Answers
ax² +bx +c
Then the "a" and "b" in the expression -b/(2a) represent the coefficients of the squared term and the linear term, respectively. In your quadratic expression, the variable is "t", not "x", but that makes no difference. You have
a = -16
b = 96
Then the time (t) at the maximum height is
t = -b/(2a)
t = -96/(2(-16)) = 96/32 = 3
The ball is highest 3 seconds after being fired.
(b) Evaluating h for t=3, we get
h = -16*3² +96*3 +11
h = -144 +288 +11
h = 155
The maximum height of the ball is 155 ft.
Related Questions
The access code for a car's security system consists of four digits. the first digit cannot be zero or one and the last digit must be even. how many different codes are available?
Answers
Find the length of each hypotenuse such that KMN = LMN
Answers
1) KM must be congruent with LM→KM=LM→
x+2y=3x-y→x+2y-x-2y=3x-y-x-2y→0=2x-3y→2x-3y=0 (1)
2) KN must be congruent with LN→KN=LN→
5x+3y=8x-7→5x+3y-5x-3y+7=8x-7-5x-3y+7→7=3x-3y→3x-3y=7 (1)
We have a system of two equations and two unkowns:
(1) 2x-3y=0
(2) 3x-3y=7
Subtracting equation (1) from equation (2)
(3x-3y)-(2x-3y)=7-0
3x-3y-2x+3y=7
x=7
Replacing x=7 in equation (1)
(1) 2x-3y=0→2(7)-3y=0→14-3y=0→
14-3y+3y=0+3y→14=3y→14/3=3y/3→14/3=y→y=14/3
The length of the hypotenuse is:
KN=5x+3y=5(7)+3(14/3)=35+14→KN=49
or
LN=8x-7=8(7)-7=56-7→LN=49
Answer: Option C. 49
Hey can you please help me posted picture of question
Answers
PLZ HELP ASAP TANGENTS OF CIRCLES WORD PROBLEMS
Answers
70 + 90 + 90 + O = 360
O = 110 degrees.
Suppose the entering freshmen at a certain college have a mean combined application test score of 1225, with a standard deviation of 120. in the first semester, these students attained a mean gpa of 2.64, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a first-semester gpa of 2.9?suppose the entering freshmen at a certain college have a mean combined application test score of 1225, with a standard deviation of 120. in the first semester, these students attained a mean gpa of 2.64, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a first-semester gpa of 2.9?
Answers
Using the correlation coefficient, mean test scores, and mean GPA, we can predict that a freshman with a GPA of 2.9 would have an approximate combined test score of 1260.71.
Since we know the mean combined application test score is 1225, the standard deviation is 120, the mean GPA is 2.64, and the standard deviation for GPA is 0.58, we can use this information to predict scores.
First, we will use the correlation coefficient (r), which in this case is 0.44, to calculate the slope (b) of the best-fit line. The slope (b) is calculated by dividing the product of the standard deviations by the mean test score, and then multiplying by the correlation coefficient.
b = r * (Sy / Sx)
b = 0.44 * (0.58 / 120)
b = 0.44 * 0.0048333
b ≈ 0.0021
Next, we need to find the intercept (a) of the best-fit line, which can be calculated using the means of the two variables (mean test score and mean GPA).
a = mean of GPA - b * mean of test scores
a = 2.64 - 0.0021 * 1225
a ≈ 0.10
With the slope (b) and the intercept (a), we can now predict the combined test score for a student with a GPA of 2.9.
Predicted Test Score = a + b * GPA
Predicted Test Score = 0.10 + 0.0021 * 2.9
Predicted Test Score ≈ 1260.71
Thus, for a freshman with a first-semester GPA of 2.9, the predicted combined test score would be approximately 1260.71.
I need yo help B, on dis question
Answers
We have then:
[tex]5 / sine (68) = 5 / sine (x) [/tex]
From here, we clear the value of x.
We have then:
[tex]sine (x) = (5/5) * (sine (68)) [/tex]
Rewriting we have:
[tex]sine (x) = (1) * (sine (68)) sine (x) = sine (68) x = arcsine (sine (68)) x = 68[/tex]
Answer:
The angle R is given by:
x = 68 degrees
option B
Answer:
b
Step-by-step explanation:
what has to be added to the sum of 2/3 & 3/2 to get 3? give answer as whole number or fraction <question 10 in the image>
Answers
(2/3+3/2)+x=3
Solving for x:
(2*2+3*3)/6+x=3
(4+9)/6+x=3
13/6+x=3
13/6+x-13/6=3-13/6
x=(6*3-13)/6
x=(18-13)/6
x=5/6
Answer: 5/6 has to be added to the sum of 2/3 and 3/2 to get 3
20 points! plz help me
Answers
- 3 - 3
2a + a = 177
3a = 177
---- ---- = 59
3 3
59 is a.
At one store, Julia saved $10 with a coupon for 40% off her total purchase. At another store, the $29 she spent on books is 58% of her total bill. How much did Julia spend in all at the two stores?
Answers
0.40*(original price of "a") = $10
(original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
a = $25.00 -10.00 = $15.00
At the other store,
$29 = 0.58b
$29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate
Then Julia's total spending is
a + b = $15.00 +50.00 = $65.00
Julia spent $65 in all at the two stores.
Suppose that a test is standardized (normally distributed) with a mean of 75 and a standard deviation of 11. what is the probability that an individual will have a test score greater than 80
Answers
A suitable calculator can help you figure this.
how much interest is earned on 2,700 in one year if it is invested at 3%?
a. $8.10
b.$81.00
c.$810.00
Answers
Log5 wu^6/v^6
Expand each logarithm
Answers
1. You have the following logarithm:
log5(wu^6/v^6)
2. By the logarithms properties, you can rewrite it as below:
log5(wu^6)-log5(v^6)
[log5(w)+log5(u^6)]-log5(v^6)
log5(w)+6log5(u)-6log5(v)
3. Therefore, the answer is:log5(w)+6log5(u)-6log5(v)
find the circumference of a circle with an area of 254.47 square inches
Answers
A circle with an area of 254.47 square inches is given.
We have to determine the circumference of the circle.
Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.
[tex] \Pi r^{2}=254.47 [/tex]
[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]
[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]
[tex] r^{2}=80.97 [/tex]
[tex] r=\sqrt{80.97} [/tex]
r = 8.99
Therefore, r = 9 inches (approximately)
Circumference of a circle = [tex] 2\Pi r [/tex]
= [tex] 2 \times \frac{22}{7} \times 9 [/tex]
= 56.57 inches
= 56.6 inches (approximately).
Therefore, the circumference of the circle is 56.6 inches.
Name all numbers between 67 and 113 that are a multiple of 4, 9 and 12.
Answers
I believe that there are 2 number that are in between the given numbers and are multiples of 4, 9, and 12. The numbers are...
72 and 108.
You can find these numbers by counting by the given one digit numbers
For example...
9, 18, 27, 36, 45, 54, 63, 72
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30..., 68, 70, 72
You can do the same for 108 as well
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72..., 104, 108
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30..., 100, 102, 104, 106, 108
I hope this helps!
perimeter and circumference 9-1
Answers
Hey can you please help me posted picture of question
Answers
The option B gives only such a probability which can represent a simple event. The rest of the options belong to the compound events as they are sum or product of probabilities.
So, the correct answer is option B
a + 5=5a +5
[tex]a + 5 = 5a + 5 = [/tex]
Answers
a = 5a
Now subtract both sides by a:
4a = 0
a = 0
Q #6 in the figure A B || C D Find the measure ГGEB
Answers
Answer: Second option 50°
the answer is b hoped i helped
Jenya has 12 bills in her wallet. She has a total of $82. If she has twice as many $5 bill as $1 bills, and two more $10 bills than $5 bills, how many of each does she have?
Answers
if you said you had 7 instead there would be not enough bills to add up to 82
so that means 4 $5 and 6 $10
check you have 12 bills and it adds up to $82
2 $1
4 $5
6 $10
Final answer:
Jenya has 2 $1 bills, 4 $5 bills, and 6 $10 bills, which all adds up to her total of $82.
Explanation:
Jenya has a combination of $1, $5, and $10 bills in her wallet adding up to $82. To find out how many of each she has, we need to set up a system of equations based on the information provided:
Let x represent the number of $1 bills.2x will then represent the number of $5 bills, as she has twice as many $5 bills as $1 bills.2x + 2 represents the number of $10 bills because she has two more $10 bills than $5 bills.We also know that the total number of bills is 12.The total amount of money is $82.Now we can form two equations:
x + 2x + (2x + 2) = 12 (Total number of bills)1x + 2x*5 + (2x + 2)*10 = 82 (Total amount of money)Simplifying the equations gives us:
5x + 2 = 12x + 10x + 20x + 20 = 82Further simplification and solving for x yields:
5x = 10x = 2This means Jenya has 2 $1 bills, 2*2 = 4 $5 bills, and 2*2 + 2 = 6 $10 bills.
Sally bought a car for 35000 in 2017. If the car loses 5.5% semiannually, what will the value of the value of the car be at the end of 2025
Answers
A=P(1+r/100)^n
where:
A=future value
P=principle
r=rate
n=number of terms
hence for the data given;
p=35000
R=5.5
n=(2025-2017)*2=16
Thus
A=35000(1+5.5/100)^16
A=$82, 434. 20
A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?
Answers
After subtracting the principal and two counselors from the 83-person room capacity, dividing the remaining space by two shows that a maximum of 40 student-athletes can attend the meeting with their parents.
The maximum number of student-athletes that can attend a meeting in a conference room that has a capacity of 83 people while also accounting for their accompanying parents. Given that the principal and two counselors will also be in attendance, we need to subtract three from the total capacity to accommodate them, leaving us with 80 seats available. Since each student will bring a parent, we divide the remaining seats by two. Therefore, the maximum number of student-athletes that can attend each meeting is 40 students, with each accompanied by a parent.
Choose the ratio that you would use to convert 5.5 pounds to ounces. Remember that there are 16 ounces in 1 pound. A.
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The correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.
To convert 5.5 pounds to ounces, we need to use the conversion factor that relates pounds to ounces. We know that there are 16 ounces in 1 pound. Therefore, to convert pounds to ounces, we need to multiply the number of pounds by 16.
The appropriate ratio to use for this conversion would be option A : 16 ounces per 1 pound, or [tex]\( \frac{16 \text{ ounces}}{1 \text{ pound}} \).[/tex]
This ratio tells us that for every 1 pound, there are 16 ounces. Using this ratio, we can convert pounds to ounces by multiplying the number of pounds by 16.
Therefore, to convert 5.5 pounds to ounces, we would use the following calculation:
[tex]\[ 5.5 \text{ pounds} \times \frac{16 \text{ ounces}}{1 \text{ pound}} = 88 \text{ ounces} \][/tex]
So, the correct answer is option A: [tex]\( 88 \)[/tex] ounces per [tex]\( 1 \)[/tex] pound. This ratio allows us to convert pounds to ounces effectively and accurately, ensuring that we obtain the correct conversion result.
The complete question is:
Choose the ratio that vou would use to convert 5.5 pounds to ounces Remember that there are 16 ounces in 1 pound.
A. 88 ounces/1 pound
B. 16 ounces/1 pound
C. 1 pound/16 ounces
D. 1 ounce/88 pounds
How many pounds of hamburger worth $1.05 per pound must be mixed with 60 pounds of hamburger worth $0.90 per pound to produce hamburger worth $1.00 per pound? Which of the following systems represents the word problem if x = pounds of hamburger worth $1.05 per pound? x + y = 60 and 1.05x + 0.90(60) = 1.00y x + 60 = y and 1.05x + 1.00y = 0.90(60) x + 60 = y and 1.05x + 0.90(60) = 1.00y
Answers
The appropriate choice is the last one:
x + 60 = y and 1.05x + 0.90(60) = 1.00y
Answer:
[tex](x+60)=y[/tex] and [tex]1.05x+0.90(60)=1.00y[/tex]
Step-by-step explanation:
Let
x-----> pounds of hamburger worth [tex]\$1.05[/tex] per pound
we know that
The equation that represent the situation is
[tex]1.05x+0.90(60)=1.00(x+60)[/tex] ------> equation A
Let
[tex]y=(x+60)[/tex] -----> equation B
substitute equation B in equation A
[tex]1.05x+0.90(60)=1.00y[/tex]
Pete has the option of borrowing $380 for one week at an APR of 600% or borrowing the $380 for one week with a fee of $45. Which is the "better" deal?
Answers
Since Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.
There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.
[tex] \frac{600}{365} = 1.643[/tex]
The daily interest rate of the loan will be 1.643%.
The following equation is used to find the total interest payment:
[tex]A = P(1+ \frac{r}{365})^{t} - P[/tex]
A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.
Plug in your values into the equation.
[tex]P = 380, r = 1.643, t = 7[/tex]
[tex]380(1+ \frac{1.643}{365})^{7} - 380 = 12.136[/tex]
Rounded to the nearest hundredths value, the total interest paid will be $12.14.
Compare the total amounts paid for both loans.
$12.14 < $45
The better deal is the loan with the 600% APR.
The better deal is the loan with the 600% APR.
What is interest rate?An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum).
Given that, Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.
There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.
600/365 = 1.643
The daily interest rate of the loan will be 1.643%.
The following equation is used to find the total interest payment:
[tex]A = P(1+\frac{r}{365} )^{t} -P[/tex]
A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.
Plug in your values into the equation.
P = 380 r = 1.643 and t = 7
380(1+1.643/365)^7 - 380 = 12.136
Rounded to the nearest hundredths value, the total interest paid will be $12.14.
Compare the total amounts paid for both loans.
$12.14 < $45
Hence, The better deal is the loan with the 600% APR.
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Solve x2 − 7x + 12 = 0.
a. x = −3, x = −4
b .x = 3, x = 4
c. x = 2, x = 6
d. x = −2, x = −6
Answers
So,
x^2 - 7x + 12 = 0
(x-4)(x-3) = 0
x-4 = 0 or x-3 = 0
x = 4 or x = 3
Answer is choice B
Select three ratios that are equivalent to 11:1
Answers
B. 22 : 2. 22 : 2 is equivalent to 11 : 1.
C. 55 : 5. 55 : 5 is equivalent to 11 : 1.
E. 110 : 10. 110 : 10 is equivalent to 11 : 1.
In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective common multiple (numerator or denominator):
For 22 : 2, we would divide all through by 11;
22 : 2 = 11 : 1
For 55 : 5, we would divide all through by 5;
55 : 5 = 11 : 1
For 110 : 10, we would divide all through by 10;
110 : 10 = 11 : 1
Complete Question:
Select three ratios that are equivalent to 11 : 1.
Choose 3 answers:
1 :11
22 : 2
55 : 5
9 : 99
110 : 10
SOMEONE PLEASE HELP ME ASAP
Answers
For this case we can use the following trigonometric relationship:
sine (45) = (5 * root (2)) / h
From here, we clear the value of h:
h = (5 * root (2)) / sine (45)
Rewriting we have:
h = (5 * root (2)) / (root (2) / 2)
h = (2 * 5) * (root (2) / root (2))
h = 2 * 5
h = 10
Answer:
h = 10
Option F
Suppose a1=2,an+1=12(an+2an). assuming an has a limit, find limn→∞an= . hint: let a=limn→∞. then, since an+1=12(an+2an), we have a=12(a+2a). now solve for
a.
Answers
[tex]a_{n+1}=\dfrac{a_n+\frac2{a_n}}2[/tex]
Assume that [tex]\displaystyle\lim_{n\to\infty}a_n=L[/tex]. Then taking the limit of both sides, we have
[tex]L=\dfrac{L+\frac2L}2\implies L=\pm\sqrt2[/tex]
But in order for the sequence to converge, only one of these values must be true. Since [tex]a(1)=2>0[/tex], each successive number will also be positive, so the limit must be [tex]L=\sqrt2[/tex].
The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).
Explanation:This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).
To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).
By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.
Therefore, the limit of the sequence as n tends to infinity is 0.
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How can I derive the first equation to get the second equation?
Answers
[tex]\bf s^2=R^2+r^2-2Rrcos(\theta )\implies 2s^1=0+0-2Rr\left[ \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{ds}} \right] \\\\\\ 2s=2Rrsin(\theta )\cfrac{d\theta }{ds}\implies 2s=\cfrac{2Rrsin(\theta )d\theta }{ds}\implies \cfrac{2s\cdot ds}{2Rr}=sin(\theta )d\theta \\\\\\ \cfrac{s\cdot ds}{Rr}=sin(\theta )d\theta[/tex]
To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.
Explanation:To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps:
Start with the equilibrium equation for the problem.Substitute the expression for T₂ in terms of T₁ into the equation.This will eliminate one unknown and result in a new equation with only one unknown left.In the equation 6x − 2 = −4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain
Answers
Spencer: 6x - 2 = -4x + 2 /+4x6x - 2 + 4x = -4x + 2 + 4x10x - 2 = 2
Jeremiah:6x - 2 = -4x + 2 /-6x6x - 2 - 6x = -4x + 2 - 6x-2 = -10x + 2
They both are correct. But in Jeremiah's version of solving the equation, we would have to multiply equation by -1, which we don't have to do in the Spencer's version.
Source: Brainly.com
Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.