Answer:
BC ≈ 10.94
Step-by-step explanation:
Base on the triangle we were given 2 sides and an angle. We were also asked to find the last length BC.
we can use cosine rule to find the side BC.
Base on cosine rule
a² = b² + c² - 2bc cos A
a = BC
b = AC = 14
c = AB = 10
a² = 14² + 10² - 2 × 14 × 10 cos 51°
a² = 196 + 100 - 280 cos 51°
a² = 296 - 280 × 0.62932039105
a² = 296 - 176.209709494
a² = 119.790290506
square root both sides
a = √119.790290506
a = 10.9448750795
BC ≈ 10.94
Answer:
BC = 10.94
Step-by-step explanation:
its a las of cosines
a² = b² + c² - 2bc cos A
AB = 10
AC = 14
angle A = 51°
BC² = 10² + 14² - (2 * 10 * 14 cos 51°)
BC = sqrt 119.8
BC = 10.94
If a 1/5 of a gallon of paint is needed to cover 1/4 of a wall, how much paint is needed to cover the entire wall
Answer:
4/5 gallon per wall
Step-by-step explanation:
We can find the unit rate
1/5 gallon
------------------
1/4 wall
1/5 ÷ 1/4
Copy dot flip
1/5 * 4/1
4/5 gallon per wall
Answer:
4/5 gallon of paint
Step-by-step explanation:
1/5 gallon of paint is needed to cover 1/4 of the wall.
To cover the whole wall:
1/4 × 4 = 1 (whole)
1/5 × 4 = 4/5
Express it in slope-intercept form.
In the diagram below, if AD= 100 and AC = 34, find CD.
A 59
B 76
C 45
D 66
Answer:
D. 66
Step-by-step explanation:
Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.
Answer:
D. 66
Step-by-step explanation:
AD = 100
AC = 34
The whole line is 100. A part of the line is 34. The other part will be 66.
100 - 34 = 66
Solve the algebraic expressio (0.4)(8)−2
Answer: -6.4
Step-by-step explanation:
(0.4)(8)(-2)
3.2*-2
-6.4
I NEED HELP PLEASE, THANKS! :)
Answer:
Option D
Step-by-step explanation:
x is given to be 4 in this case, so all we would have to is plug it into the following function -
[tex]f ( x ) = \left \{ {{x - 2, x < 4 } \atop {x + 2, x \geq 4 }} \right[/tex]
Through substitution, you would receive the following function -
[tex]f ( x ) = \left \{ {{2, 4 < 4 } \atop 6, 4 \geq 4 }} \right[/tex]
Now the graph proves that this function is closer to 4, and thus proves that the y - coordinate is about 2 at the same time. However, the graph is cut off, so the limit doesn't exists.
At noon, ship A is 120 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answer:
1.39 km/h
Step-by-step explanation:
Let the initial position of ship B represent the origin of our coordinate system. Then the position of ship A as a function of time t is ...
A = -120 +20t . . . (east of the origin)
and the position of B is ...
B = 15t . . . (north of the origin)
Then the distance between them is ...
d = √(A² +B²) = √((-120 +20t)² +(15t)²) = √(625t² -4800t +1440)
And the rate of change is ...
d' = (625t -2400)/√(625t² -4800t +14400)
At t = 4, the rate of change is ...
d' = (625·4 -2400)/√(625·16 -4800·4 +14400) = 100/√5200 = 1.39 . . . km/h
The distance between the ships is increasing at about 1.39 km/h.
state which triangle congruence postulate explains that the triangles are congruent
Answer:
Step-by-step explanation:
Angle-angle-side since they have two similar angles and one common sideOn a normally distributed anxiety test with mean 48 and standard deviation 4, approximately what anxiety test score would put someone in the top 5 percent? Group of answer choices
Answer:
Anxiety score close to 54.58.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 48, \sigma = 4[/tex]
Approximately what anxiety test score would put someone in the top 5 percent?
We have to find the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 48}{4}[/tex]
[tex]X - 48 = 1.645*4[/tex]
[tex]X = 54.58[/tex]
Anxiety score close to 54.58.
Pls help with this area question
Answer:
1
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = 2πrh
The total area is that added to the areas of the two circular bases:
A = 2πr² +2πrh
We want the ratio of these to be 1/2:
LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr
Multiplying by 2(r+h) gives ...
2h = r+h
h = r . . . . . subtract h
So, the desired ratio is ...
h/r = h/h = 1
The ratio between height and radius is 1.
. The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be a. more than 2 such accidents in the next month?
Answer:
Probability (N more than 2) = 0.3773
Step-by-step explanation:
Given:
Average number of crashes (N) = 2.2
Find:
Probability (N more than 2)
Computation:
Probability (N more than 2) = [1-P(N=0)-P(N=1)-P(N=2)]
Probability (N more than 2) = [1 - e⁻²°² - 2.2e⁻²°² - (2.2²e⁻²°²)/2]
Probability (N more than 2) = 0.3773
A graph is given to the right. a. Explain why the graph has at least one Euler path. b. Use trial and error or Fleury's Algorithm to find one such path starting at Upper A, with Upper D as the fourth and seventh vertex, and with Upper B as the fifth vertex. A C B D E A graph has 5 vertices labeled A through E and 7 edges. The edges are as follows: Upper A Upper C, Upper A Upper B, Upper A Upper D, Upper C Upper D, Upper C Upper E, Upper B Upper D, Upper D Upper E. a. Choose the correct explanation below. A. It has exactly two odd vertices. Your answer is correct.B. It has exactly two even vertices. C. It has more than two odd vertices. D. All graphs have at least one Euler path. b. Drag the letters representing the vertices given above to form the Euler path.
Answer:
a. It has exactly two odd vertices
b. A C E D B A D C
Step-by-step explanation:
(a) There will not be an Euler path if the number of odd vertices is not 0 or 2. Here, the graph has exactly two odd vertices: A and C.
__
(b) We are required to produce a path of the form {A, _, _, D, B, _, D, _}.
Starting at A, there is only one way to get to node D as the 4th node on the path: via C and E. Node B must follow. From B, there is exactly one way to cover the remaining three edges that have not been traversed so far.
The Euler path meeting the requirements is ...
A C E D B A D C
It is shown by the arrows on the edges in the graph of the attachment.
A map's scale is 1 inch : 3.5 miles.
If the distance on the map is
8 inches, then the actual distance
in real life is __miles.
Answer:
28 miles
Step-by-step explanation:
to fin the actual distance you must multiply the didtance on the map by the map scale
3.5*8=28
by which number -7 /25 should be divided to get -1/15?
Answer:
21/5
Step-by-step explanation:
if a/b = c, then b=a/c
in other words:
divide -7/25 by -1/15 to get the answer
It also helps to use the fact that a/b / c/d = a/b * d/c
-7/25 / -1/15 = -7/25 * -15/1
= 105 / 25
= 21 / 5
Answer:
[tex]4 \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]
[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]
[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]
[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]
A math teacher asks Nico and Katya to solve the following word problem. A car travels 98 miles in 1.7 hours on a freeway where the speed limit is 55 mph. Was the car speeding? Nico and Katya both agree that they should use their calculators to divide the miles by the hours to find the speed of the car, and then compare the answer to 55 mph. However, Nico says it's okay to round what his calculator says to the nearest whole number. Katya says that because the calculator displays eight numbers after the decimal point, they shouldn't round. She says they should write down exactly what the calculator shows. Do you agree with Nico or with Katya? In a short paragraph, explain who you agree with and provide the reasons why.
Answer:
- Was the car speeding?
Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.
- Do you agree with Nico or with Katya?
I agree somewhat with both Nico and Katya, but, I agree more with Nico.
- Explain your reasoning.
Like I said, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.
Step-by-step explanation:
Speed during a travel is given as distance travelled divided by time taken
Speed = (Distance/time)
Distance = 98 miles
Time = 1.7 hours
Speed = (98/1.7) = 57.6470588235 = 57.65 mph = 58 mph
- Was the car speeding?
The speed limit for the road is 55 mph and the current speed of the car = 57.65 mph
Since 57.65 > 55
The car was overspeeding.
- Nico says it's okay to round what his calculator says to the nearest whole number. Katya says that because the calculator displays eight numbers after the decimal point, they shouldn't round. She says they should write down exactly what the calculator shows. Do you agree with Nico or with Katya?
I agree somewhat with both Nico and Katya as the both methods of recording the speed ate right, depending on what the speed is required for.
Although, I agree more with Nico's method as it seems like a better fit for the situation described in the question.
- explain who you agree with and provide the reasons why.
Like I said earlier, I agree more with Nico's method of rounding the speed to the nearest whole number. This is because in this question, the standard speed we want to compare the calculated speed with is given as a whole number. Hence, it is more proper to estimate the calculated speed to its nearest whole number too.
Katya's method of writing the calculated speed as is will be correct in cases where extreme accuracy is required, not an estimate. For this question, the estimate will do.
Hope this Helps!!!
Answer:
Yes, the car was speeding as its current speed of 57.65 mph was more than the speed limit of that freeway.
Step-by-step explanation:
Nico and Katya i agree with.
Which equation represents the statement below?
Thirteen less than a number is forty-two.
Select one:
a. n – 13 = 42
b. 42 – 13 = n
c. 13 – n = 42
d. 13 – 42 = n
The answer is option A
Step-by-step explanation:
Thirteen less than a number is written as
n - 13
Equate it to 42
We have
n - 13 = 42
Hope this helps you
Some friends tell you they paid 25,404 down on a new house and are to pay $843 per month for 30 years. If interest is 4.5% compounded monthly, what was the selling price of the house?
How much interest will they pay in 30 years?
Answer:
Selling price = $190003.206 and total interest paid is $135640.794
Step-by-step explanation:
The down payment of house = $25404
Monthly payment = $834 per month.
Total number of years = 30 years = 30*12 = 360 months.
Interest rate compounded monthly = 4.5 % * 1/12 = 0.375% per month or 0.00375.
Now we have to calculate the selling price of house and total interest paid.
Loan amount = Present value of monthly payments.
[tex]\text{Loan amount} = \frac{ Monthly \ payment \times [1- (1+r)^{-n}]}{r} \\= \frac{ 834 \times [1- (1+ 0.00375)^{-360}]}{0.00375} \\= 164599.206[/tex]
Selling price of house = 25404 + 164599.206 = 190003.206
Interest amount = total amount of installment – loan amount
Interest amount = 834*360 – 164599.206 = 135640.794 dollars.
The completion times for a job task range from 11.1 minutes to 19.2 minutes and are thought to be uniformly distributed. What is the probability that it will require between 14.8 and 16.5 minutes to perform the task?
Answer:
[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]
The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210
Step-by-step explanation:
Let X the random variable "completion times for a job task" , and we know that the distribution for X is given by:
[tex] X \sim Unif (a= 11.1, b= 19.2)[/tex]
And for this case we wantto find the following probability:
[tex] P(14.8< X<16.5)[/tex]
And for this case we can use the cumulative distribution given by:
[tex] F(x) =\frac{x-a}{b-a} , a\leq X \leq b[/tex]
And using this formula we got:
[tex] P(14.8< X<16.5)= \frac{16.5-11.1}{19.2-11.1} -\frac{14.8-11.1}{19.2-11.1}= 0.667-0.457= 0.210[/tex]
The probability that it will require between 14.8 and 16.5 minutes to perform the task is 0.210
It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store
Answer:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=15, p=0.23)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find the following probability:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Simplify (20x^-3/10x^-1)^2
Answer: 4 / x^4
Step-by-step explanation:
(20x^-3 / 10x^-1)^2
Simplify,
(2 / x^2)^2
= 4 / x^4
given that f(x) = x² + 6x and g(x) = x + 9 calculate
a) f•g (4) =
B) g•f (4) =
Answer:
247
49
Step-by-step explanation:
a) f•g (4) =
f•g (x) = f(g(x)) = (x + 9)^2 + 6(x + 9)
f•g (4) = (4 + 9)^2 + 6(4 + 9)
= 13^2 + 6(13)
= 247
B) g•f (4) =
g•f (x) = g(f(x)) = x^2 + 6x + 9
g•f (4) = 4^2 + 6(4) + 9
= 16 + 24 + 9
= 49
What is the value of a?
Answer:
[tex]\huge\boxed{a=\dfrac{16}{3}=5\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\triangle ZYW\sim\triangle WYX\ (AAA)\\\\\text{Therefore corresponding sides are in proportion}\\\\\dfrac{YX}{YW}=\dfrac{YW}{ZY}\\\\\text{substitute}\\\\YX=a;\ YW=4;\ ZY=3\\\\\dfrac{a}{4}=\dfrac{4}{3}\qquad\text{multiply both sides by 4}\\\\4\cdot\dfrac{a}{4}=4\cdot\dfrac{4}{3}\qquad\text{cancel 4}\\\\a=\dfrac{16}{3}[/tex]
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it.
The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pie.
A. 1,980
B. 1,788
C. 1,034
D. 1,884
Answer:
B. 1788
Step-by-step explanation:
The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by
length * height * width
The volume for current object is :
12 * 28 * 5
= 1788 cubic yards.
Answer: 1778
Step-by-step explanation:
because Ik I had the question
Find an equation of the tangent line to the curve at the given point.
y = √ (x) , (16, 4)
Answer: y=1/8*x+2
Step-by-step explanation:
The equation of any tangent line is y=a*x+b (1)
To the equation of the tangent line we have to find the coefficients a and b and the to substitute them to equation (1).
As we know a=y'(x0) ( where x0=16)
So y'(x)= (√ (x) )' = 1/(2*√x)
a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8
So lets substitute a in equation (1):
y=1/8 *x+b
Now we have to find b
We know that the point (16, 4) belongs to the tangent line.
That means
4=1/8*16+b => 4=2+b => b=2
SO the equation of the tangent line is y=1/8*x+2
A child is playing games with empty soda cups. There are three sizes: small, medium, and large. After some experimentation
she discovered she was able to measure out 160 ounces in the following ways:
1) 2 small, 2 medium, 4 large
2) 2 small, 6 medium, 1 large
3) 5 small, 1 medium, 3 large
Determine the size of the cups.
Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz
Mary won £5000 in a competition.
She used the money to pay for herself and 8 friends
to go on a holiday.
Flights cost £279 for each of them.
Accommodation cost £184 for each of them.
How much of the £5000 did she have left after paying for
flights and accommodation for herself and the 8 friends?
Answer:
$833
Step-by-step explanation:
Since there are 9 people, we need to determine the cost of accommodation and flights for all 9 people:
9(273) + 9(184) = 2457 + 1656 = 4167 for 9 people
We then subtract that amount from the amount of money she won:
5000 - 4167 = 833
Please answer this correctly
Answer:
Question 1
Step-by-step explanation:
1) Let the outside temperature = x ° F
Now, the inside temperature = (x + 3)° F
Outside temperature has increased by 3,
So, outside temperature at lunch time = (x + 3)°F
So, at lunch time the outside & inside temperature are same.
So, the difference in temperature at lunch time is 0
Which number is a solution of the inequality: B > 2.1
A: -8
B: -12
C:5
D: 1
Answer:
C. 5 is solution of the inequality: B>2.1
volume of a cube size 7cm
Answer:
343 cm3
Step-by-step explanation:
Answer:
side(s) =7cm
volume (v)=l^3
or, v = 7^3
therefore the volume is 343cm^3.
hope its what you are searching for..
Find the area of a triangle whose two sides are 12 inches and 14 inches long, and has a perimeter of 34 inches.
Answer:
[tex]\huge\boxed{A=3\sqrt{255}\ in^2\approx47.91\ in^2}[/tex]
Step-by-step explanation:
We have two sides
[tex]a=12in;\ b=14in[/tex]
and the preimeter
[tex]P=34in[/tex]
We can calculate the length of the third side:
[tex]c=P-a-b[/tex]
substitute
[tex]c=34-12-14=8\ (in)[/tex]
Use the Heron's formula:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)[/tex]
where
[tex]p=\dfrac{P}{2}[/tex]
substitute:
[tex]p=\dfrac{34}{2}=17\ (in)\\\\A=\sqrt{17(17-12)(17-14)(17-8)}=\sqrt{(17)(5)(3)(9)}\\\\=\sqrt{9}\cdot\sqrt{(17)(5)(3)}=3\sqrt{255}\ (in^2)\approx47.91\ (in^2)[/tex]
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Learn more about line Scale factors here:
https://brainly.com/question/22312172
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