Answer:
y=4x+14
Step-by-step explanation:
1. Amy is practicing target shooting at a special facility. A target projectile is launched
into the air from a platform 10 feet above the ground at a rate of 96 feet per second.
Amy aims and shoots at her target. Her bullet follows a linear path with a slope of 17
feet per second and she fires from a height of 5 feet.
The equation used to determine height and time is y = 16x² + 96x + 10 and y = 17x + 5
What is Projectile Motion ?
A projectile is something that has only one force acting on it the entire time, which is gravity, with the exception of the beginning.There are numerous types of projectiles.A projectile is something that is launched from the position of rest.A projectile is also any object that is hurled vertically upward as long as air resistance has no effect. Additionally, a projectile is any object that is fired upward at an angle to a horizontal plane.
The height of projectile after t seconds is given,
h(t) = 1/2 gt² + v₀t + s₀
where,
v₀ ( initial velocity ) = 96 feet per second
s₀ ( initial height ) = 10 feet
g = 32 feet per second²
put the values,
h(t) = 1/2 (32)t² + 96 t + 10
h(t) = 16 t² + 96 t + 10
so, let h(t) = y and t = x
y = 16x² + 96x + 10
We know, Amy's bullet follows a linear path,
The linear equation is,
y = mx + b
where, slope (m) = 17 feet per second and,
y-intercept (b) = 5 feet
plug in the values in linear equation,
y = 17x + 5
Therefore, The equation used to determine height and time is y = 16x² + 96x + 10 and y = 17x + 5
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Is -4 a solution to the following equation? 4 + 3(x + 2) = 12x + 20 -4x
Answer:
-4 is not a solution to the following equation.
Step-by-step explanation:
It you replace x with -4 on both sides of the equation you get -2=-12 and they are not equal to each other. Therefore, -4 is not a solution to the equation.
The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.
1,320 1,264 1,215 1,271 1,268 1,316 1,275 1,317 1,275
(a)
Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to four decimal places.)
A.D.
s =
yr
(b)
When finding an 90% confidence interval, what is the critical value for confidence level? (Give your answer to three decimal places.)
tc =
What is the maximal margin of error when finding a 90% confidence interval for the mean of all tree-ring dates from this archaeological site? (Round your answer to the nearest whole number.)
E =
Find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site. (Round your answers to the nearest whole number.)
lower limit
A.D.
upper limit
A.D.
Using the t-distribution, it is found that:
a)
The mean is: 1280.1111The standard deviation is: 33.5799.b)
The critical value is: 1.86.The margin of error is: 21.The interval is: (1259, 1301).What is a t-distribution confidence interval?The bounds of the confidence interval are given according to the rule presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The margin of error of the interval is:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
Then the interval can be interpreted as the sample mean plus/minus the margin of error.
For the confidence interval in this problem, using a calculator, the parameters are given as follows:
[tex]\mu = 1280.1111, s = 33.5799, n = 9[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 9 - 1 = 8 df, is t = 1.86.
Then the margin of error of the interval is:
M = 1.86 x 33.5799/sqrt(9) = 21.
Then the bounds of the interval are:
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Enrique has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages. Find the number of talk minutes, text messages, and picture messages he used.
The number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.
What is Equation Modelling?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 Enrique who has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages
Assume that [x], [y] and [z] represents the number of minute talk's, text message's and picture message's respectively. Then -
0.1x + 0.2y + 0.25z = 30.95 ..[1]
y + z = 87 ..[2]
0.1x = 0.2y - 1.6 ...[3]
We can write Eq[1] as -
0.2y - 1.6 + 0.2y + 0.25z = 30.95
z = 87 - y
0.2y - 1.6 + 0.2y + 0.25(87 - y) = 30.95
Solving, we get y = 72.
So z = 87 - 72 = 15
and
0.1x = 0.2 x 72 - 1.6
0.1x = 14.4 - 1.6
x = 128
Therefore, the number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.
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Which ordered pairs in the form (x,y) are solutions to equation 3x -4y =21? SELECT MORE THAN ONE ANSWER. a- (11,30) b-(7,0) c-(-1,-6) D- (-3,3) please help
In linear equation, option A,B,C are equal expect D .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.The given equation is 3x -4y =21.
A. (11, 3)
3(11) - 4(3) = 21
21 = 21 > equal
B. (7, 0)
3(7) - 4(0) = 21
21 = 21 > equal
C. (−1, −6)
3(-1) - 4(-6) = 21
21 = 21 > Equal
D. (−3, 3)
3x – 4y = 21
3(-3) - 4(3) = 21
-21 = 21 > not equal
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At a supermarket, oranges cost $1.30 per pound and pears cost $1.90 per pound. Misha spent less than $10.00 on 2 pounds of oranges and x pounds of pears. Which inequality represents this situation?
Answer:
kind423
Step-by-step explanation:
Answer: 2(1.9)+1.30x<10
Step-by-step explanation:
Orange= $1.30/lb
Pear= $1.90/lb
$1.30/lb = $y/2lb
y=1.30*2
y=$2.6 for 2lb of orange
So
She spent
2(1.30)+1.90x< $10
2.6+1.90x<10
1.90x<10-2.6
1.90x<7.4
x<7.4/1.90
x<3.89
According to 2(1.30)+1.90x< $10
2.6+1.90*3.89<10
9.991<10
A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.24t2 + 12t feet per second after t seconds (for 0 ≤ t < 30).
a.
Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time
t = 0.]
b.
Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.)
The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.
What is the relation between speed and distance?Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.
The speed formula is speed = distance/time.
We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).
Then the distance that it will travel from its starting point in the first t seconds is;
[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]
At zero it will be 12 feet.
b. the distance (in ft) that the car will travel in the first 10 seconds.
-0.48(10) + 12 = 16.8 feet.
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In an electrical circuit, the current passing through a conductor varies inversely with the resistance. Suppose that when the current is 10 A (amperes), the resistance is 13 ohms. What is the resistance when the current is 26 A?
Answer:
33.8ohms
Step-by-step explanation:
10A : 13ohm
26A : 33.8ohm
In the fraction three-fifths, which statement best describes the denominator?
A. It tells the number of equal parts out of the total number of parts.
B. It tells how many are shaded.
C. It represents the number of equal parts into which the whole is divided.
D. The denominator means three out of five are shaded.
Answer:
D. The denominator means three out of five are shaded
Select the values that make the inequality
The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.
Given,
In the question:
To see the figure:
To select the values that makes the inequality s ≤ 4 true.
Number table are given in figure.
To see the figure and analysis.
Now, According to the question;
To make the inequality s ≤ 4 true.
The selected value must be less than 4 {Properties of Inequality}
The values are sorted from small to large:
So, The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.
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Help me please it’s confusing
Answer: 1/6
Step-by-step explanation:
To subtract fractions, you must have a common denominator. To do this, the common multiple of 3 and 2 is 6. So 2/3 is multiplied by 2/2 and 1/2 is multiplied by 3/3. The multiplication is valid since we multiplied by one, it didn't alter the value but rather it put it into an alternate, equivalent form.
If x = -4 and y = 3, what is the value of 1/2x + 3xy^2
If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
What is a value function?
The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.
What is a variable?
A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.
Here, we have
x = -4 and y = 3
then by putting the value of a function in a given equation, we get
1/2*(-4) + 3*(-4)*(3)²
= -110
Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
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Three middle schools in a city had enrollments of 296,315 and 278 what was the total middle school enrollment
The total middle school enrollment is 889 for the given city.
According to the question,
We have the following information:
Three middle schools in a city had enrollments of 296,315 and 278.
Now, the total middle school enrollment can be easily found by adding the enrollments in three middle schools of the city.
So, we have the following expression:
Total middle school enrollment = 296+315+278
(We already know that the digits are first added from the right hand side and then we move to the left hand side.)
Total middle school enrollment = 889
Hence, the total middle school enrollment is 889 for the given city.
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The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
Using the stem-and-leaf plot, the mean of the data is 3.85.
It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.
How to calculate the Mean of a Data Set represented by Stem-and-Leaf Plot?To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values and divide by the number of values that was represented on the stem-and-leaf plot.
Given the stem-and-leaf plot above, using the key, the data points represented are:
2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5
Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12
Mean = 46.2/12
Mean = 3.85 feet
The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.
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The Answer is:
3.85 ft.
* *
-
Ellie bought cookies and cupcakes for $102.44. If she spent $36.44 on cookies
and the cupcakes are $11 per box, how many boxes did she buy?
Answer:
Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars
66/11=6 cupcake boxes
6 cupcake boxes + 1 cookie box = 7 boxes in total
Find the 14th term of the geometric sequence 1,-5,25
The 14th term of the geometric sequence will be -1220703125.
What is geometric sequence?
The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.
Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.
[tex]1*(-5)^{13}[/tex]The terms are given, 1,-5,25
a = 1
r = -5/1 = -5
The 14th term will be= [tex]ar^{13}[/tex]
= [tex]1*(-5)^{13}[/tex]
= -1220703125
Hence, the 14th term of the geometric sequence will be -1220703125.
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NO LINKS!! Please help me with these graphs Part 4a
Answer:
a. x = 1.75, x = 4.25
b. y = -7
c. Maximum point at (3, 5).
d. Domain: (-∞, ∞)
e. Range: (-∞, 5]
f. See attachment.
Step-by-step explanation:
Given function:
[tex]\text{f}(x)=-4|x-3|+5[/tex]
As per the question, use a graphing calculator to graph the given function.
Part aThe x-intercept(s) are the points at which the curve crosses the x-axis.
x-intercepts: x = 1.75, x = 4.25Part bThe y-intercept is the point at which the curve crosses the y-axis.
y-intercept: y = -7Part cFrom inspection of the graph:
Maximum point at (3, 5).Part dThe domain of a function is the set of all possible input values (x-values).
The domain of the given function is unrestricted.
Domain: (-∞, ∞)Part eThe range of a function is the set of all possible output values (y-values).
As the function has a maximum point at y = 5, the range is restricted.
Range: (-∞, 5]Part fGraph label the axes using a scale of 1 (see attachment).
Plot the maximum point (3, 5). Plot the y-intercept: (0, -7).Draw a straight line from the maximum point through the y-intercept.Substitute x = 5 into the function to find the value of y at that point:
[tex]\begin{aligned}\implies \text{f}(5)&=-4|5-3|+5\\&=-4|2|+5\\&=-4(2)+5\\&=-8+5\\&=-3\end{aligned}[/tex]
Plot found point (5, -3).Draw a straight line from the maximum point through point (5, -3).Which graph represents an odd function?
There are 6 points on a coordinate plane. The points are (negative 5, 3), (negative 3, 1), (negative 1, 1), (1, 3), (3, negative 5), (5, negative 1).
There are 8 points on a coordinate plane. The points are (negative 4, 2), (negative 3, negative 1), (negative 1, negative 3), (0, 1), (1, 0), (2, negative 4), (4, 5), (5, 4).
There are 8 points on a coordinate plane. The points are (negative 4, 0), (negative 3, 1), (negative 2, negative 3), (negative 1, negative 2), (1, 2), (2, 3), (3, negative 1), (4, 0)
There are 11 points on a coordinate plane. The points are (negative 4, 3), (negative 4, 4), (negative 3, 5), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 1), (2, 1), (3, 5), (4, 3), (4, 4).
Answer: first graph
Step-by-step explanation:
The equation for line u can be written as y = -x + 1. Line v, which is perpendicular to line
u, includes the point (-3, 2). What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
미미
Submit
Answer:
Line v: y = x + 5
Step-by-step explanation:
Given two lines are perpendicular and the equation of one line, we use the following formula to find the slope of the other line where m1 is the slope of the line we're given and m2 is the slope of the line we want to find:
[tex]m_{2}=-\frac{1}{m_{1} }\\m_{2}=1[/tex]
The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Therefore we plug in our slope and the point (-3, 2) to find the y-intercept of line v:
[tex]2=1(-3)+b\\2=-3+b\\5=b[/tex]
If LM = 2x - 9 and KN = x + 15 in rhombus KLMN, find the value of x.
The value of x in the rhombus is 24 units.
According to the question,
We have the following information:
LM = 2x - 9 and KN = x + 15 in rhombus KLMN.
Now, we know that in a rhombus opposite sides are equal. In this case, LM and KN are opposite sides.
So, we have the following expression:
2x-9 = x+15
Adding 9 to both sides of the equation:
2x = x+15+9
2x = x+24
Subtracting x from both sides of the equation:
2x-x = 24
x = 24
Hence, the value of x for the given rhombus is 24 units.
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100 POINTS!!!
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answer:
Step-by-step explanation:
I
Which expression has the same value as 3 ÷ 5/9? A. 3 × 5/9 B. 1/3 ÷ 5/9 C. 3 ÷ 9/5 D. 3 × 9/5
Answer:
D: 3x9/5
Step-by-step explanation:
the formula for dividing fractions is skip flip multiply where we keep the first term the same and then flip the second to multiply
Hopes this helps please mark brainliest
One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal.
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.
What is the z distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.
This is the z distribution given that the value of n is more than 30.
We have to make use of z when n which is the number of samples is greater than 30.
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On average, Jaya drinks of a 6-ounce glass of water in 13 hours. How many glasses of water does she drink in one hour?
On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.
Average:
Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
On average, Jaya drinks of a 6-ounce glass of water in 13 hours.
Here we need to find the number of glasses of water does she drink in one hour.
Let x be the number of glasses of water does she drink in one hour.
We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.
So, in order to find the average we have to divide the number of glasses by the time taken.
So, it can be written as,
=> 6/13
=> 0.46
Therefore, for one hour Jaya drinks 0.46 ounces of water.
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A company's identification card consists of 4 letters followed by 2 digits. How many cards can be
made if repetition of digits are allowed, but letters must only be consonants and have NO
repetition. Note: y is not a vowel.
The possible cards can be made 6719448100.
What is permutation & combination?
Subsets of a set can be created in two separate ways combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.
We have,
Letters must only be consonants = 26 - 5.
So, the total number of consonants are 21.
There are 21 choices for the first letter, 21 choices for the second letter, 21 choices for the thirds letter, 21 choices for the fourth letter. For each of these letters, therefore 21 × 21 × 21 × 21 = 194481 possible pairs of letters.
There are 10 possibilities for the first digit & 10 possibilities for the second. therefore there are 10 x 10 = 100 different numbers.
Combining these results, it follows that there are 67194481 x 100 = 6719448100 different cards.
Hence, The possible cards can be made 6719448100.
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In a study of helicopter usage and patient survival, among the 49,401 patients transported by helicopter, 244 of them left the treatment center against medical advice, and the other
49,157 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left
the treatment center against medical advice?
The probability is
(Round to three decimal places as needed)
Answer:
40%
Step-by-step explanation:
Kaleigh paid $37.45 for a calculator, after-tax, and the tax rate is 7%. What was the original cost of the calculator?
Step-by-step explanation:
that means that
$37.45 = 107%
as the price was 100% base price + 7% tax.
1% = 107%/107
100% = 1% × 100 = 107% × 100 / 107
so, the basic price (the "original cost") is
37.45 × 100/107 = $35.00
find the distance between two points rounding to the nearest tenth if needed. (-5,4) and (4,-8)
Answer:
d = 15
Step-by-step explanation:
(-5, 4), (4, -8)
(x₁, y₁) (x₂, y₂)
d = √(x₂ - x₁)² + (y₂ - y₁)²
d = √(4 - (-5))² + (-8 - 4)²
d = √(4 + 5)² + (-12)²
d = √(9)² + (-12)²
d = √81 + 144
d = √225
d = 15
I hope this helps!
The second and fifth terms of a geometric sequence are 750 and -6 respectively. Find the
common ratio and first term of the sequence.
Step-by-step explanation:
T2= -6
T5=750
ar=-6
ar4=750
both a's cancel each other
we have;
r=-6
r4=750
r4-1(The law of indices) =750
r3=750
r=3√750
r=9.1
What is the x value of the solution to the following system
x + y =40
x - 3y = -4
Answer:
x=y , x-3y=4. x = y x = y , x − 3y = 4 x - 3 y = 4. Replace all occurrences of x x with y y in each equation. Tap for more steps... −2y = 4 - 2 y = 4. x = y x = y. Divide each term in −2y = 4 - 2 y = 4 by −2 - 2 and simplify. Tap for more steps... y = −2 y = - 2.
Step-by-step explanation:
Just smart
Answer:
C) 29
Step-by-step explanation:
1st equation - 2nd equation,
x+y - (x-3y) = 40-(-4)
x+y-x+3y = 40+4
4y = 44
y = 44÷4
y = 11
substituting y into the first equation,
x + 11 = 40
x = 40-11 = 29
answer is C
hope it helps. :)