Initial velocity of the ball (u) = 80 ft/ sec
Final velocity of the ball after reaching the ground (v) = 0
Distance covered by the ball to reach the ground (s) = 8 ft
Let "a" be the acceleration of the ball.
We know, [tex]2as=v^{2}-u^{2}[/tex]
[tex]2a(8)=0-80^{2}=-6400[/tex]
[tex]a=-\frac{6400}{16}[/tex]
[tex]a=-400ft/s^{2}[/tex]
Let "t" be the time required to reach the ground.
We know,
[tex]v=u+at[/tex]
[tex]t=\frac{v-u}{a}[/tex]
[tex]t=\frac{0-80}{-400}[/tex]
[tex]t=0.2s[/tex]
The ball will hit the ground in 0.2 second.
Adam currently runs about 20 miles per week,aND he wants to increase his weekly mileage by 40% How many miles will Adam run per week
28 miles
increasing by 40% = original + increase = 100 + 40 = 140% = 1.4
multiplying 20 by 1.4 gives total he will run
miles run = 1.4 × 20 = 28
Answer:
28 miles
Step-by-step explanation:
Just multiply (20 miles per week) by 1.40: 1.40(20 mpw) = 28 miles
I NEED HELP!!!!!!!!!!!! FAST!!!!!
On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system.
y ≥ 3x + 2
A. Region B
B. Region C
C. Region A
D. Region D
From the graph, we know the y-intercepts (look at the picture).
y = 2 → y = 3x + 2
y = 3 → y = -1/3x + 3
We have
y ≥ 3x + 2 (shadow up of a line)
y ≤ -1/3x + 3 (shadows down of a line)
the common region is D.
Answer: D. Region D.Answer:
Option (a) and (d) are correct.
region A and region D satisfies the given inequality y ≥ 3x + 2.
Step-by-step explanation:
Given : The graph of the system of inequalities y ≥ 3x + 2.
We have to determine which region contains the solution to the system.
We will chose a test point in each region and see which point satisfies the given inequality.
For region A)
(0,6) is in region A
Put x = 0 and y = 6 in given inequality
We get,
6 ≥ 3(0) + 2.
6 ≥ 2 (True)
For region B)
(4,6) is in region B
Put x = 4 and y = 6 in given inequality
We get,
6 ≥ 3(4) + 2.
6 ≥ 12 + 2 = 14 (False)
For region C)
(0,0) is in region C
Put x = 0 and y = 0 in given inequality
We get,
0 ≥ 3(0) + 2.
0 ≥ 2 (False)
For region D)
(-2,2) is in region A
Put x = -2 and y = 2 in given inequality
We get,
2 ≥ -3(2) + 2.
2 ≥ -6+ 2 = -4 (True)
Thus, region A and region D satisfies the given inequality
Thus, Option (a) and (d) are correct.
Help with algebra please
If it is like in the picture, then:
Domain = [-3, 3] (we read from the x axis)
Range = [-3, 1] (we read from the y axis)
If there are no points at the ends of the segments, then:
Domain = all real numbers
Range = (-∞ , 1]
A running coach checks on his team's best recorded sprinting times during practice. Drag the runners in order from the greatest to the least unit rate in meters per second.
Carla
Amir
Carlo
Esther
From greatest to least!
Answer:
1. Carla
2. Amir
3. Carlo
4. Esther
What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) ?
Enter your answer in the box.
Given
A triangle.
with vertices at (−2, 1) , (2, 1) , and (3, 4)
Find out the area of a triangle.
To proof
Formula
[tex]Area\ of\ triangle = \frac{1}{2}[ x_{1} (y_{2} -y_{3} ) + x_{2} (y_{3} - y_{1})+x_{3}(y_{1}-y_{2})[/tex]
As given the vertices at (−2, 1) , (2, 1) , and (3, 4)
put in the above equation
we get
[tex]= \frac{1}{2} [-2(1-4)+ 2 (4-1) + 3 ( 1-1) ][/tex]
solving
[tex]= \frac{1}{2} [6 + 6][/tex]
thus
[tex]=\frac{1}{2} [12][/tex]
area of the triangle is 6 units².
Hence proved
The area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) is; Area = 6 units²
The formula for the area of a triangle when given the 3 vertices is;
Area = ½[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]
In this question, the vertices coordinates are; A(−2, 1), B(2, 1), and C(3, 4)
Thus;
Ax = -2
Bx = 2
Cx = 3
Ay = 1
By = 1
Cy = 4
Plugging in the relevant values into the area equation gives;
Area = ½[-2(1 - 4) + 2(4 - 1) + 3(1 - 1)]
Area = ½(6 + 6 + 0)
Area = ½ × 12
Area = 6 units²
Read more at; https://brainly.com/question/19044159
Isaiah puts a kilogram weight on a pan balance, how many
100 gram weights does he need to balance the scale
Isaiah would have to put 10 one-hundred gram weights to balance it out because there are 1000 grams in a kilogram.
4xy + 9x + 24y + 54 please help!!!
You can't simplify this equation anymore.
What is the value of x? x+4/5=11 Enter your answer in the box in simplest form. Please explain how you got your answer.
x = [tex]\frac{51}{5}[/tex]
subtract [tex]\frac{4}{5}[/tex] from both sides of the equation
x = 11 - [tex]\frac{4}{5}[/tex] = [tex]\frac{55}{5}[/tex] - [tex]\frac{4}{5}[/tex] = [tex]\frac{51}{5}[/tex]
Answer:
10.92 or 10 23/25
Step-by-step explanation:
What you do is you try to get X by itself so put the fraction 4/5 on the other side so that is turns out to be 11-4/5. Now you can turn 4/5 into a decimal which would be .8 and subtract that by 11which gives you 10.92 or if you want to keep it as a fraction .92 as a fraction is 23/25 so you get 10 23/25
Plot the data points on the graph below. Make sure you use the corresponding color dot for the point according to the following: 1st point - yellow dot, 2nd point - blue dot, 3rd point - green dot, 4th point - red dot, 5th point - pink dot, 6th point - purple dot. x values y values 1 18 2 9 3 6 6 3 9 2 18 1 (Inverse relationship, k = 18)
Hello,
Please, see the attached graph.
Thanks.
Answer: :)
Step by Step: :)
Please help me
10 points
In step 2 multiply what is inside the parenthesis by 7 (distributive property):
7 * x = 7x
7 * 3 = 21
In step 3 subtract -7x on both sides of the equation. (Property of subtraction of equality)
Then -7x + 4x = -3x
7x-7x + 21 = 21
In step 4, both sides of the equation are divided by -3. (owned by the equality division)
So:
-3x / -3 = x
-21 / -3 = 7
Recall that the division of equal signs results in a positive number.
A die was rolled 6 times and the results are displayed in matrix A. If the die rolls were repeated with the same results, which formula shows how to find the matrix that would display these results?
Answer:
None of the above. (Ask your teacher to show you how to work this problem.)
Step-by-step explanation:
Since the results are identical, the matrix of the next three rolls will look exactly like this matrix. (A)
The matrix of all 6 rolls will look like a 6-row matrix with the bottom 3 rows identical to the top 3 rows.
Adding or multiplying A by a constant will not produce these results.
_____
You can replicate columns using matrix multiplication, so you can transpose A, multiply it by a suitable version of an identity matrix, then transpose the result:
((A^T)·[I | I ])^T will turn the 3-row matrix to a 6-row matrix where I is a 3x3 identity matrix. I've used [I | I] here to mean the 3x3 identity matrix is itself replicated horizontally to make a 6-column matrix. ^T indicates transpose.
To represent the results of repeating die rolls in a matrix, each entry in the initial results matrix A is multiplied by the scalar value of the experiment repetition. If matrix A reflects 6 die rolls, the matrix for repeating these results would be 2A.
The student's question pertains to outcomes from rolling a six-sided die and recording the results in a matrix. To find the matrix representation of repeating the same die rolls, we would need to multiply the matrix A by the scalar value that represents the number of times the experiment is repeated. For example, if we denote matrix A as the initial 6 results and they repeated the experiment for the same number of times, then we would just need to multiply each entry in matrix A by 2 (since the results were repeated once more).
If matrix A is represented as:
A = [a b cWhat is the value of the number 3 in the the number 12,532.628
What is the value of the number 3 in the the number 12,532.628
Solution
Here we need to use the place chart. I have attached the place value chart.
According to the place chart 3 is in tens place.
Therefore, the value of the number 3 in the number 12,532.628 is 3 x 10 = 30.
The answer is 30.
In the number 12,532.628, the digit 3 is located in the hundreds place, which means its value is 300.
The value of the number 3 in the number 12,532.628 is located in the hundreds place. To determine the place value of this digit, we start from the rightmost digit after the decimal point and move towards the left before the decimal point, labeling each position as follows: tenths, hundredths, thousandths, then units, tens, hundreds, thousands, and so on.
In 12,532.628, there are 2 units, 5 tens, 3 hundreds, 2 thousands, and 1 ten-thousands. Hence, the value of the number 3 here is 300. The digit 3 represents three hundred because it is in the hundreds place value.
The davis family traveled 35 miles in 1/2 hour if it is currently 2:00pm any the family destination is 245 miles away at what time will they arrive explain
The distance traveled by Davis family = 35 miles
Time taken to cover the distance = [tex]\frac{1}{2}[/tex] hour
Speed = Distance [tex]\div[/tex] Time
Speed = [tex]35 \div \frac{1}{2}[/tex]
Speed = [tex]35 \times 2[/tex]
So, speed = 70 miles/hour.
At 2:00 pm, the family destination was 245 miles away.
So, the number of hours, when the family was 245 miles away = [tex]245 \div 70[/tex]
= 3.5 hours
So, after 3.5 hours, that is at 5:30 pm, the Davis family will be 245 miles away.
To find the Davis family's arrival time, you calculate the average speed, find the time needed for the remaining distance, and then add it to the current time of 2:00pm. Their arrival time is calculated to be 5:30pm.
The student asked: The Davis family traveled 35 miles in 1/2 hour. If it is currently 2:00pm and the family destination is 245 miles away, at what time will they arrive? To solve this, we need to calculate the total travel time based on their average speed and the remaining distance to the destination.
First, we find their speed by dividing the distance traveled by the time taken: 35 miles / 0.5 hours = 70 miles per hour. Next, we calculate the remaining distance to travel, which is 245 miles.
To find the time needed to cover the remaining distance, we divide the distance by the speed: 245 miles / 70 miles per hour = 3.5 hours.
Now, we add the travel time to the current time. Since it's 2:00pm, adding 3.5 hours gives us 5:30pm, which is the arrival time.
what is x and y math help
x and y are whatever you want them to be.
It can be convenient for solving a problem like this to use x and y to represent what the problem is asking for: the number of cans of cola and the number of cans of root beer. It is also convenient (less confusing) to use those variable names in the same order that the nouns of the problem are named:
... x = # of cans of cola
... y = # of cans of root beer
Then the problem statement tells you ...
... x + y = 30 . . . . . . . 30 cans total were bought
... x = 2y . . . . . . . . . . the number of cans of cola is twice the number of cans of root beer
_____
This set of equations is nicely solved by substitution: use the second equation to substitute for x in the first.
... (2y) +y = 30 . . . . . put 2y where x was
... 3y = 30 . . . . . . . . collect terms
... y = 10 . . . . . . . . . divide by 3
... 2y = x = 20
You're not done yet. You need to answer the question the problem asks.
Jared bought 20 cans of cola and 10 cans of root beer.
_____
Comment on x and y
You customarily see x and y as the variables of a problem. Personally, I like to use variables that remind me what they stand for. In this problem, I might use "c" for cans of cola and "r" for cans of root beer. Then when I've found the solution, I know exactly how it relates to what the question is asking.
Always start by writing down what the variables stand for (as we did here). Sometimes, this is called writing a Let statement: Let x = number of colas; let y = number of root beers.
Comment on problems of this type
When a proportional relationship is given between the items in a sum (2 cola cans for every root beer can), it is often convenient to work the problem in terms of groups of items. Here, a group of 3 items can consist of 2 cola cans and 1 root beer can. Then 30 items will be 10 groups, so 10 root beers and 20 colas. The problem is solved even before you can name the variables.
Even when the relationship isn't exactly proportional, you can add or subtract the extras and still work the problem this way. Had we said colas numbered 3 more than twice as many root beers, we could have our groups of 3 total 27 (30 less the 3 extra), giving 9 root beers and 21 colas (3 + 2·9).
3,8,13,18, and 23 are the actual _____ of this sequence
Answer: The 3,8,13,18 and 23 the actual common difference of this sequence.
Explanation:
The given terms of the sequence are 3,8,13,18 and 23.
Where first term is 3, second is 8, thirst term is 18, fourth term is 18 and fifth term is 23.
The difference between second and third term is 5.
[tex]8-3=5[/tex]
The difference between third and fourth term is 5.
[tex]13-8=5[/tex]
So, the common difference of the sequence is 5. Since the difference between terms are same, therefore it is an arithmetic progression.
The formula to find the nth term is ,
[tex]a_n=a+(n-1)d[/tex]
Where a is the first term and d is the common difference.
Given one factor of the polynomial, factor the polynomial completely.
16. f(x)=x^3-4x^2-7x+10;x-5
17. g(x)=2x^3+3x^2-23x-12;2x+1
Use synthetic division to solve these problems
5 | 1 -4 -7 10
| v 5 5 -10
1 1 -2 0
This leads to x^2+x-2
Next we find what adds to 1 and multiplies to -2
The factors of f(x) are 2 and -1, written out as (x+2) and (x-1)
-1/2 | 2 3 -23 -12
| v -1 -1 12
2 2 -24 0
This leads to 2x^2+2x-24
Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with -24, which is -48
Now find what adds to 2 and multiplies to -48
The values for this are 8 and -6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)
2x^2+8x-6x-24
When group factoring, you'd get 2x(x+4) -6 (x+4)
So, the factors of g(x) are (x+4) and (2x-6)
Modeling and Solving a Problem:
An isosceles triangle has two sides of equal length. The third side is 5 less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm, what is the length of the third side?
Explain how you would define a variable for this problem.
The third side is 9 cm long
Let [tex]x[/tex] represent one of the equal sides. Then the` other side will be [tex]2x-5[/tex].
Adding all the length of the sides should give 23. Thus,
[tex]x+x+2x-5=23[/tex]
This implies that,
[tex]4x-5=23[/tex]
We group like terms and simplify to obtain.
[tex]4x=23+5[/tex]
[tex]4x=28[/tex]
Divide through by 4 to get
[tex]x=7[/tex]
Hence the length of the other side is
[tex]2(7)-5=9[/tex]
If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de
Answer:
de=11
Step-by-step explanation:
We are given that b is the midpoint of ac
ac=cd, ab=3x+4,ac=11x-17 and ce=49
We have to find the value of de
b is the midpoint of ac therefore we have
ab=bc
ac=ab+bc=ab+ab=2ab
[tex]11x-17=2(3x+4)[/tex]
[tex]11x-17=6x+8[/tex]
[tex]11x-6x=8+17=25[/tex]
[tex]5x=25[/tex]
[tex]x=\frac{25}{5}=5[/tex]
Then , substitute the value of x
[tex]ab=3(5)+4=19[/tex]
ac=[tex]11(5)-17=55-17=38=cd[/tex]
ce=cd+de
49=38+de
[tex]de=49-38[/tex]
de=11
The measure of segment DE is 11.
Given:
[tex]AB = 3x+4\\AC = 11x-17\\CE=49[/tex]
See image in the attachment below showing the information given in the question.
Since B is the midpoint of AC, therefore:
[tex]AB = AC[/tex]
[tex]2(AB) = AC[/tex]
Substitute
[tex]2(3x+4)=11x-17[/tex]
Solve for x
[tex]6x +8=11x-17\\17 + 8 = 11x-6x\\25 = 5x\\[/tex]
Divide both sides by 5
[tex]5 = x\\x=5[/tex]
Find DE:
[tex]DE = CE - CD[/tex] (Segment Addition Postulate)
[tex]AC = CD = 11x-17[/tex]
Plug in the value of x
[tex]CD = 11(5) -17 = 38[/tex]
[tex]CE = 49 (given)[/tex]
Substitute
[tex]DE = 49 - 38\\DE = 11[/tex]
Therefore the length of DE = 11.
Learn more about segments here:
https://brainly.com/question/16553579
What is standard form in this number 4,000,000 300,000 10,000 500 30 7
What is m∠SVT?
Enter your answer in the box.
Answer:
m∠SVT= 79
Step-by-step explanation:
8y-33= 5y+9
Subtract 5y from both sides
8y-33= 5y+9
8y-33= 5y +9
-5y -5y
3y - 33= 9
Then add 33 to the other side
3y-33 = 9
+33 +33
= 3y= 42
Side by Side need to divide (divide by 3 on each side)
3y= 42
/3 /3
y= 143
m∠SVT = 5y + 9
m∠SVT = 5(14) + 9
m∠SVT = 70 + 9
m∠SVT = 79
Need help evaluate the expression 5x - 7 for x =9? What is the answer?
An expression involving a variable is a way to express an idea, rather than a specific number. So, writing [tex] 5x-7 [/tex] means that there is a certain quantity, x, and you want to multiply it by 5, and then subtract 7.
Note that we don't want to know the value of x, we're only saying that we will multiply it by 5 and then subtract 7.
So, if we know that x=9, we will multiply it by 5 and then subtract 7:
[tex] 5x-7 = 5\cdot 9 - 7 = 45-7 = 38 [/tex]
How you could use a number line to show that -4 plus 3 and 3 plus (-4) have the same value. Which property of addition states that these sums are equivalent
Using a number line to show what -4 + 3 equals:
Start at the -4. Move three spaces to the right (+3). You land on -1.
Using a number line to show what 3 + (-4) equals:
Start at the 3. Move four spaces to the left (-4). You land on -1.
The commutative property of addition states that a + b = b + a.
what is the length of chord CD in O below?
A. 4.01 units
B. 16.04 units
C. 8.02 units
D. 8.31 units
why hello there
Your answer is C 8.02
If u can please mark me as brainliest i really want genius!
Answer:
The correct option is C.
Step-by-step explanation:
Given information: In circle O, AB=8.02, the distance of cord AB from the center is 8.31, the distance of cord CD from the center is 8.31.
According to the chords equidistant from the center theorem, if two cords are equidistant form the center, the length of both cords are equal.
Since the cords AB and CD are equidistant form the center O, therefore
[tex]AB=CD[/tex]
[tex]8.02=CD[/tex]
The length of cord CD is 8.02 units.
Therefore correct option is C.
Which numbers are 3 units from −6 on this number line?
Drag and drop all of the numbers that are 3 units from −6 to their correct position on the number line.
The numbers -9 and -3 are 3 units from −6 on this number line.
What is a number line?
In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.
In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.
A horizontal number line is the most common representation and can be extended infinitely in any direction.
Given a number line,
The 3 units left to the -6 is ⇒ -6 - 3 = -9
The 3 units right to the -6 ⇒ -6 + 3 = -3
Hence "The numbers -9 and -3 are 3 units from −6 on this number line".
To learn more about the number line,
https://brainly.com/question/13189025
#SPJ6
The numbers that are 3 units from -6 on the number line are determined as: -9 and -3.
What is a number line?
A number line is a visual tool that displays numbers in a linear sequence, extending endlessly in both positive and negative directions, illustrating their comparative sizes and positions.
To find numbers that are 3 units from -6 on the number line, you need to consider both numbers that are 3 units to the right and 3 units to the left of -6.
To the right of -6: -6 + 3 = -3
To the left of -6: -6 - 3 = -9
So, the correct numbers are:
D. -3
B. -9
Place them on the number line accordingly.
Calculate the variance for the data set. Round your answer to the nearest hundredth. Show all of your steps. { 10 , 19 , 21 , 28 , 12 , 20 , 16 }
Answer:
Variance of the given data = 31.143
Explanation:
Variance, [tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2[/tex], where n is the number of observations, μ is the mean and [tex]x_i[/tex] is the observations made.
Number of observations, n = 7
Mean, μ = [tex]\frac{10+19+21+28+12+20+16}{7} = 18[/tex]
[tex]\sum_{i=1}^{n}(x_i-\mu)^2=(10-18)^2+(19-18)^2+(21-18)^2+(28-18)^2+(12-18)^2+(20-18)^2+(16-18)^2\\ \\ \sum_{i=1}^{n}(x_i-\mu)^2=64+1+9+100+36+4+4=218[/tex]
[tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2=\frac{218}{7} =31.143[/tex]
So variance of the given data = 31.143
Final answer:
The variance of the given data set {10, 19, 21, 28, 12, 20, 16} is calculated by finding the mean, squaring the deviations from the mean, summing these squares, and dividing by the number of data points minus one, resulting in a variance of approximately 36.33.
Explanation:
Calculating Variance of a Data Set
To calculate the variance, we first need to find the mean (average) of the data set. Then, we subtract the mean from each data point (deviation), square each deviation, sum them all up, and finally, divide by the total number of data points minus one to account for sample variance.
The given data set is {10, 19, 21, 28, 12, 20, 16}. Let's calculate the mean:
Mean = (10 + 19 + 21 + 28 + 12 + 20 + 16) / 7 = 126 / 7 = 18
Next, calculate each deviation from the mean, square it, and sum these squared deviations:
(10 - 18)² = 64
(19 - 18)² = 1
(21 - 18)² = 9
(28 - 18)² = 100
(12 - 18)² = 36
(20 - 18)² = 4
(16 - 18)² = 4
Sum of squared deviations = 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218
The variance is then the sum of the squared deviations divided by n - 1 (where n is the number of data points in our sample):
Variance = 218 / (7 - 1) = 218 / 6 ≈ 36.33
Evaluate |-6| + 3|4| + |-5| - 0 × 6.
First of all, let's get rid of the absolute values. If the number inside is positive, don't do anything. If it's negative, switch the sign. So, the expression becomes
[tex] 6 + 3\cdot 4 + 5 - 0 \cdot 6 [/tex]
We have to perform multiplications first:
[tex] 6 + 12 + 5 - 0 [/tex]
The last subtraction by 0 doesn't affect the number in any way, so we can ignore it:
[tex] 6 + 12 + 5 [/tex]
Now you can perform the sums just as they appear:
[tex] 6 + 12 + 5 = 18 + 5 = 23 [/tex]
|-6| + 3|4| + |-5| - 0 * 6
Note: absolute value makes the number positive
6 + 3(4) + 5 - 0 * 6
Now, use the order of operations (multiply first)
6 + 12 + 5 - 0
Next, add and subtract
18 + 5 - 0
23 - 0
23
Answer: 23
Select the multiplication sentence that applies the associative property of multiplication to the example. Example: 1 × (9 × 5) = 45 A. 1 × (9 + 5) = 14 B. (8 × 5) + 5 = 45 C. (1 + 9) × 5 = 50 D. (1 × 9) × 5 = 45
The example is 1 x (9 x 5) = 45
Using the associative property of multiplication, we basically rearrange the parenthesis to group the first two terms like so: (1 x 9) x 5
So this is why choice D (1 x 9) x 5 = 45 is the answer
This means that 1 x (9x 5) = (1 x 9) x 5 is a true equation
What number rounds to 168,356 when rounding to the nearest ten thousand
Let C ( t ) be the number of US cell phone subscribers in millions in t years since 1995. A linear model for the data is F ( t ) = 18.997 t + 17.711 .
Use the model to predict the year in which the number of subscribers will 324 million
ANSWER
In 16 years time.
EXPLANATION.
If the number of subscribers is 324 million, then it means
[tex]f(t)=324[/tex]
But we were given that,
[tex]f(t)=18.997t+16.711[/tex]
This implies that,
[tex]324=18.997t+16.711[/tex]
We now solve for t,
[tex]324-16.711=18.997t[/tex]
[tex]307.289=18.997t[/tex]
[tex]\frac{307.289}{18.997}=t[/tex]
[tex]16.17566=t[/tex]
That will be approximately in the 16th year.
In order to calculate the year where the number of US cell phone subscribers matches a certain number using the given linear model equation, you solve for the time variable. With the specified 324 million subscribers, the corresponding year would be approximately 2011.
Explanation:To use the provided linear model F(t) = 18.997t + 17.711 to predict the year where the number of subscribers will be 324 million, we need to solve the equation for t with C(t) set to 324:
324 = 18.997t + 17.711
To do so, subtract 17.711 from both sides to isolate the term with t:
324 - 17.711 = 18.997t
Then, divide both sides by 18.997 to solve for t:
(324 - 17.711) / 18.997 = t
After calculating, you will get approximately t = 16.123. Remember, t is the number of years after 1995, so you would add 16 (rounded from 16.123) to 1995. Thus, the model predicts that the number of US cell phone subscribers will reach 324 million in 2011.
Learn more about Linear Model here:https://brainly.com/question/29122305
#SPJ3
HEEEEEEEEEEEEELP WILL GIVE TEN POINTS
Question:
Evaluate. Show all work for full credit.
If c = 30 and d = 8, then 2c + 4d = ?
2c + 4d = 92
substitute the given values into the expression and evaluate
2c + 4d = (2 × 30) + (4 × 8) = 60 + 32 = 92
The answer is 92. First substitute in 30 for c and multiply it by 2, and you get 60. Then, substitute in 8 for d and multiply it by 4 to get 32. Add 60 + 32 and it equals 92.