Answer:
The fraction of the applicants who have passed the two phases of the selection process is [tex]\frac{10}{63}[/tex].
Step-by-step explanation:
The question is:
In the first phase of the selection process for the body of teachers they eliminate four-ninth of the applicants while in the second phase they eliminate 5/7 of those who passed the first phase. If there were 315 applicants what is the fraction of the applicants who have passed the two phases of the selection process?
The total number of applicants is
N = 315.
It is provided that 4/9th of the applicants were eliminated in the first phase.
Then the fraction of candidates who passed the first phase is:
Fraction who passed phase I = [tex]1-\frac{4}{9}=\frac{5}{9}[/tex]
Now, it is also provided that 5/7 of those who passed the first phase were eliminated in the second phase.
Then the fraction of candidates who passed the second phase is:
Fraction who passed phase II = [tex]1-\frac{5}{7}=\frac{2}{7}[/tex]
That is, 2/7 of the remaining applicants passed the second phase.
The fraction of the applicants who have passed the two phases is:
[tex]\frac{5}{9}\times \frac{2}{7}=\frac{10}{63}[/tex]
Thus, the fraction of the applicants who have passed the two phases of the selection process is [tex]\frac{10}{63}[/tex].
Assignment
eo
equation.
Solve x2 - 64 = 0.
1. Isolate x2: x2 = 64
V x2 = 1764
Apply the square root property of equality:
3. Isolate the variable:
7
x=
x=
Answer:
x= 8, x= -8
Step-by-step explanation: 8 and -8
An initial population of 2 bunnies each has 6 babies per month. Using x for months and y for the number of bunnies, write the equation that models this situation.
Answer:
x = 3y
Step-by-step explanation:
In this question, we are asked to model an equation that clearly mimics what we have in the question using certain type of variables.
Now initially, we are told that we have 2 bunnies having 6 babies. what does this tell us?
Looking at this, we can see that the number of babies is exactly 3 times the number of bunnies. More like saying 3 times the number of bunnies equal the number of babies.
so leveraging in this finding and applying the variable, we can say each of the 2 bunnies has 3 babies per month.
Mathematically, this is same as x bunnies = 3y babies per month
Kerri Payne is employed by Carterer's Central company. She has a family membership in the health insurance program. The annual premium is $6,486. Payne's employers pays 80 percent of the total cost. Her contribution is deducted from her paycheck. What is Payne's annual contribution?
Final answer:
To calculate Payne's annual contribution, multiply the annual premium by 20% and subtract that amount from the annual premium.
Explanation:
To calculate Payne's annual contribution, we need to determine 20% of the total cost of the health insurance premium and then subtract that amount from the annual premium.
Step 1: Find 20% of $6,486. Multiply $6,486 by 0.2 to get $1,297.20.
Step 2: Subtract the 20% contribution from the annual premium. $6,486 - $1,297.20 = $5,188.80.
Payne's annual contribution is $5,188.80.
Chris is an appliance repairman. He charges $80 to come out and $60 per hour, thereafter. a) Using h for the number of hours and C for his total cost to his customer, state an equation describing this situation.
Answer:
$80 + $60h =C
Step-by-step explanation:
$80 is the amount charged to come out
$60 times h (h is the number of hours)
add them together for total cost
The equation C = 80 + 60h describes Chris's total cost.
Independent variable: Hours of work, represented by h.
Dependent variable: Total cost, represented by C.
Equation: C = 80 + 60h
Y-intercept: $80, as it is the initial charge when no hours are worked.
Slope: $60 per hour, indicating the rate at which the cost increases per hour of work.
Darcia made a snack mix using the following recipe.
1 ¼ cups granola, ¾ cup peanuts, ½ cup raisins, ¼ cup chocolate chips. If she used 3 cups of granola and wanted to keep the ingredients proportional, how much would she use of each of the other ingredients. Write your answer as a fraction in simplest form. Use / for the fraction bar.
cup(s) peanuts
cup(s) raisins
cup(s) chocolate chips
Answer:
1 4/5 = peanuts
1 1/5 = raisins
3/5 = chocolate chips
Step-by-step explanation:
3 ÷ 1 1/4 = 2 2/5
2 2/5 × 3/4 = 1 4/5
2 2/5 × 1/2 = 1 1/5
2 2/5 × 1/4 = 3/5
To keep proportions with 3 cups of granola, Darcia would need 1 ½ cups of peanuts, 1 ¼ cups of raisins, and 3/5 cup of chocolate chips in her snack mix.
Explanation:Darcia has increased her granola measurement to 3 cups, which is 2.4 times more than the original 1 ¼ cups used in the snack mix recipe (since 3 ÷ 1.25 equals 2.4). To keep the other ingredients proportional to the new quantity, we need to multiply their original amounts by the same factor of 2.4
Therefore, if she used 3 cups of granola, she would use 1 ½ cups of peanuts, 1 ¼ cups of raisins, and 3/5 cup of chocolate chips to maintain the proportions in her snack mix.
PLEASE HURRY DOUBLE POINTS+BRAINLY my question is in the picture
Answer:
(6, - 5)
Step-by-step explanation:
The equation of circle in centre radius form is:
[tex](x - h)^{2} + (y - k)^{2} = {r}^{2} \\ plugging \: h = 3 \: \: k = - 9 \: and \: r = 5 \\ (x - 3)^{2} + \{y - ( - 9) \}^{2} = {5}^{2} \\ (x - 3)^{2} + (y + 9)^{2} = 25 \\ let \: us \: plug \: x = 6 \: and \: y = - 5 \: in \: lhs \\ lhs = (6 - 3) ^{2} + ( - 5 + 9) ^{2} \\ = (3) ^{2} + ( 4) ^{2} \\ = 9 + 16 \\ = 25 \\ = rhs \\ hence \: (6, \: \: - 5) \: is \: on \: the \: circle.[/tex]
Answer:
Answer is option b) (6,-5)
Step-by-step explanation:
[tex]given \: that \: \\ centr e\: of \: circle \: is(3, - 9) \\ and \: radius \: is \: 5 \\ when \: \: we \: calculate \: the \: distance \: between \: (3, - 9) \: and \: (6, - 5) \\ distance \: = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ here \: x1 = 3 \: \: y1 = - 9 \\ x2 = 6 \: \: \: \: y2 = - 5 \\ on \: substituting \: the \: values \\ = \sqrt{(3 - 6) + {( - 9 + 5)}^{2} }^{2 } \\ = \sqrt{ { - 3}^{2} + { - 4}^{2} } \\ = \\ = \sqrt{9 + 16} \\ = \sqrt{25} \\ = 5[/tex]
(6 -5) is a point on the circle.
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
- 3√45-√ 125 + √200-√150
Answer:
=-80-5√5
this is the answer
hope this helps
What was the temperature 1 hour ago
Answer:
it depends what country you are referring to
In order to find a place's temperature, you have to have the continent and the place you are looking for. Temperatures are different every hour. Hope this helps! Stay safe and have a great day!
- Dhruva :)
Suppose the number of bacteria in a certain population increases according to a continuous exponential growth model. a sample of 2200 bacteria selected from the population reached the size 2300 bacteria in one and a half hours. Find the hourly growth rate parameter.
The hourly growth rate is 2%
An exponential growth is in the form:
y = abˣ;
where y, x are variables, a is the initial value of y and b > 1
Let y represent the number of bacteria after x hours.
There was initially 2200 bacteria, hence a = 2200. The equation becomes:
[tex]y=2200(b)^x\\\\\\After\ 1.5\ hours,y=2300:\\\\\\2300=2200(b)^{1.5}\\\\\\b^{1.5}=1.045\\\\1.5lnb=ln(1.045)\\\\ln(b)=0.0296\\\\b=1.02[/tex]
Therefore the hourly growth rate is 1.02 - 1 = 0.02 = 2%
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after how many places the decimal expansion of 13497/1250 will terminate
Answer:
4
Step-by-step explanation:
13497/1250
12500 + 997/1250
12500 + 0.7976
12500.7976
Answer:
4 places of decimals.
Step-by-step explanation:
13497.1250 = 10.7976.
I need help please!! Thanks
Answer:
if I'm correct it's 22 don't quote me on it
Answer:
Surface area = 942.688
Round 4.377 to the nearest hundredth.
Answer:
Submit
Answer:
4.38
Step-by-step explanation:
Answer:
Its 4.38
Step-by-step explanation:
Its because 4.377¨s hundredth place is the 7 near the 7 so rounding a digit with a number of 5 or greater would lead to changing the hunderedth place into a bigger number.
NEED THIS ANSWERED ASAP.
y=–5x + 30x=10
What is the solution to the system of equations?
(–20, 10)
(10, –20)
(10, 4)
(4, 10)
The answer is B, i had to find out on my own....
Answer:
(10, -20) because y=_5x + 30x=10 and there are only 2 answers with 10 in the beginning so also 20 is greater than 40.
Step-by-step explanation:
B
Answer:
Step-by-step explanation:
Can someone please help me ASAP
[tex]y=4-x^2\\x-y=2 \\ \\ y = 4 - {x}^{2} \\ x = 2 + y \\ \\ y = 4 - {(2 + y)}^{2} \\ {y}^{2} + 5y = 0 \\ y(y + 5) = 0 \\ y = 0 \\ y = - 5[/tex]
[tex]x = 2 + 0 = 2[/tex]
[tex]x = 2 + ( - 5) = -3[/tex]
Write a quadratic function f whose zeros are 4 and -5
Answer:
x^2+x-20
Step-by-step explanation:
x = 4
x - 4 = 0
x = -5
x + 5 = -5
(x + 5)(x - 4)
x^2+x-20
The quadratic function with zeros 4 and -5 is f(x) = x² + x - 20.
To write a quadratic function f(x) whose zeros are 4 and -5, we can use the fact that the zeros of a quadratic function correspond to the values of x that make the function equal to zero.
A quadratic function can be represented in the form:
f(x) = a(x - r1)(x - r2)
where r1 and r2 are the zeros of the function.
Given zeros are 4 and -5. Substituting these into the formula, we get:
f(x) = a(x - 4)(x + 5)
Expanding this, we obtain:
f(x) = a(x² + x - 20)
To simplify, we can choose a value for a, usually 1 for simplicity:
f(x) = x² + x - 20
This is the quadratic function with zeros at 4 and -5.
Company Mailing Of a company's mailings 1.5% are returned because of incorrect or incomplete addresses. In a mailing of 200 pieces, find the probability that none will be returned
Answer:
0.0487 = 4.87%
Step-by-step explanation:
The probability of one mail being returned is 1.5% = 0.015, so the probability of the mail not being returned is 1 - 0.015 = 0.985. If we want 0 mails returned from a total of 200 mails, we have 0 mails returned (probabilitity of 0.015) and 200 mails not returned (probability of 0.985), then the final probability is calculated as follows:
Probability = (0.985)^200 * (0.015)^0 = 0.0487 = 4.87%
To find the probability that none of the 200 mailings will be returned because of incorrect or incomplete addresses, we can calculate the probability of an individual mailing not being returned and multiply it by itself 200 times.
Explanation:To find the probability that none of the 200 mailings will be returned, we need to calculate the probability that each individual mailing is not returned. Given that 1.5% of mailings are returned, the probability of an individual mailing not being returned is 1 - 0.015 = 0.985. We can then find the probability that none of the mailings are returned by multiplying this probability by itself 200 times.
P(no mailings returned) = (0.985)200
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How much is $25/ an hour
Answer:
$50,000 per year
($1,000 per week)
What is the surface area of the cube shown?
6.5 lenth 6.5 hieght
Answer:
253.5
Step-by-step explanation:
basically i had the same question so yeah! and im a pro at math
Answer:
Yup, It's 253.5 :)
Step-by-step explanation:
I checked it. It was right ^^
Noah jumped rope for 9 minutes. What percentage of Diego’s time is that? Diego's time is 20.
Answer:
45%
Step-by-step explanation:
Diego's time is 20 and a whole is 100% so multiply 9 by 5 because 20 x 5 is 100 9x5=45. This means Noah's time is 45% of Diego's time
Answer:
45% or 45 percent
Step-by-step explanation:
Yes oof
Use the distributive property to evaluate each expression (5-7)(-30
Answer:
60
Step-by-step explanation:
You first have to do the parenthesis
(5-7)= 5-7= -2
Then just multiply -30 by -2
Since negative x negative = positive, the answer will be positive.
(-2)(-30)= -2 x -30= 60
60
Solve the following system of equations (ASAP please)
Answer:
The answer to your question is the letter A. (4, -8) and (1, -5)
Step-by-step explanation:
Data
x + y = -4 Equation l
y = x² - 6x Equation ll
Process
1.- Substitute equation ll in equation l
x + x² - 6x = -4
2.- Solve the quadratic equation
x² - 5x + 4 = 0
Factor (x - 4)(x - 1) = 0
-Solve for x
x₁ - 4 = 0 x₂ - 1 = 0
x₁ = 4 x ₂ = 1
3.- Substitute x₁ and x₂ in equation l
4 + y₁ = -4 1 + y₂ = -4
y₁ = -4 - 4 y₂ = -4 - 1
y₁ = -8 y₂ = -5
4.- Solutions
(4, -8) and (1, -5)
can 5ft 9ft 14ft make a triangle?
Answer:
Any dimensions can make a triangle, however
this does not make a right angled triangle.
Step-by-step explanation:
Determine the length of the hypotenuse of a right angle triangle with side lengths 5ft and 9ft by using the formula:
[tex]a^2+b^2=c^2\\[/tex]
[tex]\sqrt{a^2+b^2} = c[/tex]
[tex]c=10.29[/tex]
This is not equal to 14ft.
Answer: No, those measurements cannot make a triangle
Why not? Because of the fact that the first two sides (5 and 9) add to 5+9 = 14, which is exactly as long as the third side. I recommend you using a ruler to measure out 5 inches, 9 inches and 14 inches. Mark all three as separate segments on a piece of paper. Then cut out those segments to form strips of paper with the given lengths. Then try to form a triangle. You'll find that it is impossible since the smaller segments combine perfectly to get the longest segment. Instead of a triangle, you'll only have a line segment forming.
As a rule, when you add any two sides of a triangle, they must add to something larger than the third side. The rule more formally is
For any triangle with sides a,b,c, the following three inequalities must hold true
a+b > ca+c > bb+c > aA support wire is tied diagonally from the middle of a tree to a stake on the ground. The length of the wire is 10 ft and the angle of
elevation from the stake is 55". Approximately how high on the tree is the connection point of the wire?
Answer:
8.2 ft
.Step-by-step explanation:
Sketch this situation. Label the 55° angle. The adjacent side is the distance from the stake to the bottom center of the tree. The opposite side is the distance from the ground to the connection point of the wire on the tree. The wire length represents the hypotenuse of this triangle. We want to find the length of the side opposite the 55° angle. Thus, we write
sin 55° = (opposite side)/(hypotenuse), or
(hypotenuse)(sin 55°) = (10 ft)(0.819) = 8.2 ft
Using trigonometry and the sine function, we can calculate the height of the tree as 10 ft * sin(55), which equals approximately 8.19 ft.
Explanation:This problem can be solved using trigonometry, specifically the sine function. In a right triangle, the sine of an angle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the tree forms the opposite side of our triangle, the support wire forms the hypotenuse and the angle of elevation is 55 degrees.
To express this mathematically, we can write: sin(55) = height / 10 ft. Solving this equation for height gives us: height = 10 ft * sin(55). Using a calculator, we find that sin(55) is approximately 0.81915, so the height is around 8.19 ft. Therefore, the connection point of the wire to the tree is at approximately 8.19 ft high.
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1. Walter stopped at the grocery store and
purchased the items on the list below. The
sales tax on the items was 6.25%. How
much did Walter spend at the grocery
store?
Item
Price
Soup
$1.99
Oranges
$3.49
Newspaper
$2.50
Answer:
$8.48
Step-by-step explanation:
Total of Items:
Add up the prices of all the items he bought
soup+oranges+newspaper
1.99+3.49+2.50=7.98
$7.98
Sales Tax:
Multiply his total by the sales tax rate
7.98*6.25%
Convert 6.25% to a decimal
6.25/100=0.0625
7.98*0.0625=0.49875
0.49875
Total With Tax
Add the tax to his total without tax
7.98+0.49875=8.47875
Round to the nearest cent, or hundreth
$8.48
In order to answer the question correctly, please use the following image below:
Use the diagram below to find the measure of LM. (The symbol is in the image below)
What is the degree measurement of LM?(The symbol is in the image below)
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
The value of ∠LPM is 60°
Step-by-step explanation:
It is given that a straight line is 180° and line LN is a straight line. So in order to find angle LM, you have to substract angle MN from 180° :
∠LPN = 180°
∠MPN = 120°
∠LPM + ∠MPN = 180°
∠LPM = 180° - ∠MPN
= 180° - 120°
= 60°
Answer:
60°
Step-by-step explanation:
LPN is a diameter (straight line passing through the centre)
X + 120 = 180
X = 60°
A local newspaper said that the city of Luttrell is expected to grow by 10% each year. The population in 2012 is 130,457 people. Let t represent the number of years after 2012. Which equation could be used to determine the total expected population, P, of Luttrell in t years?
The formula to calculate the expected population of Luttrell in t years, with a 10% annual growth rate, is P = 130,457 × (1 + 0.10)^t.
Explanation:To determine the total expected population, P, of Luttrell in t years, given an annual growth rate of 10%, you would use the formula for exponential growth: P = P0 × (1 + r)t, where P0 is the initial population, r is the growth rate (expressed as a decimal), and t is the number of years after the initial time. In this case, since the population in 2012 (which is our initial time) is 130,457, and the growth rate is 10% or 0.10, the equation becomes P = 130,457 × (1 + 0.10)t. This equation will calculate the expected population after t years.
Final answer:
The equation to determine the total expected population of Luttrell in t years is P = [tex]130,457 × (1 + 0.10)^t,[/tex] where P is the population and t represents the number of years after 2012.
Explanation:
To determine the total expected population, P, of Luttrell in t years, given that it is expected to grow by 10% each year, you can use an exponential growth formula. The formula incorporating this percentage growth rate and starting population in 2012 is:
P = 130,457 × (1 + 0.10)^t
Here, 130,457 is the initial population in the year 2012, 1 + 0.10 represents the growth factor (where 0.10 is the 10% growth converted to a decimal), and t is the number of years after 2012.
For example, to find the population after 1 year (t = 1), you would calculate:
P =[tex]130,457 × (1 + 0.10)^1 = 130,457 × 1.10 = 143,502.7,[/tex] which you would round to the nearest whole person.
Alyssa has 48 muffins which he need to box up in dozens how many boxes does she need
Answer:
4 boxes
48/12 = 4
Step-by-step explanation:
IF THIS ANSWER HELPS YOU, PLEASE MARK IT AS BRAINLIEST!
Answer:
4 boxes
Step-by-step explanation:
This problem is fairly simple all you need to do is divide 48 by 12 and you should get 4. If that is too hard than you can see what 12 multiplyes by to get 48.
Hope that Helped :)
The scale on a map of Indiana is 1 inch = 42 miles. Jill measured the distance on the map from the eastern border to the western border, and it was 3.375 inches. How far is the actual distance? Round to the nearest mile. (whole number) Group of answer choices
Answer: The actual distance is 142 miles.
Step-by-step explanation:
First, you multiply the 3.375 inches by 42 miles since you are trying to scale. It equals 141.75. If you round it to the nearest mile, it equals 142 miles.
Which of the following statements about a variable are true?
A variable cannot be subtracted.
A variable is represented by a letter.
A variable represents a quantity.
A variable cannot be multiplied.
Answer:
option b and c are true ...
Which student solved the equation 107 d = 1,733.4 correctly?
Answer: Sammi's work:
107d=1,773.4
1773.4 divided by 107 = 16.2
Step-by-step explanation:
The value of d for the given expression will be d = 16.2.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the expression is 107d = 1,733.4. The value of d will be calculated as:-
107d=1,773.4
To calculate the value of d the number 1773.4 is divided by 107.
107d=1,773.4
d = 1,773.4 / 107
d = 16.2
Hence, the value of d will be 16.2.
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