Answer:
17 boys and 11 girls
Step-by-step explanation:
Create a system of equations where b is the number of boys and g is the number of girls:
b + g = 28
b = g + 6
Solve by substitution, by substituting the second equation into the first one:
b + g = 28
(g + 6) + g = 28
2g + 6 = 28
2g = 22
g = 11
So, there are 11 girls.
Since there are 6 more boys than girls, there are 17 boys.
So, there are 17 boys and 11 girls in the class.
If any of the graphs below have a Hamiltonian circuit, list the vertices of the complete circuit. There may be many possibilities. For full credit, just list one for each graph, if the circuit exists
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Answer:
ABHGEFDCAdoes not existECBADFEStep-by-step explanation:
A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.
__
For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.
__
For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.
Find the area of an equilateral triangle with apothem length 4 cm.
If necessary, write your answer in simplified radical form.
Step-by-step explanation:
Hey there!
According to the question;
Side (a) = 4cm
To find : area
Now;
[tex]area = \frac{ \sqrt{3} }{4} {(a)}^{2} [/tex]
[tex]or \: area = \frac{ \sqrt{3} }{4} ( {4)}^{2} [/tex]
[tex]area \: = 4 \sqrt{3} [/tex]
Therefore, area of triangle is 6.92 cm² or 4√(3) cm².
Hope it helps!
Find the perimeter of each figure select the figure that have a perimeter of 20 units
Find the mean of the set of data: 10,12,29,2,19,42,23,23
Answer:
20
Step-by-step explanation:
mean is average
add all numbers get 160
divide by number of numbers (8) and get 20
Answer:
when you find the mean of a data set, you add all the numbers up then you divide the sum by the numbers in total. the sum is 160, you then divide by total of number which is 8 . your answer is 20. not sure if that made sense lol
I stores having a sale on jellybeans in trail mix. For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. Find the cost for each pound of jellybeans and each pound of trail mix
Answer: The cost of each pound of jellybean is $2.5
The cost for each pound of trail mix is $1.5
Step-by-step explanation:
Let the cost for each pound of jellybeans be x.
Let the cost of each pound of trail mix be y.
Based on the information given, we can form an equation which will be:
For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $23. This will be:
2x + 12y = 23 ...... i
For 5 pounds of jellybeans and 3 pounds of trail mix, the total cost is $17. This will be:
5x + 3y = 17...... ii
2x + 12y = 23 ...... i
5x + 3y = 17...... ii
Multiply equation i by 5
Multiply equation ii by 2
10x + 60y = 115 ...... iii
10x + 6y = 34 ..... iv
Subtract iv from iii
54y = 81
y = 81/54
y = 1.5
The cost for each pound of trail mix is $1.5
From equation i
2x + 12y = 23
2x + 12(1.5) = 23
2x + 18 = 23
2x = 23 - 18
2x = 5
x = 5/2 = 2.5
The cost of each pound of jellybean is $2.5
Mona wants to buy carpet for a floor in her house.
The floor is rectangular with a width of 8 m and a length of 9 m.
Two shops sell carpet with the prices shown below.
How much will Mona save by going to Carpet World ?
Multiple incorrect password attempts for a single login can, of course, sometimes be suggestive of an attempt to gain unauthorized access to an account. Typically there are about 52 such attempts noted each day. An analyst examining web server logs notes what appears to be an increase in these incidents over the previous 30 days in which there were an average of 57 attempts each day with a standard deviation of 17.2. Has there been a statistically significant increase in the number of attempts? Use the standard level for alpha.
Answer:
The p-value of the test is 0.0613 > 0.05, which means that there has not been a statistically significant increase in the number of attempts.
Step-by-step explanation:
Typically there are about 52 such attempts noted each day. Test if there has been a statistically significant increase.
At the null hypothesis, we test if the mean is the same, that is of 52. Thus:
[tex]H_0: \mu = 52[/tex]
At the alternative hypothesis, we test if there has been an increase, that is, if the mean is greater than 52. So
[tex]H_1: \mu > 52[/tex]
Use the standard level for alpha.
So [tex]\alpha = 0.05[/tex]
The test statistic is:
We have the standard deviation for the sample, so t-distribution.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
52 is tested at the null hypothesis:
This means that [tex]\mu = 52[/tex]
Over the previous 30 days in which there were an average of 57 attempts each day with a standard deviation of 17.2.
This means that [tex]n = 30, X = 57, s = 17.2[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{57 - 52}{\frac{17.2}{\sqrt{30}}}[/tex]
[tex]t = 1.59[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 57, which is a right-tailed test with t = 1.59 and 30 - 1 = 29 degrees of freedom.
Using a t-distribution calculator, this p-value is of 0.0613.
The p-value of the test is 0.0613 > 0.05, which means that there has not been a statistically significant increase in the number of attempts.
The interior angle of a polygon is 100 . The other interior angle are all equal to 110. how many sides has the polygon?
There is a formula for the total interior angles of a polygon:
180(sides−2)=total interior angles
One of the angles is 100 and all the others are 110.
We can rewrite the equation.
Assume there is x number of sides.
There are x−1 number of angles, 110 degrees
180(x−2)=100+110(x−1)
180x−360=100+110x−110
70x−360=100−110
70x−360=−10
70x=3507x=35
x=5
There are 5 sides to the polygon.
We can check our answer:
180(sides−2)=total interior angles
Therefore it is true:
The polygon has 5 sides
I HOPE IT HELPS
HAVE A GREAT DAY
#Liliflim
A population analysist is using the formula Pn = 25.8(1.0219)h to predict the population for Ghana, a country in Africa. What does the number in in parenthesis tell us?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the formula :
Pn = 25.8(1.0219)^h to predict the population of Ghana ;
The equation given is in the form of an exponential function:
The general form of an exponential distribution :
y = ab^x
a = Initial value ; b = constant multiplier or growth or Decay factor
Comparing :
The number in parenthesis = 1.0219 = b
b = Decay or growth factor :
Since b > 1 ; then We have a growth factor;
b = 1 + rate
1.0219 = 1 + rate
Rate = 1.0219 - 1
Rate = 0.0219
Hence, the population is growing at a rate of about (0.0219)*100% = 2.19%
Derek is skiing on a circular ski trail that has a radius of 0.6 km. Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.
a. How many radians does Brian sweep out?
b. When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?
c. When Brian stops skiing, how many km is Brian above of the center of the ski trail?
Answer:
a) Brain sweep out 4 radians
b) Brian is -0.3922 km to the right of the center of the ski trail
c) Brian is -0.4541 km above of the center of the ski trail
Step-by-step explanation:
Given the data in the question;
circular ski trail radius = 0.6 km
Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.
a) How many radians does Brian sweep out?
arc length = 2.4 km
from the diagram;
arc length = rθ
θ = arc length / r
θ = 2.4 / 0.6
θ = 4 radians
Therefore, Brain sweep out 4 radians
b) When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?
from the diagram;
x = rcosθ
we substitute
x = 0.6 × cos(4)
x = 0.6 × -0.65364
x = -0.3922 km
Therefore Brian is -0.3922 km to the right of the center of the ski trail
c) When Brian stops skiing, how many km is Brian above of the center of the ski trail?
from the diagram;
m = rsinθ
m = 0.6 × -0.7568
m = -0.4541 km
Therefore, Brian is -0.4541 km above of the center of the ski trail
A person travels 620 mi in 10 hours. What is the rate in miles per hour?
Answer:
62 miles per hour
Step-by-step explanation:
620mile/10hrs
62miles/hr
62 miles per hour
what is the solution
Answer:
c 13 over 12
Step-by-step explanation:
it help I makeit
Use first principal to determine the equation of tangent to f(x)= 3x^2-6 Answer please
Answer:
final answer:
y-1= 3x_6
To solve our given problem, we must find the equation of the tangent line of the function f(x)=(x−1)3, at x=2.
.
.
If bob gives away 7 blocks, he will have 12 left. How many blocks did he have originally
Answer:
h
Step-by-step explanation:
19 blocks
Answer:
original blocks =19
Step-by-step explanation:
original blocks -7 =12
Add 7 to each side
original blocks -7+7 =12+7
original blocks =19
PLZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
tell me about your hobbies?
can you profit from the ?
do you learn from them? What do they teach you?
do your family members have hobbies?
explain to me?
Does your parents country have any particular customs/hobbies?
what is a hobby you could see developimg?
What do you think are some of the qualities that hobbies teach us?
WRITE 2 PARagraph
Answer:
Hobbies give teenagers a chance to meet new people, discover new passions, develop skills outside of school, and do something all kids (yes, teens are part kid) should do: have fun. ... That's where hobbies come in. Hobbies are a great way for teens to form an identity outside their family.
Step-by-step explanation:
Answer:
ok ok ok ok ok ok ok ok
Step-by-step explanation:
i don't know
what is the solution to the equation 9x+27=9( x+2) +9
Let's solve the equation:
9x + 27 = 9 ( x + 2 ) + 9 ← Distribute 9 to the x and 2
9x + 27 = 9x + 18 + 9 ← Combine like terms
9x + 27 = 9x + 27 ← Subtract 27 from both sides
9x = 9x
0 = 0
{Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.}
hope this helps..........
Answer:
x=1
Step-by-step explanation:
9x+27=9(x+2)+9
9x+27=9x+18+9
9x+27=9x+27
9x=9x
x=1
What is the amplitude of the sine graph shown??????plz help asapppp
Answer:
Amplitude = 2
Step-by-step explanation:
The amplitude is the distance between the midline and the maximum/minimum. Because the midline is located at y=1, then the maximum and minimum are both 2 units apart from the midline. That is your amplitude.
A survey of 423 people shows that 321 have never received a traffic violation. Find the sample proportion of those who have received a traffic violation. *
1 point
A. 13%
B. 24%
C. 32%
D. 76%
Get brainly if right?
10 points!
Answer:
Tn = -13n +37
ordered list is 24, 11 , -2 , -15, -28 ,-41
What index of y make value 1/y^2
Answer:
(-2) is the index of y make value 1/y².
Step-by-step explanation:
We need to find what index of y makes value 1/y².
Here, the numerator is 1 and the denominator is y².
We know that,
[tex]\dfrac{1}{a^x}=a^{-x}[/tex]
So, the given expression is :
[tex]\dfrac{1}{y^2}=y^{-2}[/tex]
Hence, (-2) is the index of y make value 1/y².
PLSSSSS HELP ASAP PLSSSS !!!
Answer:
15
Step-by-step explanation:
6x+3 = 7x-12
6x-7x=-12-3
-x= -15
x= 15
6x+3 = 7x-12
6x-7x=-12-3
-x= -15 from now on we know that x is now 15
so the answer is 15
From CambridgeConvert 6 qt/min to gallons per hour
Answer:
90
Step-by-step explanation:
See image below:)
A business student is interested in estimating the 90% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within seven percentage points of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population proportion is available
Answer:
n = 106
Step-by-step explanation:
Given
p = 0.5 and 1-p = q = 0.5
Margin of error = 0.08
Confidence level = 90%
Z score for 90% confidence level = 1.65
As we know -
Margin of error = z * Sqrt (pq/n)
Substituting the given value, we get –
0.08 = 1.65 * Sqrt (0.5*0.5/n)
Squaring both the sides and solving, we get
n = 1.65^2*0.5^2/0.08^2
n = 106.34 = 106
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 cm
How far did Chubby run?
Round your answer to the nearest cm
PLEASE HELP ILL GIVE BRAINLIEST
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Answer:
6283 cm
Step-by-step explanation:
The circumference of the wheel is given by ...
C = πd
C = π(20 cm) ≈ 62.83185 cm
100 turns of the wheel will be a distance 100 times this value, or ...
race = 100C = 100(62.83185 cm) = 6283.185 cm
Chubby ran about 6283 cm.
__
Additional comment
To get the required 4 significant figures in the answer, we used the "pi button" on the calculator. Alternatively, you could use the ratio π ≈ 355/113, which is good for 6 significant figures.
Some help figuring out the answer?? Also explain a little how you got there
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Answer:
x = 10·cos(θ) -4·cot(θ)
Step-by-step explanation:
Apparently, we are to assume that the horizontal lines are parallel to each other.
The relevant trig relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If the junction point in the middle of AB is labeled X, then we have ...
sin(θ) = 4/BX ⇒ BX = 4/sin(θ)
cos(θ) = x/XA ⇒ XA = x/cos(θ)
Then ...
BX +XA = AB = 10
Substituting for BX and XA using the above relations, we get
4/sin(θ) +x/cos(θ) = 10
Solving for x gives ...
x = (10 -4/sin(θ))·cos(θ)
x = 10·cos(θ) -4·cot(θ) . . . . . simplify
_____
We used the identity ...
cot(θ) = cos(θ)/sin(θ)
HELP DUE SOON 20 POINTS
Answer:
x = 10
Step-by-step explanation:
m∠KNL = 90
10x - 10 = 90
10x = 100
x = 10
tv originally cost $400 if the price of the TV increase by 15% what is the new price
Answer:
$460
Step-by-step explanation:
Thus, a product that normally costs $400 with a 15 percent discount will cost you $340.00, and you saved $60.00. You can also calculate how much you save by simply moving the period in 15.00 percent two spaces to the left, and then multiply the result by $400 as follows: $400 x .15 = $60.00 savings.
Evaluate the expression.
4!
Answer:
4! = 24
Step-by-step explanation:
4! = 4 * 3 * 2 * 1
4! = 24
The two given figures are similar. Which statements must be true? Select all that apply.
Answer:
angle B=74°
Step-by-step explanation:
the shapes are similar
A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 8 ft.
(a) Find the force exerted by the milk on one end of the tank when the tank is full. (Round your answer to the nearest integer.) lb
(b) What if the tank is half full?
Answer:
a) 12989 Ib
b) 2756.3 Ib
Step-by-step explanation:
Density of milk = 64.6 Ib/ft^3
Diameter of tank = 8 ft
radius = 4 ft
a) Calculate force exerted by milk on one end of tank when Tank is full
pressure on strip ≈ 64.6 ( 4 - yi ) i.e. surface of milk = 4
Total force = 129.2 * [tex]\int\limits^4_4 {4-y} \sqrt{16-y^2} \, dx[/tex]
∴Force exerted = 129.2 * Area of semicircle( radius =4 ) * radius
= 129.2* 8π * 4 ≈ 12989 Ib
b) Force exerted when Tank is half full
pressure on strip ≈ 64.6 ( 0 - yi ) i.e. surface of milk = 0
Total force = 129.2 * [tex]\int\limits^0_4 {0-y} \sqrt{16-y^2} \, dx[/tex]
∴ Force exerted ≈ 2756.3 Ib
