +983}{4}[/tex]
[tex]\bar x_{15} = 984.75[/tex]
[tex]R_{15} = 993-977[/tex]
[tex]R_{15} = 16[/tex]
HELP!!!!!!!! 15 POINTS
Answers
Answer:
x=5 is in the domain
Step-by-step explanation:
sqrt(x-5) ≥ 0
Square each side
(sqrt(x-5))^2 ≥ 0^2
x-5≥0
x≥5
This is the domain of x
find the intercept and graph the following linear equations: 2x+y=1
plz include x and y intercepts
Answers
Answer:
2(1)+y =1 for × intercept
2x+(1)=1 for y intercept
Explain how the given graph is deceptive.
Complete the statements based on the bar graph.
By not starting the horizontal axis at 0, the
bar appears to be about one-fourth the height of the Pecan bar. The
bar appears to be about one-half the height of the Pecan bar. The
bar appears to be less than one-half the height of the Pecan bar. This misleads the viewer to
the number of each type of nut used
Ans:
Pine Nut
Walnut
Almond
Understimate
Answers
Answer:
In the picture below.
Step-by-step explanation:
From the commenter and answer above, confirmed on edge 2022.
The dotplots below display the scores for two classes on a 30-point statistics quiz. Class A has 26 students and Class B has 25 students.
2 dot plots. For Class A, the dots are spread out more. For Class B, the dots are more grouped together.
Which statement best compares the variability of the quiz scores for Class A and Class B?
The scores on the quiz for Class A have more variability than the scores for Class B.
The scores on the quiz for Class B have more variability than the scores for Class A.
The scores on the quiz for Class A have less variability than the scores for Class B.
The scores on the quiz for Class B have about the same variability as the scores for Class A.
I think its (A), The scores on the quiz for Class A have more variability than the scores for Class B. Can someone check me?
Answers
The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.
How does the dot plot work?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
LEt suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
The dot plot is skewed to the right due to majority of the data occur to the right of the dot plot.
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. Outliers usually occur with a frequency of one.
For Class A the dots are spread out more.
For Class B, the dots are more grouped together.
Here, Looking at the dot plot, it can be seen that the numbers that range from 16 to 21 have only one dot.
The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.
To learn more about outliers, please check: brainly.com/question/27197311
SPJ2
PLEAZE HELPPPPPPPSPPSPAP
Answers
Answer:
Step-by-step explanation:
345ftyfthftyft.plk,k,
Answer:
Hello,
Anwser is C
Step-by-step explanation:
[tex]y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\[/tex]
.80 to the 8th power
Answers
Answer:
0.16777216
Step-by-step explanation:
(. 8)^8=0.16777216
Which key correctly represents the information below? A. 11 | 2 = 12 B. 1 | 2 = 12 C. 11 | 2 = 112 D. 11 | 2 = 13
Answers
Answer:
The answer is (B) 1/2=12
Need help!
given rectangle ABCD find m<CAB
Answers
Answer:
∠ CAB = 60°
Step-by-step explanation:
∠ CAD and ∠ BCA are alternate angles and congruent , so
∠ CAD = 30°
∠ BAD = 90° ( angle in a rectangle ) , then
∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°
The measure of the angle m∠CAB is 60.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The rectangle has 90 degrees on all the vertices.
So,
In ΔABC,
The sum of the angles = 180
So,
30 + 90 + m∠CAB = 180
m∠CAB = 180 - 120
m∠CAB = 60
Thus,
The measure of the angle m∠CAB is 60.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ2
My friend needs help on this sorry!
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
Answers
9514 1404 393
Answer:
$144
Step-by-step explanation:
Multiplication is used to simplify repeated addition. To find the total cost, add up the costs of each of the tickets.
6 child tickets will cost $10 +10 +10 +10 +10 +10 = 6×$10 = $60
6 adult tickets will cost $14 +14 +14 +14 +14 +14 = 6×$14 = $84
Then the total cost of all of these tickets will be ...
$60 +84 = $144 . . . . cost of zoo tickets in all
Hi so sorry this is so long, would rlly appreciate an answer
Answers
Answer:
Step-by-step explanation:
Calculate the Standard Deviation of the following set of data. 14, 15, 16, 16, 9, 3, 16, 20, 29, 12
Answers
Answer:
6,78
Step-by-step explanat
ion:data size :10
Sample mean:15
Standard sample deviation :6,782
Answer:
6,78
Step-by-step explanation:
A boat has a rip-hole in the bottom while 20 miles away from the shore. The water comes in at a rate of 1.5 tons every minute, and the boat would sink after 70 tons of water came in. How fast must the boat go in order to reach the shore before sinking?
Answers
Answer:
t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks
S = V * t
V = S / t = 20 mi * 5280 ft/mi / 2800 sec = 37.7 ft/sec
Since 88 ft/sec = 60 mph
the speed is 60 * 37.7 / 88 = 25.7 mph
A concert promoter sells tickets and has a marginal-profit function given below, where P'(x) is in dollars per ticket. This means that the rate of
change of total profit with respect to the number of tickets sold, x, is P'(x). Find the total profit from the sale of the first 380 tickets, disregarding any
fixed costs.
P'(x) = 2x - 1198
The total profit is $
Answers
Answer:
The answer is "-310840".
Step-by-step explanation:
[tex]\begin{array}{l} P'(x) = 2x - 1198\\ \\ \frac{{dP}}{{dx}} = 2x - 1198\\ \\ dP = \left( {2x - 1198} \right)dx\\ \\ \int {dP} = \int\limits_0^{380} {\left( {2x - 1198} \right)dx} \\ \\ P = \left( {2\frac{{{x^2}}}{2} - 1198x} \right)_0^{380}\\ \\ P = {380^2} - 1198 \times 380 = 144400-455240=-310840\\ \end{array}[/tex]
Peaches cost $5 a dozen. Use a table to determine the following:
A. The cost of 3dozen peaches.
B. The cost of 60peaches.
C. The number of peaches you can buy for $35
Answers
Answer:
A. $15
B. $25
C. 84 peaches
Answer:
a)3dozenx$5=$15
b)60=5 dozen 5x$5=$25
c)35/5=7,7 dozen, 7 x 12= 84
Step-by-step explanation:
Jean can swim 100 meters in 1.86 minutes. Sean can swim the same distance in 2.12 minutes.
Answers
please where is the question
