Answer:
189
Step-by-step explanation:
Annie brought 10 bagels to school, 7 of which are Asiago cheese.
If Annie randomly gives away 5 bagels to teachers, what is the probability that e
the chosen bagels are Asiago cheese?
Answer:
The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%
Step-by-step explanation:
Given:
Total bagels brought to school = 10
Number of Asiago cheese bagels = 7
To find the probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese.
Solution:
Let probability of choosing an Asiago cheese bagel be the successful event.
Probability of choosing one Asiago cheese bagels = [tex]\frac{7}{10}=0.7[/tex]
Probability of success = 0.7
Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success = [tex]1-0.7=0.3[/tex]
Using Bernoulli Trials
To calculate the binomial probability of obtaining exactly [tex]r[/tex] events in [tex]n[/tex] trials the formula used is:
⇒ [tex]nCr.p^r.q^{(n-r)}[/tex]
where [tex]p\rightarrow[/tex] Probability of success
[tex]q\rightarrow[/tex] Probability of failure
Thus, probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :
⇒ [tex]5C3(0.7)^3(0.3)^2[/tex]
⇒ [tex]\frac{5!}{(5-3)!3!}(0.343)(0.09)[/tex]
⇒ [tex]\frac{5!}{(2)!3!}(0.343)(0.09)[/tex]
⇒ [tex]10(0.343)(0.09)[/tex]
⇒ [tex]0.3087\ or\ 30.87\%[/tex] (Answer)
Find the interquartile range.
6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93
Based on the calculations, the interquartile range of a data set is equal to 53.
In order to determine the statistical measures or the five-number summary, we would arrange the data set in an ascending order:
6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93
Based on the data set, the first quartile can be calculated as follows;
First quartile = [(n + 1)/4]th term
First quartile = (13 + 1)/4
First quartile = 3.5th term
First quartile = (30+9)/2
First quartile = 19.5.
For the third quartile, we have:
Third quartile = [3(n + 1)/4]th term
Third quartile = 3 × 3.5th term
Third quartile = 10.5th term
Third quartile = (75+70)/2
Third quartile = 72.5
Mathematically, the interquartile range of a data set is the difference between third quartile (Q₃) and the first quartile:
Interquartile range of data set = Third quartile - First quartile
Interquartile range of data set = 72.5 - 19.5
Interquartile range of data set = 53.
e - 2f = -10
8e + 4f = 0
Answer:
f = 4 e = -2
Step-by-step explanation:
e - 2f = -10
8e + 4f = 0
Solve by substitution
8e + 4f = 0
8e = -4f
e = -0.5f
Substitute into e - 2f = -10
-0.5f - 2f = -10
-2.5f = -10
2.5f = 10
f = 4
Substitute into 8e + 4f = 0
8e + 16 = 0
8e = -16
e = -2
Answer:
e=-2, f=4. (-2, 4).
Step-by-step explanation:
e-2f=-10
8e+4f=0
-------------
e=-10+2f
e=2f-10
8(2f-10)+4f=0
16f-80+4f=0
20f=0+80
20f=80
f=80/20
f=4
e-2(4)=-10
e-8=-10
e=-10+8
e=-2
how is it possible that all proportional relationships are linear functions but not all linear functions are proportional relationships
Step-by-step explanation:
A line that passes through the origin is proportional (y = mx). But a line that doesn't pass through the origin isn't proportional (y = mx + b). So all proportional relationships are linear, but not all linear relationships are proportional.
proportional relationship is just a linear relationship where the line passes through the origin (0, 0).
How many yards are in 7 3/5 feet?
A. 15 1/5
B. 3 4/5
C. 2 8/15
D. 22 4/5
Please help me!
Answer:
22 4/5 yards
Step-by-step explanation:
(7 3/5) x 3 = 22 4/5
To convert 7 3/5 feet to yards, you use the conversion 1 yard = 3 feet. After converting the mixed number to an improper fraction, you divide by 3, yielding the answer 2 8/15 yards, which corresponds to option C.
To convert feet to yards, we can use the conversion factor that 1 yard is equal to 3 feet. Since the student needs to find out how many yards are in 7 3/5 feet, we can convert mixed numbers to improper fractions to simplify the calculation.
The mixed number 7 3/5 can be converted to an improper fraction by multiplying the whole number 7 by the denominator 5 and adding the numerator 3, then placing the result over the original denominator: (7 * 5) + 3 = 35 + 3 = 38, so 7 3/5 becomes 38/5.
To convert 38/5 feet to yards, divide by 3 because there are 3 feet in 1 yard:
38/5 feet * 1 yard/3 feet = (38/5)/3 = 38/5 * 1/3
This simplifies to 38/5 * 1/3 = 38/15 yards
Then divide 38 by 15 to get 2 with a remainder of 8, so we have 2 and 8/15 yards.
Therefore, the answer is C. 2 8/15 yards.
What is the value of y?
Enter your answer in the box.
Answer:
y = 20
Step-by-step explanation:
Since AB and AC are congruent then the triangle is isosceles, thus
∠B = ∠C = 25°
To find ∠A subtract the sum of the 2 angles from 180°
∠A = 180° - (25 + 25)° = 180° - 50° = 130°, thus
3y + 70 = 130 ( subtract 70 from both sides )
3y = 60 ( divide both sides by 3 )
y = 20
Can someone tell me the answer to this please!!!
the answer is 38
16+18+4
Answer:
46
Step-by-step explanation:
The picture are irrelevant and is used to trick you.
Let swirly hair = s
Let curly hair = c
Let flat hair = f
Ok, now we can rewrite the picture in math terms
s = 16
c = 2 + s = 2 + (16) = 18
s = 4 + f → f = s - 4 = (16) - 4 = 12
s + c + f = 16 + 18 + 12 = 46
What is the solution to the following equation?
х+ (-21) = 8
ОА. x= 27
B. х = 29
с.
x
х = 13
х = 17
What is the solution to the following equation?
х+ (-21) = 8
О А. x= 27
B. х = 29
с. х = 13
D. х = 17
Answer:Option B
The solution to given equation is x = 29
Solution:Given that we have to find the solution of given equation
Given equation is x + (- 21 ) = 8
The value of the variable is found by adding, subtracting, multiplying or dividing both sides of the equation to simplify the equation and isolate the variable.
The goal is to have the variable on one side of the equation and numbers on the other.
From given equation,
x + ( -21) = 8
Let us first remove the brackets around -21
We know when we multiply a positive sign number with negative sign number, we get a negative sign number
x + 1( - 21 ) = 8
x - 21 = 8
Move -21 from L.H.S to R.H.S
x = 21 + 8
x = 29
Thus solution to given equation is x = 29 Thus Option B is correct
Three-fourths of a number multiplied by seven
Answer:
5 1/4 or 5.25
Step-by-step explanation:
Multiplying fractions means that we can multiply the numerator by the numerator and the denominator by the denominator straight across without needing a common denominator.
3*7 = 21
4*1 = 4
We end up with the improper fraction 21/4. We can convert this into a mixed number.
Because 4 goes into 21 a total of 5 times with 1 left over, we end up with the mixed number of 5 1/4, or as a decimal, 5.25
NEED HELP ASAP!!
why we can multiply by the reciprocal of a fraction when completing a division problem?
Answer:we multiply by the reciprocal of a fraction when completing a division problem because it is a rule in mathematics that when you divide two fraction, you change the division sign to multiplication and flip the fraction at the right of the multiplication sign.
Step-by-step explanation:
For example if you have 4÷ 1/2. It basically means how many 1/2 can one get in 4. And the answers is 8.
Therefore multiplying by the reciprocal of a fraction when completing a division problem is a short cut method that has been tested and proven to be correct.
HELP PLEASE I NEED HELP I DONT UNDERSTAND THIS
Answer:
t=44°
Step-by-step explanation:
The sum of the interior angles of any pentagon is always 540 degrees.
Let's set up an equation with this information: (all figures are in degrees)
[tex]t+3t+t+32+149+139=540[/tex]
Now we combine all like terms.
[tex]5t+320=540[/tex]
Now begin to isolate t be subtracting 320 from both sides.
[tex]5t=220[/tex]
Finally divide both sides by 5 to isolate t.
t=44°
1. Write the first ten multiples of these pairs of number and find their LCM
a) 2, 3
Answer:
Multiples:
2: 2 4 6 8 10 12 14 16 18 20
3: 3 6 9 12 15 18 21 24 27 30
The LCM is 6 (underlined)
A culture started with 3,000 bacteria. After 8 hours, it grew to 3,300 bacteria. Predict how many bacteria will be present after 12 hours. Round your answer to the nearest whole number.
Answer:
[tex]3,462\ bacteria[/tex]
Step-by-step explanation:
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
x is the time in hours
y is the numbers of bacteria
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
we have that
[tex]a=3,000\ bacteria[/tex]
For x=8, y=3,300
substitute in the exponential function
[tex]3,300=3,000(b^8)[/tex]
solve for b
[tex]1.1=(b^8)[/tex]
[tex]b=\sqrt[8]{1.1}[/tex]
[tex]b=1.0120[/tex]
Find the value of r
[tex]r=b-1=1.0120-1=0.0120=1.20\%[/tex]
The equation is equal to
[tex]y=3,000(1.012^x)[/tex]
For x=12 hours
substitute the value of x in the equation
[tex]y=3,000(1.012^{12})[/tex]
[tex]y=3,462\ bacteria[/tex]
26 eggs in a carton were broken. this was 5% of the total number of eggs in the carton. how many eggs were in the carton altogether?
Answer:
520 eggs
Step-by-step explanation:
5%*2 is 10%.
10%*10 is 100%,that is the full carton of eggs.
26*2*10 is 520.
There were 520 eggs in the carton altogether.
Hope this helps :)
To find the total number of eggs in the carton, we use the information that 26 eggs (5% of the total) were broken. By solving the equation 0.05x = 26, we determine there were 520 eggs in the carton.
The question at hand is, "26 eggs in a carton were broken. This was 5% of the total number of eggs in the carton. How many eggs were in the carton altogether?"
To solve this problem, let us consider the total number of eggs in the carton as x. Given that 5% of x is equal to 26 eggs, we can write this relationship as an equation: 0.05x = 26. To find x, we divide both sides of the equation by 0.05, yielding x = 26 / 0.05. Calculating this result, we find that x = 520.
Therefore, there were 520 eggs in the carton altogether.
write the first five terms of the sequence by the recursive formula t1=2 and tn=tn-1+3
Answer:
T1 =2 , Tn = 1 /tn-1 For The Geometricseries 6 + 3 + 3/2 + 3/4 + .
Step-by-step explanation:
Answer:
2, 5, 8, 11, 14
Step-by-step explanation:
Find the first 5 terms by substituting n = 2, 3, 4, 5 into the recursive formula
t₂ = t₁ + 3 = 2 + 3 = 5
t₃ = t₂ + 3 = 5 + 3 = 8
t₄ = t₃ + 3 = 8 + 3 = 11
t₅ = t₄ + 3 = 11 + 3 = 14
The first 5 terms are 2, 5, 8, 11, 14
AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.
Answer:
The required points of the given line segment are ( - 1, - 5 ).
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] ) then the mid points M are-
M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )
Here,
Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -
then by the midpoint formula M are-
( 3, - 2 ) = ( [tex]\frac{7 + x}{2}[/tex] , [tex]\frac{ - 9 + y}{2}[/tex] )
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{ 7 + x}{2}[/tex] = 3 , [tex]\frac{- 9 + y}{2}[/tex] = - 2)
( 7 + x = 6, - 9 + y = - 4 )
( x = 6 - 7, y = - 4 + 9 )
( x = - 1, y = -5 )
Hence the required points A are ( - 1, - 5 ).
We can also verify by putting these points into Midpoint formula.
4x3+12+14+40x20-32+43/32+90-12
Answer:
40x20+4x3+
2347
32
Step-by-step explanation:
Let's simplify step-by-step.
4x3+12+14+40x20−32+
43
32
+90−12
=4x3+12+14+40x20+−32+
43
32
+90+−12
Combine Like Terms:
=4x3+12+14+40x20+−32+
43
32
+90+−12
=(40x20)+(4x3)+(12+14+−32+
43
32
+90+−12)
=40x20+4x3+
2347
32
Answer:
Step-by-step explanation:
=40x^20+4x^3+2347/32
Hope this helps mark me as brainiest pls
A group of 3 adults and 5 children pay a total of 52$ for movie tickets
A group of 2 adults and 4 children pay a total of 38$ for tickets what is the cost of one adult ticket and what is the cost for one child ticket
Answer:
$9 adult$5 childStep-by-step explanation:
Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:
3a +5c = 52
2a +4c = 38
__
We can solve this system of equations using "elimination" as follows:
Dividing the first equation by 2 we get
a +2c = 19
Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:
3(a +2c) -(3a +4c) = 3(19) -(52)
c = 5 . . . . . . collect terms
a +2·5 = 19 . . substitute for c in the 3rd equation above
a = 9 . . . . . . subtract 10
One adult ticket costs $9; one child ticket costs $5.
For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?
Answer: 31.43 cm
Step-by-step explanation:
The length of an arc is calculated using the formula:
[tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r
where : theta is the angle in degree
r = radius
If the angle is given in Radian , the length can be calculated using the formula:
L = r∅
Since , the angle is given in degree , we will use the first formula.
L = [tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r
L = [tex]\frac{120}{360}[/tex] X 2 X π X 15
L = [tex]\frac{1}{3}[/tex] X 2 X [tex]\frac{22}{7}[/tex] X 15
L = [tex]\frac{660}{21}[/tex]
L = 31.42857143
L ≈ 31.43 cm
what is 3+ 11t - 9u when t = 9 and u = 11.
Answer:
3
Step-by-step explanation:
3+11t-9u=3+11(9)-9(11)=3+99-99=3
Which of the following is a quadratic function?
Answer:
First answer at the top.
Step-by-step explanation:
if a rectangle has an area of 6 2/3 and a length of 2 1/2 inches what is the width of the rectangle
Answer:
Step-by-step explanation:
Item 14 Question 1 You have at most $60 to spend on trophies and medals to give as prizes for a contest. A drawing of a trophy and some medals are shown. The trophy is labeled 12 dollars each and the medals are labeled 3 dollars each. a. Write an inequality that represents the numbers of trophies x and medals y you can buy. The inequality is:
Answer:
[tex]12x+3y\leq 60[/tex]
Step-by-step explanation:
Let
x ----> the numbers of trophies you can buy
y ----> the numbers of medals you can buy
we know that
The term "at most" means "less than or equal to"
so
The number of trophies multiplied by $12 plus the number of medals multiplied by $3 must be less than or equal to $60
The inequality that represent this situation is
[tex]12x+3y\leq 60[/tex]
[tex]3x + 12y\leq 60[/tex]
Step-by-step explanation:
If function g has the factors (x − 7) and (x + 6), what are the zeros of function g?
A.
-7 and 6
B.
-6 and 7
C.
6 and 7
D.
-7 and -6
Answer:
B)
Step-by-step explanation:
Do the zero property.
x-7=0, x+6=0
x=0+7=7,
x=0-6=-6
Answer:
b 100% true
Step-by-step explanation:
I have way more questions than this answer them if you want pleaseee!!
The right answer is Option C.
Step-by-step explanation:
Given inequality is
6(2x-1) > 24
Solving the inequality
[tex]6*2x-1*6>24\\12x-6>24[/tex]
Adding 6 on both sides
[tex]12x-6+6>24+6\\12x>30[/tex]
Dividing both sides by 12
[tex]\frac{12x}{12}>\frac{30}{12}\\x>\frac{5}{2}[/tex]
Therefore,
[tex]x>\frac{5}{2}[/tex]
The right answer is Option C.
Keywords: inequality, division
Learn more about division at:
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write the ratio as a fraction in simplest form
30 to 18
Answer:
5/3
Step-by-step explanation:
30/18=5/3
To see how fast the moss was growing students recorded how long it took the moss to cover a rule. After one hour, the moss had covered 1 1/8 inches of the ruler. After two hours, it had covered another 1 1/3 inches of the ruler. How much of the ruler did the moss cover altogether after two hours?
Answer:
The moss will cover [tex]2\frac{11}{24}[/tex] inches of the ruler after 2 days.
Step-by-step explanation:
After one hour, the moss had covered [tex]1\frac{1}{8}[/tex] inches of the ruler.
Again, after two hours, it had covered another [tex]1\frac{1}{3}[/tex] inches of the ruler.
Therefore, after two hours the moss covers altogether ([tex]1\frac{1}{8} + 1\frac{1}{3}[/tex]) inches of the ruler.
Now, ([tex]1\frac{1}{8} + 1\frac{1}{3}[/tex])
= [tex]\frac{9}{8} + \frac{4}{3}[/tex]
= [tex]\frac{9\times 3 + 4 \times 8}{24}[/tex]
= [tex]\frac{59}{24}[/tex]
= [tex]2\frac{11}{24}[/tex] inches
Therefore, the moss will cover [tex]2\frac{11}{24}[/tex] inches of the ruler after 2 days. (Answer)
building A has 7500 square feet of office space for 320 employees. building B has 9500 square feet of office space for 370 employees.which building offers more square feet per employee, and how much more
Building B offers more square feet per employee
Building B offers 2.2375 square feet more space for 1 employee than building A
Solution:
Building A has 7500 square feet of office space for 320 employee
Let us find the square feet needed for 1 employee
[tex]\text{ square feet needed for 1 employee } = \frac{7500 square feet}{320 employee}[/tex]
[tex]\text{ square feet needed for 1 employee } = \frac{7500}{320} = 23.4375[/tex]
Thus unit rate for building A is 23.4375 square feet per employee
Building B has 9500 square feet of office space for 370 employees
[tex]\text{ square feet needed for 1 employee } = \frac{9500}{370}\\\\\text{ square feet needed for 1 employee } = 25.675[/tex]
Thus unit rate for building B is 25.675 square feet per employee
On comparing the unit rate of both buildings, we can clearly see that Building B offers more square feet per employee
To find out how much more Building B offers more square feet per employee than building A, we can find difference between unit rates of both buildings
[tex]\rightarrow 25.675 - 23.4375 = 2.2375[/tex]
Thus Building B offers 2.2375 square feet more space for 1 employee than Building A
Final answer:
Building B offers 25.68 square feet per employee, which is 2.24 square feet more per employee than Building A, which offers 23.44 square feet per employee.
Explanation:
To determine which building offers more square feet per employee, we calculate the square footage per employee for each building:
Building A: «Building A has 7500 square feet of office space for 320 employees.
Building B: «Building B has 9500 square feet of office space for 370 employees.
Now we calculate the square footage per employee for both buildings:
For Building A: 7500 square feet / 320 employees = 23.44 square feet per employee.
For Building B: 9500 square feet / 370 employees = 25.68 square feet per employee.
Comparing the two, Building B offers more square footage per employee. To find out how much more:
25.68 - 23.44 = 2.24 square feet more per employee in Building B than Building A.
Mary's dog needs medication she told the veterinarian that the dog weighs 30 pounds the medicine is measured as 16 mg for each kilogram of the animals mass how much medicine should be given to Mary's dog
Answer:
217.6 mg of medicine
Step-by-step explanation:
13.6 kilograms in 30 pounds
13.6*16
The surface area of the box of cereal displayed is 2x^2+48x+88. What is the value of x if the box of cereal has a total surface area of 192 in
To find the value of x for the box of cereal, set the given expression for the surface area equal to 192 and solve for x.
Explanation:To find the value of x, we need to set the given expression for the surface area of the box equal to 192 and solve for x. So, we have:
2x^2 + 48x + 88 = 192
2x^2 + 48x - 104 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's factor it:
(2x - 4)(x + 26) = 0
Setting each factor equal to zero and solving for x, we get:
2x - 4 = 0, x = 2
x + 26 = 0, x = -26
So, the possible values of x are 2 and -26. However, since the dimensions of a box cannot be negative, the value of x for the box of cereal is 2.
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