20 points Surd question Work out the area of the triangle. ABC
Answer:
sqrt( 150)
Step-by-step explanation:
it can also be 5sqrt(6)
The solution is, the area of the triangle. ABC is 10 cm^2.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
from the given diagram, we get,
we have to find the area of the triangle. ABC
now, we have,
using the Pythagorean theorem, we get,
BD = √AB² - AD²
=√50 - 45
=√5
now, we know that,
area of triangle = 1/2 * base * height
= 1/2 * √5 * 4√5
= 10
Hence, The solution is, the area of the triangle. ABC is 10 cm^2.
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Find the equation of line b in slope-intercept form. Line a is parallel to line b. Line a passes through the points (1,8) and (2,-1), line b passes through the point (4,13)
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Answer:
y = -9x +49
Step-by-step explanation:
The slope of line b is the same as the slope of line a. That can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-1 -8)/(2 -1) = -9
The y-intercept can be found from the given point using the formula ...
b = y - mx
b = 13 -(-9)(4) = 13 +36 = 49
Then the slope-intercept equation of line b is ...
y = -9x +49
At rush hour, two people per second step onto an escalator. The escalator takes 24 seconds to bring a person from the bottom to the top. How many people are on the escalator during rush hour
Answer:
"48" is the appropriate solution.
Step-by-step explanation:
Given:
Flow rate,
R = 2 people per sec.
Flow time,
T = 24 seconds
By using the Little's Law,
⇒ [tex]I = R\times T[/tex]
The no. of people during rush hour will be:
⇒ [tex]=24\times 2[/tex]
⇒ [tex]=48[/tex]
An efficiency expert is doing a study of a certain fast food restaurant. She observes that a particularly clumsy waiter drops 30% of all the hamburgers that he serves. What is the probability that he will drop exactly four of the next ten?
Answer:
Hello,
I don't know the words used for that binominal exercice.
Step-by-step explanation:
The probability that the waiter will drop exactly four of the next ten is 0.2
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.
Now it is given that,
Waiter drops hamburgers = 30%
Therefore, Probability of drop, p = 0.3
Now For the next ten,
⇒ number of trials, n = 10
⇒ q = 1 - p = 1 - 0.3
⇒ q = 0.7
Thus, probability that he will drop exactly four of the next ten,
P(x = x) = nCx * p^x * q^(n-x)
For exactly 4, x = 4
⇒ P(x = 4) = ¹⁰C₄ * 0.3^4 * 0.7^(10 - 4)
⇒ P(x = 4) = 210*0.0081*0.1176
⇒ P(x = 4) = 0.2
Thus, the probability that the waiter will drop exactly four of the next ten is 0.2
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Ravi has 33 marbles his brother has twice as many how many marbles do they have all together
Answer
Together, they have 99 marbles.
Explanation
Ravi has 33 marbles.
His brother has twice (two times) as many marbles as him. Ravi's brother has 33×2=66 marbles.
Together, they have 33+66=99 marbles.
Together, they have 99 marbles.
What is multiplication?A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics. For instance, the product of 5 and 6 is 30.
given
Ravi has 33 marbles.
His brother has twice (two times) as many marbles as him. Ravi's brother has 33×2=66 marbles.
Together, they have 33+66=99 marbles.
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Solve 3t + 2 = 5t - 4
Answer:
3
Step-by-step explanation:
3t + 2 = 5t - 4
3t - 5t = -4 - 2
-2t = -6
t = 6/2
t = 3
Answer:
t = 3
Step-by-step explanation:
3t + 2 = 5t - 4
3t - 5t = - 4 - 2
-2t = -6
(Cut those two -)
t = 6÷2
t = 3
What is the order of rotational symmetry for the figure?
A. 3
B. 1
C. 2
D. 4 or more
Answer:
This rotational symmetry has 4 or more order .
OAmalOHopeO
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Answer:
B. 1
Step-by-step explanation:
The figure has no symmetry, so only maps to itself with 360° of rotation.
The order of rotational symmetry is 1.
HELP ON THIS PLS MATH
Answer:
7
Step-by-step explanation:
1 hour = 118 guests
826 / 118 = 7 hours
Answer:
I think h is 7
if two of the three points (0,0) ,(2,3) (3,4) lie on one side and other on another side of line x-3y+3
Answer:
Opposite sides
Step-by-step explanation:
Given equation of line is
L=3x−2y+1=0
For the point (2,1), L=5>0
For the point (−3,5),L=−18<0
Opposite signs shows that the two points lies on the opposite side of the line L=0.
sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height. suppose the height of the pile infcreases at a rate of 1cm/s when the pile is 12 cm hight. at what rate is the sand leaving the bin at that instant
Answer:
[tex]\frac{dv}{dt} =7239.168 cm/sec[/tex]
Step-by-step explanation:
From the question we are told that:
Rate [tex]\frac{dh}{dt}=1cm[/tex]
Height [tex]h=12cm[/tex]
Radius [tex]r=4h[/tex]
Generally the equation for Volume of Cone is mathematically given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
[tex]V=\frac{1}{3}\pi (4h)^2h[/tex]
Differentiating
[tex]\frac{dv}{dt} =\frac{16}{3}\pi3h^2\frac{dh}{dt}[/tex]
[tex]\frac{dv}{dt} =\frac{16}{3}*3.142*3*12^2*1[/tex]
[tex]\frac{dv}{dt} =7239.168 cm/sec[/tex]
What is the median
number of students for the
five class rooms?
Answer:
28
Step-by-step explanation:
The median is the middle number when the numbers are listed from smallest to largest
26, 27, 28, 31, 33
The middle number is 28
The median is 28
8. What is the domain and range of the graph below?
Answer:
Domain: [-5, 4]
Range: [-5, 0] U (2, 4]
Step-by-step explanation:
The domain encompasses whatever the input (in this case, the horizontal values) can be and the range is what the output (in this case, the vertical values) can be.
As shown on the graph, all horizontal values including and between -5 and 4 are used on the graph. It does not matter that they are on two separate lines. Therefore, the domain is [-5, 4]. Note that the closed brackets signify that -5 and 4 are used
The y values used in the bottom line range from -5 to 0, and in the top one they range from 2 to 4 (not including the 2, as shown by the open circle). Therefore, the bottom range is [-5, 0] and the top range is (2, 4]. We can combine these to say the range is [-5, 0] U (2, 4]
The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 110 minutes, the monthly cost will be $73.5. If the customer uses 760 minutes, the monthly cost will be $301. Find an equation in the form y = m x + b, where x is the number of monthly minutes used and y is the total monthly of the NextFell plan.
Answer:
[tex]y = 0.35x + 35[/tex]
Step-by-step explanation:
Linear equation:
A linear equation has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Finding the slope:
We have two points: (110, 73.5) and (760, 301).
The slope is given by the change in y divided by the change in x. So
Change in y: 301 - 73.5 = 227.5
Change in x: 760 - 110 = 650
Slope: [tex]m = \frac{227.5}{650} = 0.35[/tex]
So
[tex]y = 0.35x + b[/tex]
Finding the y-intercept:
(760, 301) means that when [tex]x = 760, y = 301[/tex]. So
[tex]301 = 0.35(760) + b[/tex]
[tex]b = 301 - 0.35(760)[/tex]
[tex]b = 35[/tex]
So
[tex]y = 0.35x + 35[/tex]
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 3 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min
Answer:
0.6121 = 61.21% probability that the sample average amount of time taken on each day is at most 11 min.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Normal distribution with mean value 10 min and standard deviation 3 min.
This means that [tex]\mu = 10, \sigma = 3[/tex]
First day:
5 individuals, so [tex]n = 5, s = \frac{3}{\sqrt{5}}[/tex]
The probability is the p-value of Z when X = 11. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 10}{\frac{3}{\sqrt{5}}}[/tex]
[tex]Z = 0.745[/tex]
[tex]Z = 0.745[/tex] has a p-value of 0.7719.
Second day:
6 individuals, so [tex]n = 6, s = \frac{3}{\sqrt{6}}[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{11 - 10}{\frac{3}{\sqrt{6}}}[/tex]
[tex]Z = 0.817[/tex]
[tex]Z = 0.817[/tex] has a p-value of 0.793.
What is the probability that the sample average amount of time taken on each day is at most 11 min?
Each day is independent of other days, so we multiply the probabilities.
0.7719*0.793 = 0.6121
0.6121 = 61.21% probability that the sample average amount of time taken on each day is at most 11 min.
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a non-picture card.
Picture cards are Jacks, queens and Kings. There are 4 of each for a total of 12 picture cards.
52-12 = 40 non picture cards.
Probability of being dealt a non picture card would be 40/52
The probability of not being dealt a non picture card would be 1 - 40/52 = 12/52 = 3/13
Answer: 3/13
The angles in a triangle are represented by x, x+10, and x+50. What is the measure of the largest angle?
A.70 degrees
B.80 degrees
C.100 degrees
D.90 degrees
Answer:
90
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
x+x+10 +x+50 = 180
3x+60= 180
3x = 180-60
3x = 120
Divide by 3
3x/3 = 120/3
x = 40
The largest angle is
x+50
40+50 = 90
We have to,
find the measure of the largest angle.
Given that,
The angles in a triangle are represented by x, x+10, and x+50.
Let's start to solve,
→ x+ (x+10) + (x+50) = 180°
→ x + x + x = 180° (-50-10)
→ 3x = 180° -60
→ 3x = 120
→ x = 120/3
→ [x = 40°]
Then the value of x + 10,
→ x + 10
→ 40 + 10
→ 50°
Then the value of x + 50,
→ x + 50
→ 40 + 50
→ 90°
The measure of the largest angle is,
→ D. 90 degrees
Thus, option (D) is the correct answer.
Can anyone help me with this?
Answer:
[tex]\sqrt{7}[/tex]
Step-by-step explanation:
Given
4[tex]\sqrt{7}[/tex] - 10[tex]\sqrt{7}[/tex] + 7[tex]\sqrt{7}[/tex] ( add the coefficients of the terms )
= (4 - 10 + 7) [tex]\sqrt{7}[/tex]
= 1[tex]\sqrt{7}[/tex]
= [tex]\sqrt{7}[/tex]
Riley wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 4.5% and the other bank is offering a rate of 4.5% compounded annually. Which is the better deal?
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=4
Step-by-step explanation:
[tex]\frac{16}{12}= \frac{6x}{5x-2}[/tex]
assuming that the triangles are similar, we can create this ratio of 16 or 12+4 to 6x and 12 to 5x-2
we can cross multiply to get 16(5x-2)=6x(12)
that leaves you with 80x-32=72x
we can then subtract 80x to both sides to get -32= -8x
solve by diving -8 from both sides which means that x=4
Answer:
[tex]this \: triangles \: are \: similar \: so \\ sides \: must \: be \: in \: a \: ratio \\ \frac{16}{12} = \frac{6x}{5x - 2} \\ \frac{4}{3} = \frac{6x}{5x - 2} \\ 4(5x - 2) = 3 \times 6x \\ 20x - 8 = 18x \\ x \: terms \: togather \\ 20x - 18x = 8 \\ 2x = 8 \\ x = \frac{8}{2} \\ x = 4 \\ thank \: you[/tex]
Find the intersection of the parabola y=-2x^2-4x+2 and the line -6x+y=14
Answer:
(-2,2) and (-3,-4)
Step-by-step explanation:
by graphing the line and parabola, you should get this graph
What is the L.C.M of 4,6and 3
Answer:
12
Step-by-step explanation:
12
For 3, 4 and 6 the smallest number which would be perfectly divisible by them is their LCM which is 12.
Have a nice day!
Answer:
12
Step-by-step explanation:
We want to find the least common multiple of 4,6,3
4:
4,8,12,16,20
6:
6,12,18,24
3:
3,6,9,12,15
The first number that appears in all 3 lists is 12
❤✔
PLEASE HELP ME MAKE SURE YOUR ANSWER IS RIGHT BEFORE ANSWERING
Answer:
Always. Always.
Step-by-step explanation:
All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.
Find the interest on the loan using the Banker's rule. P= $8550. r=8.8%, t= 105 days The interest on the loan using the Banker's rule is $
use the figure to find x
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Answer:
x = 5
Step-by-step explanation:
The given side is opposite the angle, and the unknown is the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(30°) = (5/2)/x
x = (5/2)/sin(30°) = (5/2)/(1/2) = 5/1
x = 5
__
Additional comment
In this 30°-60°-90° "special" right triangle, the long leg is √3 times the short leg, so ...
y = (5/2)√3
resolve 3x-1÷(x+1)^2 into partial fraction
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Answer:
3/(x +1) -4/(x +1)^2
Step-by-step explanation:
The partial fraction expansion will be of the form ...
A/(x+1)^2 +B/(x+1)
We can find the values of A and B by writing the sum of these terms:
= (A +B(x +1))/(x +1)^2
Then we require ...
B = 3
A +B = -1 ⇒ A = -4
So, the desired expansion is ...
3/(x +1) -4/(x +1)^2
In a process control study, the overall process average over 15 samples is 63.45 with an average corresponding range of 5.6. What is the lower control limit of the R-chart
Answer:
[tex]LCL=1.94[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=15[/tex]
Mean [tex]\=x=63.45[/tex]
Range [tex]R=5.6[/tex]
Generally at [tex]n=15[/tex]
Value of Control chart constant,
[tex]LCL=D*R[/tex]
Generally the equation for Lower Control Limit is mathematically given by
[tex]LCL=D*R[/tex]
[tex]LCL= 0.347*5.6[/tex]
[tex]LCL=1.94[/tex]
A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 were dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
Will mark you BRAINLIEST!
Answer:
x = 9/8
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
AB BC
---- = -----------
AD ED
x 1
---- = -----------
x+9 9
Using cross products
9*x = 1(x+9)
9x = x+9
Subtract x from each side
9x-x = x+9-x
8x = 9
Divide by 8
8x/8 = 9/8
x = 9/8
Take the triangle as,
→ AB/AD = BC/ED
→ x/x+9 = 1/9
Now by using cross products,
→ 9 × x = 1(x+9)
→ 9x = x+9
Now subtract x from both sides,
→ 9x-x = x+9-x
→ 8x = 9
Then divide by 8 from both sides,
→ 8x/8 = 9/8
→ x = 9/8
So, the value of x is 9/8.
Which expression represents the total volume of the pictures shown if each cube has a side length of e?
Answer: I believe that you have to do e^3 to find the volume of a cube.
If you had the side, you would do a^3 (a stands for the side length)
Hyo-Jin makes bracelets and sells them on an online craft website. Last month, she sold 6 bracelets. After paying the website a commission of $1.25 for each bracelet sold, Hyo-Jin made a total of $16.50. How much does each bracelet sell for on the website? Explain the steps you followed to get your answer
The answer at the end of the day would be 4
Answer:
I set up an equation to show that the number of bracelets multiplied by the cost of each bracelet minus the commission is equal to the total, 6(x – 1.25) = 16.50. I divided each side by 6, then added 1.25 to each side with a result of x = 4. Hyo-Jim sold each bracelet for $4.
Step-by-step explanation:
