Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
Step-by-step explanation:
Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.
If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), ( 6 anthropology, 1 psychology), (7 anthropology, 0 psychology)
Number of possible combinations = [tex]^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0[/tex]
[tex]=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716[/tex] [using formula for combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
Which pairs of angles are alternate exterior angles? select yes or no
A - No
B - No
C - Yes
D - Yes
.
C and D are alternate exterior angles
A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
Answer:
number of children ticket sold = 70
number of adult ticket sold = 70 × 3 = 210
number of student ticket sold = 500 - 4(70) = 500 - 280 = 220
The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.
What is an expression? What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.
Adult's ticket = [y]
Children's ticket = [x]
Student's ticket = [z]
and
y = 3x
Now -
x + y + z = 500
x + 3x + z = 500
4x + z = 500 ....[1]
and
12x + 18y + 15z = 8040
12x + 18(3x) + 15z = 8040
12x + 54x + 15z = 8040
66x + 15z = 8040 ....[2]
On solving [1] and [2], we get -
x = 90 and z = 140
and
y = 3x = 3 x 90 = 270
y = 270
Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.
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6th grade math, help me please
Answer:
B
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
[tex] \frac{42}{100} \times 350 = 147[/tex]
Look at this triangle work out length BC
Answer:
The length of BC is √105 cm or 10.2 cm.
Step-by-step explanation:
You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :
[tex] {c}^{2} = { a}^{2} + {b}^{2} [/tex]
[tex]let \:a =BC \:, \: b = 8 \: , \: c = 13[/tex]
[tex] {13}^{2} = {BC}^{2} + {8}^{2} [/tex]
[tex]169 = {BC}^{2} + 64[/tex]
[tex] {BC}^{2} = 169 - 64[/tex]
[tex] {BC}^{2} = 105[/tex]
[tex]BC = \sqrt{105} [/tex]
[tex]BC = 10.2 \: cm \: (3s.f)[/tex]
Answer:
[tex] \boxed{\sf Length \ of \ BC = \sqrt{105} \ cm} [/tex]
Given:
AB = 13 cm
AC = 8 cm
To Find:
Length of BC
Step-by-step explanation:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
[tex] \therefore \\ \sf {AC}^{2} + {BC}^{2} = {AB}^{2} \\ \sf \implies {8}^{2} + {BC}^{2} = {13}^{2} \\ \\ \sf {8}^{2} = 64 : \\ \sf \implies 64 + {BC}^{2} = {13}^{2} \\ \\ \sf {13}^{2} = 169 : \\ \sf \implies 64 + {BC}^{2} = 169 \\ \\ \sf Substract \: 64 \: from \: both \: sides : \\ \sf \implies (64 - 64) + {BC}^{2} = 169 - 64 \\ \\ \sf 64 - 64 = 0 : \\ \sf \implies {BC}^{2} = 169 - 64 \\ \\ \sf 169 - 64 = 105 : \\ \sf \implies {BC}^{2} = 105 \\ \\ \sf \implies BC = \sqrt{ 105 } \ cm [/tex]
So,
Length of BC = [tex] \sqrt{105} [/tex] cm
According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.
Answer:
The probability that the person is between 65 and 69 inches is 0.5403
Step-by-step explanation:
Mean height = [tex]\mu = 66[/tex]
Standard deviation = [tex]\sigma = 2.5[/tex]
We are supposed to find What is the probability that the person is between 65 and 69 inches i.e.P(65<x<69)
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
At x = 65
[tex]Z=\frac{65-66}{2.5}[/tex]
Z=-0.4
Refer the z table for p value
P(x<65)=0.3446
At x = 69
[tex]Z=\frac{69-66}{2.5}[/tex]
Z=1.2
P(x<69)=0.8849
So,P(65<x<69)=P(x<69)-P(x<65)=0.8849-0.3446=0.5403
Hence the probability that the person is between 65 and 69 inches is 0.5403
PLZ HELP IM STUPID. A teacher surveyed her class to find out how many texts the students send in a week. She created this box plot to show the data. Find the interquartile range. 50 points!
Answer:
236
Step-by-step explanation:
The interquartile range is the right edge of the box minus the left edge of the box
The right edge of the box is 301
The left edge of the box is 65
301 -65 =236
The interquartile range is 236
Answer:
65
Step-by-step explanation:
To find interquartile range, you substract upper quartile( 130 in this problem) and the lower quartile(65 in this problem)
Finally, you get the answer 65.
Hope this helps!
Which algebraic description maps the point (x, y) 8 units to the left and 12 units up? Question 14 options: A) (x, y) → (x – 8, y + 12) B) (x, y) → (x – 12, y + 8) C) (x, y) → (x + 12, y – 8) D) (x, y) → (x + 8, y – 12)
The algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)
Translation of coordinatesTranslation is the way of changing the position of an object on an xy plane.
If the coordinate points (x, y) is translated 8 units to the left and 12 units up, the resulting coordinate will be:
(x, y) -> (x - 8, y +12)
Hence the algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)
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What is the slope of the line graphed below?
(3, 3) (0,-6)
Answer:
3
Step-by-step explanation:
Use this equation
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute
-6-3/0-3 subtract
-9/-3 simplify
-3/-1 two negitives cansle out
3/1=3
Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.
Have a good day! :)
Answer:
3
Step-by-step explanation:
To find the slope, we use the slope formula
m= ( y2-y1)/(x2-x1)
= ( -6 -3)/(0 -3)
= -9/-3
= 3
What property do rectangles and parallelograms always share?
If parallelogram EFGH is a rhombus, calculate the area of rhombus EFGH if EG=1.7 and FH=1.1, if there is not enough information say there is not enough info. Picture of rhombus:
A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is cubic units. A cylinder with the same height and radius as the cone will have a volume of cubic units. If a sphere has the same radius as the cylinder, its volume is the volume of the cylinder.
The above question is not complete because it was not written and arranged properly
Complete Question
1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.
2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.
3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.
Answer:
1) Volume of the cone = 134.04cubic units
2)Volume of the cylinder = 402.12cubic units
3) Volume of the sphere= 268.08 cubic units. Hence, if a sphere has the same radius as the cylinder, its volume is 2/3 times the volume of the cylinder.
Step-by-step explanation:
1) A cone has a diameter of 8 units and a height of 8 units. Its radius is 4 units, and its volume is ______ cubic units.
Volume of a cone = 1/3πr²h
h = 8 units
r = 4 units
Volume = 1/3 × π × 4² × 8
134.04cubic units
2) A cylinder with the same height and radius as the cone will have a volume ______ of cubic units.
Volume of a cylinder = πr²h
Height and radius is the same as that of the cones hence,
h = 8 units
r = 4 units
= π × 4² × 8
= 402.12cubic units.
3) If a sphere has the same radius as the cylinder, its volume is ______the volume of the cylinder.
Volume of a Sphere = 4/3πr³
r = radius of the cylinder = 4 units
Volume of a Sphere = 4/3 × π × 4³
= 268.08 cubic units.
From the above question, we are asked to compare the volume of the sphere with the volume of the cylinder
Volume of the sphere : Volume of the cylinder
268.08 cubic units : 402.12 cubic units
268.08/402.12 = 2/3
Therefore, the volume of the sphere is 2/3 times the volume of the cylinder
The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 10001000 voters in the town and found that 29)% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 26&%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
We accept H₀
p-value = 0,1618
Step-by-step explanation:
We are going to solve a one tail proportion-test ( right tail)
We assume Normal distribution
Sample population 1000
Political strategist to test wants to test:
Null hypothesis H₀ p = p₀ or p = 26 %
Alternate hypothesis Hₐ p > p₀ or p > 26%
We assume CI 90 % then
α = 10 % α = 0,1 and z score for α = 0,1 is critical value
z = 2,32 ( note 2,32 is z score for α = 0,1017 "good approximation")
To compute z(s)
z(s) = ( p -p₀ ) / √ p₀q₀/n
z(s) = ( 0,29 - 0,26 ) /√ 0,26*0,74/1000
z(s) = 0,03 / 0,014
z(s) = 2,14
We compare z(s) and z(c)
z(s) < z(c)
2,14 < 2,32
z(s) is in the acceptance region we accept H₀
The p-value for z(s) is from z-table
p-value = 0,1618
which values will only have one zero??
If it has a single zero that means it has to be just touching the x-axis with its tip.
We know that if it has only one zero, the discriminant equals 0.
So,
[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]
Solving for k,
[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].
Hope this helps.
Find the volume of the cone.
Answer:
628 units³Step-by-step explanation:
Given,
Radius ( r ) = 10
Height ( h ) = 6
pi ( π ) = 3.14
now, let's find the volume of given cone:
[tex]\pi {r}^{2} \frac{h}{3} [/tex]
Plug the values
[tex] = 3.14 \times {10}^{2} \times \frac{6}{3} [/tex]
Evaluate the power
[tex] = 3.14 \times 100 \times \frac{6}{3} [/tex]
Calculate
[tex] = 628 \: {units}^{3} [/tex]
Hope this helps..
Best regards!!
Answer:
The answer is 200π units³ .
Step-by-step explanation:
Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :
[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]
[tex]let \: r = 10 \: , \: h = 6[/tex]
[tex]v = \frac{1}{3} \times \pi \times {10}^{2} \times 6[/tex]
[tex]v = \frac{1}{3} \times \pi \times 600[/tex]
[tex]v = 200\pi \: {units}^{3} [/tex]
A triangle has interior measures of 32° and 90°. What is the measure of the third angle?
Answer:
58°Step-by-step explanation:
Let the measure of third angle be X
The sum of interior angle of triangle = X
Let's create an equation
[tex]x + 32 + 90 = 180[/tex]
Add the numbers
[tex]x + 122 = 180[/tex]
Move constant to R.H.S and change its sign
[tex]x = 180 - 122[/tex]
Subtract the numbers
[tex]x = 58[/tex] °
Hope this helps...
Best regards!!
Waclaw needs to drive 478 miles on Oak Street and 434 miles on Pine Street to get to the nearest gas station.
Answer:
1. can
2. less
3. 5
Step-by-step explanation:
To find out if Waclaw could make it to the gas station using 10 miles, we need to add the number of miles he has to go in order to reach his destination.
[tex]4\frac{7}{8}+4\frac{3}{4} = 9\frac{5}{8}\\[/tex]
9 5/8 is less than 10, so he can make it to the gas station.
We can also find out the answer without even adding the numbers together, because both values are less than five, and when that happens, the sum cannot be 10 or more, so Waclaw can make it to the gas station.
Sketch the graph of y = –3(x – 7)^2 – 8 and identify the axis of symmetry.
Answer:7
Step-by-step explanation:
Answer:
X=7
Step-by-step explanation:
made a 100 on my quiz but i dont feel like puting my work in here and typing it
What is the rule of 72 used to determine? A. the approximate time it takes an investment to triple in value B. the approximate time it takes an investment to double in value C. the approximate time it takes to earn 10% interest D. the approximate time it takes to earn $72 on any investment amount
Answer:
b. the approx time it takes an investment to double in value
I have 5 eggs, I broke 2, I cooked 2 and I ate 2, how many do I have left?
Answer:
Step-by-step explanation:
To decipher how many eggs you have left, we must read the statement well.
I have 5 eggs if I break 2 eggs it is to cook them and when they are cooked they will be eaten, so we simply do the following:
5 -2= 3
Now you only have 3 eggs left.
Step-by-step explanation:
Given:
5 eggs
Required:
Number of eggs after breaking, cooking and eating 2.
Solution:
I won't count the eggs as 6.
Broken=cooked=eaten=2
5-2=3
Hope it helps ;) ❤❤❤
Is 3 a solution to the equation 6x – 7 = 12?
Answer:
3 is not a solution
Step-by-step explanation:
6x – 7 = 12?
Substitute 3 in for x and see if the equation is true
6*3 - 7 = 12
18-7 = 12
11 =12
This is false so 3 is not a solution
The volume of wine in liters produced by a parcel of vineyard every year is modeled by a Gaussian distribution with an average of 100 and a variance of 9. Find the probability that this year it will produce 115 liters of wine
Answer:
0.99865
Step-by-step explanation:
The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.
To solve the above question, we would be using the z score formula
The formula for calculating a z-score
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
In the above question,
x is 115 liters
μ is 100
σ is the population standard deviation is unknown. But we were given variance in the question.
Standard deviation = √Variance
Variance = 9
Hence, Standard deviation = √9 = 3
We go ahead to calculate our z score
z = (x-μ)/σ
z = (115 - 100) / 3
z = 15/ 3
z score = 5
Using the z score table of normal distribution to find the Probability of having a z score of 5
P(x = 115) = P(z = 5) =
0.99865
Therefore the probability that this year it will produce 115 liters of wine = 0.99865
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer
Answer:
15 pt
Step-by-step explanation:
to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
3 grams will be left after 6 half-lives
Step-by-step explanation:
Half-live:
Time it takes for the substance to be reduced by hall.
After n half lives:
The amount remaing is:
[tex]A(n) = A(0)(0.5)^{n}[/tex]
In which A(0) is the initial amount and n is the number of half-lives.
Starting with 210 grams of a radioactive isotope, how much will be left after 6 half-lives?
This is A(6) when A(0) = 210. So
[tex]A(n) = A(0)(0.5)^{n}[/tex]
[tex]A(6) = 210(0.5)^{6} = 3.3[/tex]
Rounding to the nearest gram
3 grams will be left after 6 half-lives
find all solutions of cosx-\sqrt(1-3cos^(2)x)=0 a. 60° + n360°, 300° + n360° b. 30° + n360°, 210° + n360° c. 30° + n360°, 330° + n360° d. 60° + n360°, 120° + n360°
Greetings from Brasil...
The equation is:
COS X - √(1 - 3.COS² X) = 0putting COS X for the 2nd member
- √(1 - 3.COS² X) = - COS X ×(- 1)
√(1 - 3.COS² X) = COS X everything squared
[√(1 - 3.COS² X)]² = (COS X)²
1 - 3.COS² X = COS² X
1 - 3.COS² X - COS² X = 0
1 - 4.COS² X = 0
making Y = COS X
1 - 4Y² = 0
- 4Y² = - 1 ×(- 1)
4Y² = 1
Y² = 1/4
Y = ±√1/4
Y = ± 1/2
so, as we saw above
Y = COS X
1/2 = COS X and - 1/2 = COS X
so to get COS X = ± 1/2, then
X = π/3 = 60 (cos +)
X = 2π/3 = 120 (cos -)
X = 4π/3 = 240 (cos -)
X = 5π/3 = 300 (cos +)
So the only option that includes + and - its:
60° + n360° , 120° + n360°
Show how you can determine that the inscribed figure inside a quadrilateral is a parallelogram. Support your argument with diagrams.
Answer:
Look for perpendicular lines or corresponding angles or alternate interior angles.
Step-by-step explanation:
When you want to show that a quadrilateral is a parallelogram you need to show that the oposite sides are parallel. In order to show that two segments are parallel there are various theorems and definitions you can use.
1 - Remember that two lines perpendicular to the same segment are parallel.
2 - When two lines are cut by a secant and their alternate interior angles are congruent, then the resulting lines are parallel, I will attach a drawing to illustrate what I am saying.
3 - When two lines are cut by a secant and their CORRESPONDING angles are congruent, then the resulting lines are parallel, I will also attach a drawing to illustrate what I am saying.
A scale model of a train is 1:30. If the wheel diameter is 2cm, what is the actual size of the wheel? The wheel is ______ cm on diameter
Answer:
60 cm
Step-by-step explanation:
You need to use ratios to solve. If the scale is 1:30 then the wheel is 2:(?). Cross-multiply the fractions and solve for x.
1/30 = 2/x
1x = 30*2
x = 60
The wheel is 60 cm in diameter.
Answer:
60 centimeters
Step-by-step explanation:
The scale is 1:30. The wheel diameter is 2 while the actual size of the wheel is unknown. Therefore, the scale for the wheel is 2:x
Let’s set up a proportion.
1/30=2/x
First, cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the numerator of the second by the denominator of the first.
1*x= 2*30
1x=20*30
x=20*30
x=60
Add appropriate units, in this case centimeters (cm).
x= 60 cm
The actual diameter of the wheel is 60 centimeters.
What is 25÷5what is 25 / 5
Answer:
5
Step-by-step explanation:
25/5
=5✖️5=25
=5/1
Answer:
25÷5 = 5 and 25/5 = 125
Step-by-step explanation:
hope this helps!
For the population {0, 1, 2, 3, 5, 7},
(a) List all the simple random samples of size 5.
(b) Give an example of a systematic sample of size 3 where the elements are listed
in the order : 0, 1, 2, 3, 5, 7.
(c) Give an example of a proportional stratified sample of size 3 where the strata are
{0, 1, 2, 3}, {5, 7}.
(d) Give an example of a cluster sample size of 2 where the clusters are {0, 1}, {2,3},
{5, 7}.
Which of the following is equivalent to 18 minus StartRoot negative 25 EndRoot?
Answer: 12-i
12-(√-1)
Step-by-step explanation:
[tex]18-\sqrt{-25}[/tex] Original Question
[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex] Split
[tex]18-5*(\sqrt{-1} )[/tex] Solve for square root
[tex]12-\sqrt{-1}[/tex] Subtract
You can substitute [tex]\sqrt{-1}[/tex] for i
[tex]12-i[/tex] Substitute
Answer:
18-5i
Step-by-step explanation:
Rachel is a software saleswoman. Her base salary is $1900, and she makes an additional $110 for every copy of English is Fun she sells. Let P represent her total pay (in dollars), and let N represent the number of copies of English is Fun she sells. Write an equation relating P to N. Then use this equation to find her total pay if she sells 24 copies of English is Fun.
Answer:
P = 110N + 1,900.
$4,540.
Step-by-step explanation:
Her base salary is $1,900, so your constant/y-intercept for the equation is $1,900.
She makes an additional $110 for each copy, so your slope is $110.
P (the total pay) = 110 * the number of copies sold + 1,900
P = 110N + 1,900.
She sells 24 copies.
P = 110 * 24 + 1,900
P = 2,640 + 1,900
P = 4,540.
So, her total pay is $4,540.
Hope this helps!