Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.
For example, if angle C is between the sides a and b, the equivalent cosine rule will be expressed as:[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]
Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)
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Polydactyl cats are cats with extra toes. A researcher believes that the proportion of the population of polydactyl cats in region A is greater than the proportion in region B. Let pB represent the population proportion of polydactyl cats in region A, and let pB represent the population proportion of polydactyl cats in region B. Which of the following are the appropriate hypotheses to test the researchers belief?
A. H0 : PA - PB = 0
Ha : PA is not equal to 0.
B. H0 : PA - PB = 0
Ha : PA - P > = 0
C. H0 : PA - PB = 0
Ha : PA - 0 < 0
D. H0 : P^a - P^b = 0
Ha : P^a - P^b is not equal to 0
E. H0 : P^a - P^b = 0
Ha : P^a - P^b > = 0
Answer:
The answer is "Option B".
Step-by-step explanation:
The null hypothesis relates to either the initial reality in which no significant statistically meaningful evidence stays; else the equal variances which would be the reverse of the zero become preferred rather than the zero. From the above case, that scientist claimed that 'the proportion of main coon cats' community in region A surpassed these in region B.' The alternate theory is Ha: PA - PB > = 0 whereas the Null is from the idea that Polydactyl cats were the same as in areas A and B.
what's the range of 7,5,7,8,6
Answer:
3
Step-by-step explanation:
Define the range of a list of numbers.
I'm not %100 percent certain because I learned that a long time ago.
Answer: 3
Step-by-step explanation:
The range is the difference between the largest and smallest numbers. The midrange is the average of the largest and smallest number.- source
SOO the first thing we have to do is find the smallest and largest numbers : 5 (smallest), 8 (largest).
Then we have to substract5 from 8 (8-5= 3)
The range is 3!
If you need extra help you can go to the site khanacademy as they give educational videos and practice on how to do the standards. Ever since I started using it I have become an A students.
I hope this helps and may God bless you! Have a nice day, bye!
Does 1/6, -3, square root of 7 or 4.5 come first when
the numbers are listed from least to greatest?
Explain.
From least to greatest:
-3, 1/6, √7, 4.5
-3 comes first as the least value because it is negative. It does not matter if the numbers are very small, as long as the value is positive, -3 will always be the least.
Evaluate the math problem
Answer:
b. 25
Step-by-step explanation:
The square root cancels out
and you divide only 100 and 4
Answer:
5 or 25
Step-by-step explanation:
I first got the 25 but when I tried a different formula to make sure it's correct I got 5.
A random sample of 436 mothers in the United States found that their average age at first birth was 25.9 with a standard deviation of 4.5. A random sample of 364 mothers in France found that their average age at first birth was 28.6 with a standard deviation of 9.5. We will be testing if the mothers give birth to their first birth in the United States are at younger ages than those in France.
Required:
Calculate the degrees of freedom for this hypothesis test.
Answer:
Degree of freedom = 798
Step-by-step explanation:
Given that,
First random sample, n₁ = 436
Second random sample, n₂ = 364
So,
Degree of freedom = n₁ + n₂ - 2
= 436 + 364 - 2
= 798
⇒Degree of freedom = 798
Find the x in each triangle
HELP NOW!!!! PLSSS
Answer:
8 CM
Step-by-step explanation:
(Hypotenuse)²=(Base)²+(Height)²
10²=X+6².
100=X+36
100-36=X ( by transposition method )
√64=X
8=X
Create a table of values that could represent the function f(x) = 3x + 4. Justify your response.
F(x)=3/2 x2-4+C
I looked it up
Simplify:
12(5 + 5)2 - 17 +3
Answer:
My first answer: 5 + 5 = 10 x 12 = 120 x 2 = 240 - 17 = 223 + 3 = 226
If not then,
12 x 5 + 12 x 5 = 120 x 2 = 240, 17 + 3 = 20, 240 - 20 = 220
Step-by-step explanation:
Numbers in parenthesis are evaluated first.
Answer:
1186 --- Sorry if I'm wrong -_-
Step-by-step explanation:
Add: 5 + 5 = 10
Exponentiation: the result of step No. 1 ^ 2 = 10 ^ 2 = 100
Multiple: 12 * the result of step No. 2 = 12 * 100 = 1200
Subtract: the result of step No. 3 - 17 = 1200 - 17 = 1183
Add: the result of step No. 4 + 3 = 1183 + 3 = 1186
order of operations problem please help
Answer:
36 .......................
Answer:
1/2
Step-by-step explanation:
How much work is needed to move a 40 pound box a distance of 2 feet?
????-foot pounds
Answer:
80-foot pounds
Step-by-step explanation:
As per the given data, the work needed to move the 40 pound box a distance of 2 feet is 79.86 foot-pounds.
What is work done?In physics, work is defined as the product of force and displacement, where force is the applied force and displacement is the distance moved by the object in the direction of the applied force.
To calculate the work needed to move a 40 pound box a distance of 2 feet, we need to use the formula:
Work = Force x Distance x Cos(theta)
where Force is the amount of force applied to move the box, Distance is the distance moved, and Cos(theta) is the cosine of the angle between the force vector and the direction of motion.
Assuming that the force is applied in the same direction as the motion, the angle between the force vector and the direction of motion is 0, and thus Cos(0) = 1. Therefore, the formula simplifies to:
Work = Force x Distance
We are given that the box has a weight of 40 pounds. Since weight is a type of force, we can use the formula:
Force = Mass x Acceleration due to gravity
where Mass is the mass of the box and Acceleration due to gravity is the gravitational acceleration constant, which is approximately 32.2 feet per second squared.
Converting the weight of the box from pounds to slugs (the unit of mass in the English system of units) gives:
Mass = Weight / Acceleration due to gravity = 40 pounds / 32.2 feet per second squared = 1.24 slugs
Therefore, the force required to move the box is:
Force = Mass x Acceleration due to gravity = 1.24 slugs x 32.2 feet per second squared = 39.93 pounds-force
Finally, we can calculate the work needed to move the box a distance of 2 feet as:
Work = Force x Distance = 39.93 pounds-force x 2 feet = 79.86 foot-pounds
Therefore, the work needed to move the 40 pound box a distance of 2 feet is 79.86 foot-pounds.
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HeLp PlEaSe ThAnKs! THIS IS A GRADE (SHOW WORK)
Answer:
1) 5400
2) 113.04
Step-by-step explanation:
40 x 135 = 5400
3.14 x 6² = 113.04
Answer:
A.
area of rectangle=l×b=135×40=5400ft²
B.
diameter=36ft
area =1/4×π×d²=1/4×π×36²=324π 0r 1017.87ff²
Write the word sentence as an equation. Then solve the equation.
A number k increased by 7 is 34.
An equation that represents this word sentence is
.
The solution is k=
.
Answer:
27
Step-by-step explanation:
Here's the complete question:
Write the word sentence as an equation. Then solve the equation. A number k increased by 7 is 34.
An increase in k simply means that there's an addition. This will be:
k + 7 = 34
k = 34 - 7
k = 27
Therefore, the value of k is 27
Step-by-step explanation:
Answer:
k = 34 - 7
k = 27
Step-by-step explanation:
increased by 7 = 34 which is means,
this number was 27
The solution is Equation: k = 34 - 7
Solution: k = 27
??? please help i cant do it
Answer: 111 degrees
Step-by-step explanation:
all angles added up together is 360 degrees
vertical angles = 180 degrees -> 3x+15=R, 2x+5= missing angle
360 = (2x+5)+(2x+5)+(3x+15)+(3x+15)
360 = 10x+40
320 = 10x
32 = x
plug it in
3x+15 -> 3(32)+15 = 111 degrees
Plz help me in math problem Its easy I just want to know how to solve this equation.
a car travels 60km in 36minutes.At the same average speed, how far will it travel in 1 hour 12 minutes
Answer:
120km
Step-by-step explanation:
1hr 12 min is double 36 minutes
so just double 60
Brainliest for answer
Answer:
C. 8 and -32
Step-by-step explanation:
-2 → 8 → -32 → 128
-4 -4 -4
f(n) = -2 • -4^(n–1)
The common ratio is -4, and the first term of the sequence is -2.
Where f(n) is the nth term of the sequence.
Question 4:
QA: once is the depth of each diver for three minutes from now
QB: in how many minutes will the assistant be 33.3 m below the surface
QC: according to the algebraic model, in how many minutes will the divers be at the same depth
Answer:
a. Jacques will be 46.4m below the surface and his assistant will be 78.1m below the surface.
b. 10 minutes
c. 6 minutes
Step-by-step explanation:
Let the equation for Justin's motion be J(x)=-13.9-7.5x (where J(x) is his distance from the surface in metres and x is time in minutes), because he starts off 13.9m below the surface and descends 7.5m every minutes.
Let the equation for the assistant be a(x)=-97.3=+6.4x (where a(x) is his distance from the surface in metres and x is time in minutes), because he starts off 97.3m below the surface and ascends 6.4m every minutes.
a.
J(x)=-13.9-7.5x
J(3)=-13.9-7.5(3)=-13.9-22.5=-36.4
a(x)=-97.3=+6.4x
a(3)=-97.3+6.4(3)=-97.3+19.2=-78.1
b.
a(x)=-97.3=+6.4x
-33.3=-97.3=+6.4x
64=6.4x
x=10
c.
when divers are at the same depth, J(x)=a(x)
J(x)=a(x)
-13.9-7.5x=-97.3=+6.4x
83.4=13.9x
x=6
Sorry, Here watch this
|l
|l \
|l (( \
|l / |
|l
Answer:
44
Step-by-step explanation:
Flight 101, headed straight north, climbed to 30,000 feet and started its cruising speed of 360 mph 10 miles south of the point directly above our location. Flight 222, headed straight west, already cruising at 30,000 feet at 300 mph, was 5 miles east of the point above us at that time. Clearly, the paths of the planes intersect directly above us. Do they collide? Parametrize the linear paths and give the times when they are at the intersection point. By how many seconds do they miss each other?
Answer:
The answer is "40 second".
Step-by-step explanation:
Flight 101 headed north straight, ascended to a speed of 30,000 feet, and began a 360 mph cruising speed 10 kilometers from the point above our place. Flight 222, heading right west, was at the same time five miles east of the above-used spot already at 30 000 feet at 300 mph.
[tex]flight\ 101: x=0;\\\\y-10 +360 t\\\\10=360 t\\\\t=\frac{1}{36} \ hrs\\\\flight\ 222: x=5-300t\\\\ y=0\\\\5=300 t\\\\t=\frac{1}{60} \ hr\\\\[/tex]
Their [tex]\frac{1}{36}-\frac{1}{60}=\frac{1}{90}\ hr=40[/tex]seconds are missing each other.
what is the median of 17, 12, 28, 21, 14, 74, 32, 14, 25, 23
Answer:
The median is 22.
Step-by-step explanation:
8 - 6 ÷ 3 + 11 =
what is the answer
Answer:
17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
You would use pemdas to solve this so since there is no parentheses, exponents, or multiplication you would do the division first and then the subtractions then addition because the subtraction comes first in this equation. 6 divided by 3 is 2 then 8 - 2 = 6 and then 6 + 11 = 17
Find the 4th term in the sequence
with the following definition:
a1 = 0
an = 2(an-1 -3)
Answer:
-42
Step-by-step explanation:
[tex]a_{1}=0\\a_{n}=2(a_{n-1}-3)\\a_{2}=2(a_{1}-3)=2(0-3)=-6\\a_{3}=2(a_{2}-3)=2(-6-3)=-18\\a_{4}=2(a_{3}-3)=2(-18-3)=-42[/tex]
Jenny has $120 to spend on parking and admission to the county fair. The parking will cost $9, and the
admission will cost $18.50 per person, including tax
Answer:
what is your question to help youHelene paid back $100 in the Month 1 of her loan. In each month after
that, Helene paid back $50. The graph shows the sequence. Write an
explicit rule, using function notation, to model the situation.
PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE YOU BRAIN THING IF ITS CORRECT (you can use a calculator if you want)
9514 1404 393
Answer:
BA, EDStep-by-step explanation:
Yes, it is very important. The idea here is that the decimal point in division problems like these can be moved the same number of places in the same direction in each number without changing the result.
__
1. Without a calculator, this is about 8/5, which you know to be more than 1 and less than 4. The only suitable answer choice is the correct one:
B 1.645 ft.
__
2. Moving the decimal point 1 place to the left in both numbers, we have ...
(892×10) ÷ (8×10) = 8290 ÷ 80 . . . . matches A
Moving the decimal point 3 places to the left in both numbers, we have ...
(892×0.001) ÷ (8×0.001) = 0.892 ÷ 0.008 . . . . matches E
The other choices did something other than move the decimal point the same number of places. (Your calculator can verify this.)
__
3. Moving the decimal point 3 places to the right, we have ...
(4367×1000) ÷ (0.004×1000) = 4,367,000 ÷ 4 ≈ 1,000,000
_____
Additional comment
For numbers like the ones in problem 3 that differ substantially in magnitude, it can work well to adjust the decimal points in both numbers so the divisor is between 1 and 10. This lets you easily estimate the position of the decimal point in the quotient.
Of course, if you're doing long division by hand, you always adjust the decimal points so the divisor is an integer (possibly with no trailing zeros).
-what is the area and perimeter of the trapezoid.
-what are the area and perimeter of a trapezoid that is similar to this one but reduced by a linear scale factor of 1/3.
- will give you brainliest if it’s correct
Answer:
I think its 42 can you pls give brainliest I wanna level up RSM SUCKS
Step-by-step explanation:
In ALJK, k = 480 cm, j = 420 cm and LJ=43°. Find all possible values of ZK, to the
nearest 10th of a degree.
Answer:
[tex]K \approx 51.2^\circ[/tex]
[tex]K \approx 128.8^\circ[/tex]
Step-by-step explanation:
Given
[tex]k = 480[/tex]
[tex]j = 420[/tex]
[tex]\angle J = 43^\circ[/tex]
Required
Find the measure of K
The value of K ranges from: [tex]0^\circ \le K \le 180^\circ[/tex]
To do this, we apply sine rule;
[tex]\frac{j}{\sin J} = \frac{k}{\sin K}[/tex]
So, we have:
[tex]\frac{420}{\sin 43} = \frac{480}{\sin K}[/tex]
Cross multiply
[tex]\sin K * 420 = \sin 43 * 480[/tex]
Make sin K the subject
[tex]\sin K= \frac{\sin 43 * 480}{420}[/tex]
[tex]\sin K= \frac{0.6820 * 480}{420}[/tex]
[tex]\sin K= 0.7794[/tex]
Take arc sin of both sides
[tex]K = sin^{-1}(0.7794)[/tex]
[tex]K \approx 51.2^\circ[/tex]
Recall that: [tex]0^\circ \le K \le 180^\circ[/tex]
The other possible value of K is:
[tex]K \approx 180 - 51.2[/tex]
[tex]K \approx 128.8^\circ[/tex]
Part B if the height of each prism is 10 Cm what is the surface area prism
Answer:
Prism A:
[tex]Area = 288cm^2[/tex]
Prism B:
[tex]Area =250cm^2[/tex]
Step-by-step explanation:
Given
See attachment for prisms
[tex]Height(h) = 10cm[/tex]
Required
Determine the surface area of both prisms
Prism A is triangular and as such, the surface area is:
[tex]Area = 2 * A_b + (a + b + c) * h[/tex]
Where
[tex]A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}[/tex]
and
[tex]s = \frac{a + b + c}{2}[/tex]
Such that a, b and c are the lengths of the triangular sides of the prism.
From the attachment;
[tex]a = 8; b =6; c =10[/tex]
So, we have:
[tex]s = \frac{a + b + c}{2}[/tex]
[tex]s = \frac{8 + 6 + 10}{2}[/tex]
[tex]s = \frac{24}{2}[/tex]
[tex]s = 12[/tex]
Also:
[tex]A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}[/tex]
[tex]A_b = \sqrt{12 * (12 - 8) * (12 - 6) * (12 - 10)}[/tex]
[tex]A_b = \sqrt{576}[/tex]
[tex]A_b = 24[/tex]
So:
[tex]Area = 2 * A_b + (a + b + c) * h[/tex]
[tex]Area = 2 * 24 + (8 + 6 + 10) * 10[/tex]
[tex]Area = 288cm^2[/tex]
Prism B is a rectangular prism. So, the area is calculated as:
[tex]Area = 2 * (ab + bh + ah)[/tex]
From the attachment
[tex]a = b = 5[/tex]
[tex]h =10[/tex]
So:
[tex]Area =2 * (5 * 5 + 5 * 10 + 5 * 10)[/tex]
[tex]Area =250cm^2[/tex]
help plzzzzzz!!!!!!!
Answer:
just count how many shapes like the front triangle is one face
Answer:
2 triangle faces, 3 rectangle faces. Thank me later
On the Navajo Reservation, a random sample of 218 permanent dwellings in the Fort Defiance region showed that 60 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 19 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defiance region, and let p2 be the population proportion of all traditional hogans in the Indian Wells region.
(a) Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
lower limit
upper limit
(b) Examine the confidence interval and comment on its meaning. Does it include numbers that are all positive? all negative? mixed? What if it is hypothesized that Navajo who follow the traditional culture of their people tend to occupy hogans? Comment on the confidence interval for p1 – p2 in this context.
Because the interval contains only positive numbers, we can say that there is a higher proportion of hogans in the Fort Defiance region.Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of hogans in the Fort Defiance region. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region.
Answer:
Step-by-step explanation:
On the Navajo Reservation, a random sample of 218 permanent dwellings in the Fort Defiance region showed that 60 were traditional Navajo hogans. In the Indian Wells region, a random sample of 139 permanent dwellings showed that 19 were traditional hogans. Let p1 be the population proportion of all traditional hogans in the Fort Defiance region, and let p2 be the population proportion of all traditional hogans in the Indian Wells region.
(a) Find a 95% confidence interval for p1 – p2. (Use 3 decimal places.)
lower limit
upper limit
(b) Examine the confidence interval and comment on its meaning. Does it include numbers that are all positive? all negative? mixed? What if it is hypothesized that Navajo who follow the traditional culture of their people tend to occupy hogans? Comment on the confidence interval for p1 – p2 in this context.
Because the interval contains only positive numbers, we can say that there is a higher proportion of hogans in the Fort Defiance region.Because the interval contains both positive and negative numbers, we can not say that there is a higher proportion of hogans in the Fort Defiance region. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that there is a higher proportion of hogans in the Indian Wells region.