The number of years that will take for the schools to have the same number of students is given as follows:
11 years.
How to define the linear functions?The number of students in each school is modeled by linear functions in slope-intercept format, as follows:
y = mx + b.
In which:
m is the slope, representing the yearly change.b is the intercept, representing the initial amount of students in each school.The functions for this problem are given as follows:
Seaview: Se(t) = 1206 + 7t.Springtown: Sp(t) = 1074 + 19t.They will have the same number of students when:
Sp(t) = Se(t).
Hence:
1074 + 19t = 1206 + 7t
12t = 132
t = 132/12
t = 11 years.
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determine the minimum distance (ft) it will take for a driver going at the speed limit to come to stop at the traffic light after the traffic light turns yellow. b) what will be minimum stopping distance if the driver was going at 45 mph (5 mph over the speed limit)? express it in ft and also as % of the distance you found in part a). c) what will be the minimum stopping distance if the driver was going at 50 mph (10 mph over the speed limit)? express it in ft and also as % of the distance you found in part a). g
The minimum stopping distance is 800 ft.
Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.
Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.
Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.
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The population of a city in 2015 was 36,000. The population is increasing at 15% per year.
Part A: Write an exponential equation that models the population, P(x), where x represents the number of years since 2005.
Part B: Based on your equation, what was the population in 2020? Show how you obtained your answer.
A: The exponential function for the situation is P(t) = 36,000 × (1 + 0.15)^t.
B: The population in 2020 was 72,396.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The population of a city in 2015 is 36,000 and it is increasing at 15% per year.
Model this using an exponential equation of the form -
P(t) = P0 × (1 + r)^t
Where -
P(t) is the population after t years
P0 is the initial population in 2015 (36,000)
r is the rate of growth (0.15)
t is the number of years since 2015
So the exponential equation that models the population is -
P(t) = 36,000 × (1 + 0.15)^t
Part B:
To find the population in 2020, substitute t = 5 (2020 - 2015) into the equation -
P(5) = 36,000 × (1 + 0.15)^5
P(5) = 36,000 × 1.15^5
P(5) = 36,000 × 2.011
P(5) = 72396
Calculating this gives us a population of approximately 72,396 in 2020.
To obtain this answer, the exponential equation that models the population, P(t), is used where t represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for t.
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on a fair die whose faces are numbered consecutively starting from 1, the probability of rolling an even number is less than twice the probability of rolling a multiple of 3. which could be the number of sides on the die?
Answer:
iam sorry
i don't know the answer
5b-2c + 3)-d, a +2b-c+d, 2-d + 3c + a
The sum of the given expression will be 2a+7b+-d.
What are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now
Given expressions are 1.5b-2c+3-d 2.a+2b-c+d 3.2-d+3c+a
By adding these
=a+a+5b+2b-2c-c+3c-d+d-d
=2a+7b-d
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dilate figure ABCD by a cale factor of 3 with the center of dilation at the origin
the slope of A'B' is= 1.2 ,The length of A'C' in triangle is = 3q unit.
When we dilate a triangle and the center of the dilation is at the center of the triangle, the only thing that changes are the coordinates of the summits of the triangle.
The angles remain the same, so do the slope.
So, since the slope of AB is equal to -1.2, the slope of A'B' will also be -1.2.
They say the dilation factor was 3, that means the length of every side was multiplied by 3. So, if the length of AC is q units, the length of A'C' is 3q units.
The complete question is-
ΔABC is dilated by a scale factor of 3 with the origin as the center of dilation to form ΔA′B′C′. The slope of AB is -1.2. The length of AB is p units, the length of AC is q units, and the length of BC is r units.
The slope of AB is (?). The length of is (?) units.
the slope of AB is?
A. 1.2 B. -1.2 C. -3.6
The length of AC is ?
A. 1/3q
B. 3q
C.-1.2p
D. (p+q+r)
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What is 2/3+3/7? I CAN'T FIGURE IT OUT! Work it out!
in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Lisa and Joe put $46 towards the gift
How much money did Lisa and Joe put towards the gift?Let's call the amount of money that Sara put in "x".
Joe put in twice that amount, so he put in 2x.
Lisa put in ten dollars more than Sara, so she put in x + 10.
Together, Sara, Joe, and Lisa put in x + 2x + (x + 10) = $58.
Evaluate the like terms, so we have
4x + 10 = 58.
Subtracting 10 from both sides, we get
4x = 48.
Dividing both sides by 4, we find that
x = $12.
So Sara put in $12, Joe put in $24, and Lisa put in $22.
The total amount put by Lisa and Joe is $24 + $22 = $46.
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Complete question
Three friends are put their money together to buy a $58 gift. Joe put in twice the amount of money as Sara. Lisa put in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Question
Two boxes need to be wrapped in paper (with no overlap). Both boxes are in the shape of right rectangular prisms.
Box A measures 0.8 feet high, 0.6 feet long, and 1 foot wide. Box B measures 1.4 feet high, 0.5 feet long and 1.2 feet wide.
The wrapping paper costs $6.79 per 80 square feet.
What is the cost of wrapping both boxes?
Enter your answer in the box.
$
Answer:
0.82
Step-by-step explanation:
A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76
B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96
total 9.72
cost = $6.79* 9.72/80 =$0.82
Answer:
0.92
Step-by-step explanation:
Solve the inequality. -1.5x < 7.5
Answer: x > -5
Step-by-step explanation:
-1.5x < 7.5
x > -5 (When multiplying both sides by a negative, the inequality is flipped)
[tex]-1.5x < 7.5[/tex]
Divide both sides by -1.5:
[tex]\dfrac{-1.5x}{-1.5} < \dfrac{7.5}{-1.5}[/tex]
When dividing by a negative number, the inequality sign will reverse.
Answer:
[tex]x > -5[/tex]
Nicole is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 18 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 41^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 44^{\circ} ∘ . If her eyes are 1.68 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.
The height of the antenna is 17m approximately to the nearest metre using the trigonometric ratio of tangent for angleof elevation 44°.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangle formed by the point of Nicole's eyes E with an angle of elevation 44°, top of the roof A (90°) and the top of the antenna B,
we shall evaluate for the height of the antenna AB as follows:
tan 44° = AB/18m {opposite/adjacent}
AB = 18m × tan 44° {cross multiplication}
AB = 18m × 0.9657
AB = 17.3826m
Therefore, the height of the antenna to the nearest metre is 17 metres using the trigonometric ratio of tangent for angleof elevation 44°.
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Answer:
2 meters
I got it correct in my hw (check the photos)
also mark me brainleist
Given the two functions, which statement is true?
f(x) = e^x, g(x) = e^x-2
g(x) is translated down 2 units compared to f(x)
g(x) is translated right 2 units compared to f(x)
g(x) is translated left 2 units compared to f(x)
g(x) is translated up 2 units compared to f(x)
The point (6, -2) is reflected over the and-axis. What are the coordinates resulting point, A?
WHICH one doesn’t belong
9 16
25 43
NUMBER 1
from Pam Wilson
From the set of numbers 9, 16, 25, 43 , the number does not belong to the group is prime number 43.
Set of numbers are 9, 16 , 25, 43.
9 is the composite number with 1, 3, 9 as factor.
It is perfect square of 3 also.
16 is the composite number with 1, 2, 4, 8,16 as factors.
It is perfect square of 4 also.
25 is the composite number with 1, 5, 25 as factors.
It is perfect square of 5 also.
43 is not a composite number.
It has only two factors 1, 43.
43 is a prime number.
It is not a perfect square of any number.
Here 43 does not belong to the group.
Therefore, the number which does not belong to the group from 9,16, 25, 43 is 43.
The above question is incomplete, the complete question is :
Which number does not belongs to group ?
9, 16, 25, 43.
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glassdoor four players pick a real number from [0,1]. the players with the middle two numbers are paired together, while the players with the two extreme numbers are paired together. the pair with a lower sum has to each pay the difference to the pair with a higher sum. if you are allowed to choose your number (while everyone else draws uniformly at random), which number should you choose?
The expected value of the sum of the two extreme numbers is 1/2.
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.
This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.
Therefore, the expected value of the sum of the two extreme numbers is 1/2.
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3/5 less than a number, and the result is squared
Answer:
(n - 3/5)²
Step-by-step explanation:
(n - 3/5)²
The total cost (in dollars) of a cell phone plan after x months can be represented by c(x) = 35x + 20. Find the inverse function. Then find the number of months
when the total cost is $1700.
The number of months when the total cost is $1700 is 48 months
What is a function?
A function can be defined as an expression, equation, law or rule that shows the relationship between two variables.
These variables are;
Dependent variableIndependent variableFrom the information given, we have that;
The function for the total cost is c(x) = 35x + 20x represents the number of monthsNow, substitute the values, we have;
1700 = 35x + 20
collect like terms
35x = 1700 - 20
subtract the like terms
35x = 1680
Make 'x' the subject of formula
x = 48 months
Hence, the value is 48 months
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Can anyone help?- I need it by 11:30.
Answer:
See Below
Step-by-step explanation:
5. [tex]3.1 + (8.6 + m)\\3.1 + 8.6 + m\\11.7 + m[/tex]
take expression out of brackets by distribution (multiplying both by 1), then add
6. [tex]((\frac{2}{3})(t)) (1\frac{1}{2})\\(\frac{2}{3}t) (1\frac{1}{2})\\(\frac{2}{3}t) (\frac{3}{2})\\\frac{6}{6} t\\t[/tex]
Simplify the expression in the brackets by multiplying them together, once done turn the mixed fraction back into improper fraction in order to multiply the two together. Once done, simplify the expression
7. [tex]4(x + 8)\\4x + 32[/tex]
I would argue that factored form is the most simplified but regardless using the distribution rule you multiply both numbers within the bracket in order to get rid of it
8. [tex]4t + 7 + 2t - 2\\6t + 5[/tex]
This is just combining like terms and simplifying
How do I find the median of this trapezoid?
Answer:
23.37
Step-by-step explanation:
There ya go
:)
PLEASE HELP
A restaurant plans to use a new food delivery service. The food delivery service charges $5.48 for every 2 meals delivered, plus a $3.50 service fee. What is the slope of this situation?
A.2.74
B.3.50
C.5.48
D. 6.24
8.A rocket travels at an approximate speed of 7.9 kilometers per second.
Which statements about the rocket are true?
Select all that apply.
The statement below about the rocket is true:
A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.
What is Unit conversion?A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).
Given, A rocket travels at an approximate speed of 7.9 kilometers per second.
Since, some unit conversion:
1 kilometer = 1000 meteres
1 kilometer = 100000 centimeteres = 10⁵ cm
1 kilometer = 10000000 milimeteres = 10⁷ mm
thus we can say that from the given options only "f" is correct that states:
A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.
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from a pack of cards, 2 cards are drawn in succession and the selected card is not replaced. what is the probability that both the drawn cards are diamonds? (refer to the deck of cards material shared in reference material to get better understanding of cards)
Two cards are drawn in succession from a standard deck. The probability that both the drawn cards are diamonds is 143/2,652
Probability is defined as the ratio of the number of favorable events to the the number of possible outcomes. The probability of an event A is defined as:
P(A) = n(A)/n(S)
Where:
n(A) = number of possible ways the event A occurs
n(S) = total possible outcomes
In a standard deck, there are 52 cards. The number of diamond suit = 13 cards.
First drawn: number of diamond = 13
Hence, P1(diamond) = 13/52
In the second drawn, the number of diamonds left is 13 - 1 = 12, and total number of cards left is 52 - 1 = 51.
Hence, the probability of the second card will be a diamond is:
P2(diamond) = 12/51.
Since those 2 events are independent, the probability that both cards are diamonds is:
P(diamonds) = P1 (diamond) x P2 (diamond)
= (13/52) x (11/51) = 143/2,652
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a car magazine is comparing the top speed in miles per hour of 15 different sports cars. the speeds are included in the table below. top speeds 267.71 253 187 247.16 188 250.4 240.10 224 195 212 248.5 190 205 202 245 use a calculator to create a histogram for the data. use the default window size. what is the result?
The result of a histogram of the given data is 0.8.
There are a few steps to use a TI-83, TI-83 plus, or TI-84 calculator is used to create the histogram.
1. First, the process is to press the STAT key and then press ENTER.
2. Enter the data into column L1.
3. In the third step with all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu.
4. After that press ENTER and make sure that Plot1 is set to On.
5. Use the directional keys to navigate to the Type selector, move the selection to the third type in the top row, and press ENTER.
6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1.
7. Finally, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is finished, the correct histogram will display on the calculator.
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The sum of the ages of Jaren and his brother, Daniel is 40. Four years ago, Daniel was 3 times as old as Jaren. Calculate
(i) Jaren's present age
(ii) the age of Daniel when Jaren was born
Answer:
(i) Let's call Jaren's current age J. According to the problem, the sum of J and Daniel's age is 40.
If we also know that four years ago, Daniel was 3 times Jaren's age, we can set up the following equation:
J + (J+4) = 40
Solving for J, we find that Jaren's present age is 18.
(ii) When Jaren was born, Daniel would have been 18 + 4 = 22 years old.
At the end of each month, Bianca deposits $100 into an account with an interest rate of 4.25%, compounded monthly. If no money is withdrawn from the account, what will her balance be after 5 years?
Answer:
123.630189899 or A. $1,257.72
Step-by-step explanation:
[tex]\frac{4.25}{100}=0.0425\\ 100(1 + \frac{0.0425}{12})^{12(5)} \\= 123.630189899[/tex]
3 Points
Steven rents an apartment in an all-wood building in the city suburbs. The
value of the belongings in the apartment is about $15,000. If Steven wants to
insure his belongings while renting, how much will he have to pay for
insurance per year?
Annual Premium per $100 of coverage
Brick. . Steel
Mixed
Wood
Area Building Contents Building Contents Building Contents Building Contents
rating
City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76
Suburb 0. 45 0. 52 0. 56 0. 63 0. 72 0. 74 083 085
Rural 0. 6 0. 69 0. 71 0. 8 0. 89 0. 91 1 | 102
O A. $150. 00
O B. $107. 50
OC. $127. 50
O D. $173. 50
Steven will have to pay $127. 50 for the insurance per year.
The correct answer is an option (C)
First, we need to find the corresponding value for the all-wood building in the city suburbs.
From given table, we will use the value 0.85 because he wishes to ensure his belongings.
Here, the value of the belongings in the apartment is about $15,000
Steven wants to insure his belongings while renting.
Now we can calculate the amount of money he will have to pay for insurance per year as follows:
15000 × (0.85 / 100)
= 127. 50 dollars
Therefore, he will have to pay 127. 50 dollars for insurance.
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Chase tried to evaluate an expression. Here is his work: 2(12÷2)2–14+6 = Step 1262–14+6 = Step 2236–14+6 = Step 372–14+6 = Step 472–20 = Step 552 Is Chase's work correct? PLEASE HELP FAST THIS IS FOR 6th GRADE IXL
No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.
We have 2(12 ÷ 2)2 – 14 + 6
Here according to the BODMAS rule which stands for Brackets Of Division Multiplication Addition Subtraction, we will first solve the brackets.
Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.
12 ÷ 2 = 6
Hence we get
2 X 6 X 2 - 14 + 6
Now we need to multiply.
2 X 6 X 2 = 12 X 2 = 24
Hence we get
24 - 14 + 6
Now we need to add the numbers up.
24 + 6 = 30 hence we get
30 - 14
= 16
Hence Chase's work is not correct.
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25-2x≤5(2-x) pls solve w/ steps
Answer: X has to be greater than or equal to 15/7 for the inequality to be true.
Step-by-step explanation:
here are the steps to solve the inequality 25-2x≤5(2-x):
Start by simplifying the right side of the inequality: 5(2-x) = 10 - 5x
Now we can substitute this back into the original inequality: 25 - 2x ≤ 10 - 5x
Next, we need to combine like terms on both sides of the inequality: 25 - 7x ≤ 10
Now we'll add 7x to both sides: 25 ≤ 10 + 7x
Subtract 10 from both sides: 15 ≤ 7x
Finally, divide both sides by 7: 15/7 ≤ x
The solution set is x ≥ 15/7.
So x has to be greater than or equal to 15/7 for the inequality to be true.
Answer:
-5 ≥ x or x ≤ -5
Step-by-step explanation:
25 - 2x ≤ 5(2 - x)
distribute the 5 to eliminate the parentheses:
25 - 2x ≤ 10 - 5x
now combine like terms:
15 - 2x ≤ -5x
15 ≤ -3x
-5 ≥ x or x ≤ -5
the inequality symbol gets switched whenever you multiply or divide by a negative value
You can model the arch of the fireplace using the equation y =-1/9(x+18)(x-18) when x and y are measured in inches. The x-axis represents the floor. Find the width of the arch at floor level
The width of the arch at floor level is 18 inches.
Substitute x = 0 into the equation.
y = -1/9(0+18)(0-18)
Solve for y.
y = -1/9(-18)(18)
y = 18
Therefore, the width of the arch at floor level is 18 inches.
A linear system can be algebraically solved using the substitution approach. One y-value is substituted for another in the substitution procedure. Finding the value of the x-variable in terms of the y-variable is the method's most straightforward step.
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A ball is thrown upward at an angle of elevation of 28 degrees with a force of 19n. How much of that force is horizontal and how much of that force is vertical?
19N force act in upward direction with angle of elevation 28 degrees has horizontal and vertical force is given by 16.78N and 8.92N respectively.
Angle of elevation while thrown a ball upward 'α' = 28 degrees
Force 'F' is equal to 19N.
While throwing a ball force is applied in two possible direction are:
Horizontal direction and Vertical direction.
For horizontal direction :
let 'x' represents the horizontal direction
cosα = x / F
⇒ cos28° = x / 19
⇒ x = 19 cos 28°
⇒ x = 19 × 0.8829
⇒ x = 16.78N
For Vertical direction :
let 'y' represents the vertical direction
sinα = x / F
⇒ sin28° = y / 19
⇒ y = 19 sin 28°
⇒y = 19 × 0.4695
⇒ y = 8.92N
Therefore, the horizontal force and vertical force for the given angle of elevation is equal to 16.78N and 8.92N respectively.
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Factor the quadratic expression completely.
-3x² +172-20=
Answer: The given quadratic expression is -3x²+172x-20. To factor this expression, we look for two numbers that multiply to -20 and add to 172.
We can start by dividing -20 by different numbers and checking if the product and the sum of the divisors equals -20 and 172 respectively.
-20/1 = -20, 1+-20 = -19
-20/2 = -10, 2+-10 = -8
-20/4 = -5, 4+-5 = -1
-20/-1 = 20, -1+20 = 19
-20/-2 = 10, -2+10 = 8
-20/-4 = 5, -4+5 = 1
We can see that the divisors that multiply to -20 and add to 172 are (x+8)(x-5)
So, we can factor the quadratic expression as:
-3x²+172x-20 = -3(x+8)(x-5)
Hope this helps!
Step-by-step explanation: