Answer:
Step-by-step explanation:
How long it takes to reach the ground is a y-dimension thing, and horizontal displacement is an x-dimension thing. So let's set up a table with the info we have in each dimension:
x y
V₀ 10.0 m/s 10.0 m/s
Δx ? -122.5 m
a 0 m/s/s -9.8 m/s/s
v 10.0 m/s ?
t ? ?
That seems like an awful lot of question marks, doesn't it?
The first question asks us for the time, t, it takes for the pathetic and greatly disliked Justin Bieber to hit the ground. We will use the equation:
Δx = V₀t + 1/2at²
Filling in our values using the y-dimension stuff only:
[tex]-122.5 = 10.0t+\frac{1}{2}(-9.8)t^2[/tex] which simplifies to
[tex]-122.5=10.0t-4.9t^2[/tex]
Hmmm...this is beginning to resemble a parabolic equation you probably already studied in Algebra 2!
We can solve for t by getting everything on one side and setting the equation equal to 0. We set it equal to 0 since the height on the ground is 0:
[tex]-4.9t^2+10.0t+122.5=0[/tex]
When you factor that for the 2 values of t, you get
t = -4.1 and 6.1
Of course, since time can't EVER be negative, we use a t value of 6.1. That's how long it takes to hit the ground. That t value can now be filled into the t values in our table above. We need that t value for the next part that asks us the horizontal displacement, Δx. This is x-dimension stuff now. Using the same equation:
Δx =[tex]10.0(6.1)+\frac{1}{2}(0)(6.1)^2[/tex]
Of course since the acceleration in the x-dimension is always 0, the whole portion of the equation after the equals sign is eliminated, leaving us with
Δx = 10.0(6.1)
Δx = 61 m
Poor Justin, upon his demise, hits the ground. Therefore, his final velocity is 0, since his body met the ground and stopped dead.
Ummm Hey,I don't know the answer for this question,when I solve the problem my answer always 6 but the real answer is 2 so I need help right now.
umm ok then its 2...
The school principal spent $2,000 to buy some new computer equipment.Of this money $120 was used to buy some new keyboards.What percent of the money was spent on keyboard
Answer:
6%
Step-by-step explanation:
120/2000= 60/1000= 6/100= 6%
6% of the money was spent on keyboard
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that school principal spent $2,000 to buy some new computer equipment.
Out of $2000 , $120 was used to buy some new keyboards
We need to find what percent of the money was spent on keyboard.
We need to find what is $120 of $2000
Let x/100 is the percent of amount spent for keyboard
x/100×2000=120
20x=120
Divide both sides by 20
x=6
Hence, 6% of the money was spent on keyboard
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Problem Eight days ago, I put 50 sheets of paper in my binder. I used the same number of sheets each day. Now I only have 2 sheets left. How many sheets of paper did I use each day?
As given,
Number of sheets of paper put in the binder 8 days ago = 50 sheets
Current number of sheets left after 8 days = 2 sheets
So, number of sheets used in 8 days = [tex]50-2=48[/tex] sheets
As it is stated that the same number of sheets are used each day, so number of sheets used per day = [tex]\frac{48}{8}=6[/tex] sheets.
Hence, 6 sheets of paper were used each day.
Answer:
6
Step-by-step explanation:
Given a triangle with angles of 23, 90, 67, what type of triangle is it: acute, equiangular, obtuse, or right?
Answer:
It is a right triangle because if it contains a 90 degree angle (a right angle), it's a right triangle.
Step-by-step explanation:
It would be a right angled triangle because all triangles with a 90 degree angle are right angle triangles : 90 degrees is a right angle
Complete the tables of values
The equations are shown in the top of the tables,
Replace x in the equations with the values of x given:
a = 4^-0 = 1
b = 4^-2 = 1/16
c = 4^-4 = 1/256
d = (2/3)^0 = 1
e = (2/3)^2 = 4/9
f = (2/3)^4 = 16/81
The value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
We have:
y = 4⁻ˣ
x = 0
a = 4⁻⁰ = 1
x = 2
b = 4⁻² = 1/16
x = 4
c = 4⁻⁴ = 1/256
y = (2/3)ˣ
x = 0
d = (2/3)⁰ = 1
x = 2
e = (2/3)² = 4/9
x = 4
f = (2/3)⁴ = 16/81
Thus, the value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.
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Identify the area of the rhombus. HELP PLEASE!!
Answer:
A = (x^2 - 2x - 8) m^2
Second option
Step-by-step explanation:
Area of rhombus = 1/2 d1 * d2
= 1/2(2x+4)(x-4)
= 1/2 (2x^2 -8x + 4x - 16)
= 1/2 (2x^2 - 4x - 16)
= x^2 - 2x - 8
Alaska is the biggest state in the United States of America , write this as a biconditional statement
Final answer:
A biconditional statement regarding Alaska's size is 'Alaska is the biggest state in the United States of America if and only if no other state in the United States has more territory than Alaska.' This statement clarifies that Alaska's status as the largest state is based on a measurable, verifiable fact.
Explanation:
A biconditional statement is a logical assertion that combines two statements into one, where one statement implies the other, and vice versa. In this context, the statement 'Alaska is the biggest state in the United States of America' can be written as a biconditional statement as follows:
'Alaska is the biggest state in the United States of America if and only if no other state in the United States has more territory than Alaska.'
This biconditional statement emphasizes the fact that Alaska's status as the largest state is contingent on the condition that all other states must have less territory. This is a fact that is verifiable and not subject to opinion, underscoring the importance of factual accuracy in research and the careful use of evidence.
WILL GIVE BRAINLIEST
Identify the factors of x2 + 16y2.
(x + 4y)(x + 4y)
(x + 4y)(x − 4y)
Prime
(x − 4y)(x − 4y)
Answer:
Prime
Step-by-step explanation:
Since none of the other answers work. Your answer is Prime.
Answer:
Prime
Step-by-step explanation:
(x + 4y)(x + 4y)
Appy FOIL method to multiply it
x^2 +4xy + 4xy +16y^2
x^2 + 8xy +16y^2
(x + 4y)(x − 4y)
Appy FOIL method to multiply it
x^2 -4xy + 4xy -16y^2
x^2 - 16y^2
(x − 4y)(x − 4y)
Appy FOIL method to multiply it
x^2 -4xy - 4xy +16y^2
x^2 - 8xy +16y^2
the options does not gives us x^2 +16y^2
So it is not factorable , It is prime
What is the value after 7 years of a 2014 ford mustang that originally costs $25,000.00 if it depreciates at a rate of 8% per year round your answer to the nearest dollar
Answer:
After 7 years it will have a value of $13.946 to the nearest dollar.
Step-by-step explanation:
As it depreciates by 8% (0.08) a year the value of the car after each year is
1 - 0.08 = 0.92 of the previous year's value.
So we have the formula:
Value = 25,000(0.92)^7
= $13,946.17 (answer).
Answer:
The rounded answer is equal to 14000
Step-by-step explanation:
Which expression is equivalent to 27 cubed ?
9^3
9
3^3
3
Answer:
your 3rd option because 3^3 is 27
I agree because when you do prime factorization you get 27 by doing it
Chuck's starting balance on his credit card was $268.23, and he made purchases of $125 and $98 during the month. He also made a payment of $100. If the finance charge is 1.4% per month on the unpaid balance, find the new balance at the end of the month.
Answer:
25.95
Step-by-step explanation:
Answer:
Roughly $396.71
Step-by-step explanation:
Chuck starts the month with $268.23 balance on his card
He makes a $125 and $98 purchase, add those two together to get $223, and then add that to the total starting balance of $268.23 to get $491.23.
At the end of the month, he made a $100 payment, subtracting $100 from the balance to get $391.23. $391.23 times 1.014 (Adding 1.4% converted into decimal form, to convert a percent into decimal form move the decimal left two places) equals $396.71
What is the sum of the given polynomials in standard from? (x^2 -3x) + (-2x^2+5x-3)
The pic will help you
Good luck:))
A circle has a circumference of 11{,}30411,30411, comma, 304 units. What is the diameter of the circle?
Answer:
The diameter of the circle is [tex]3,600\ units[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
In this problem we have
[tex]C=11,304\ units[/tex]
assume [tex]\pi=3.14[/tex]
substitute the values and solve for D
[tex]11,304=(3.14)D[/tex]
[tex]D=11,304/(3.14)=3,600\ units[/tex]
Answer: 3,600 units
Step-by-step explanation:
Factor completely, then place the factors in the proper location on the grid. 2a 2 + 2b 2 - 5ab
Answer:
[tex](2a-b)(a-2b) = 0[/tex]
Step-by-step explanation:
We can use the quadratic formula to factor this expression
For a quadratic function of the form:
[tex]na ^ 2 + ma + c[/tex]
Whe have:
[tex]2a^2 + 2b^2 - 5ab[/tex]
Then:
[tex]n = 2\\\\m = -5b\\\\c = 2b^2[/tex]
The quadratic formula is:
[tex]a =\frac{-m\±\sqrt{m^2-4nc}}{2n}[/tex]
Then the solutions are:
[tex]a= \frac{-(-5b)\±\sqrt{(-5b)^2 -4(2)(2b^2)}}{2(2)}\\\\a = \frac{5b\±\sqrt{25b^2-16b^2}}{4}\\\\a = \frac{5b\±3b}{4}\\\\a_1=2b\\\\a_2 =\frac{b}{2}[/tex]
Finally The factored expression is:
[tex]a-\frac{b}{2} = 0\\\\2a -b = 0\\\\[/tex]
and
[tex]a-2b= 0[/tex]
Then
[tex]2a^2 + 2b^2 - 5ab = (2a-b)(a-2b) = 0[/tex]
Which equation is an identity?
8 – (6v + 7) = –6v – 1
5y + 5 = 5y – 6
3w + 8 – w = 4w – 2(w – 4)
6m – 6 = 7m + 9 – m
Answer:
Equation 3
Step-by-step explanation:
An identity is, simply put, an equation that is always true. 1 = 1, 2 = 2, and x = x are all examples of identities, as there's no case in which 1 ≠ 1, 2 ≠ 2, and x ≠ x. Essentially, if we can manipulate and equation so that we end up with the same value on either side, we've found an identity. Let's run through and try to solve each of these equations to see which one fulfills that condition:
8 - (6v + 7) = -6v - 1
8 - 6v - 7 = -6v - 1
1 - 6v = -6v - 1
1 = -1
This is clearly untrue. Moving on to the next equation:
5y + 5 = 5y - 6
5 = -6
Untrue again. Solving the third:
3w + 8 - w = 4w - 2(w - 4)
2w + 8 = 4w - 2w + 8
2w + 8 = 2w + 8
If we created a new variable z = 2w + 8, we could rewrite this equation as
z = z, which is always true. We can stop here, as we've now found that equation 3 is an identity.
The identity among the given equations is 3w + 8 - w = 4w - 2(w - 4), as it simplifies to a true statement 2w + 8 = 2w + 8 for all values of w.
Explanation:The student asked which equation is an identity. To find the identity, we simplify and solve each equation:
8 – (6v + 7) = –6v – 1: When we simplify, we get 8 - 6v - 7 = -6v - 1, which further simplifies to 1 - 6v = -6v - 1. Adding 6v to both sides, we have 1 = -1, which is not true, so it's not an identity.
5y + 5 = 5y – 6: Simplifying this we simply subtract 5y from both sides, and we are left with 5 = -6, which is not true, so this is not an identity either.
3w + 8 – w = 4w – 2(w – 4): Simplifying we get 2w + 8 = 4w - 2w + 8, which reduces to 2w + 8 = 2w + 8. This is true for all values of w, therefore, this is an identity.
6m – 6 = 7m + 9 – m: Simplifying gives us 6m - 6 = 6m + 9. Subtracting 6m from both sides, we get -6 = 9, which is not true and thus not an identity.
The identity is the equation 3w + 8 – w = 4w – 2(w – 4) because it simplifies to a true statement regardless of the value of w.
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A helicopter flying 1600 feet above ground spots an airplane flying above. If the horizontal distance between the helicopter and airplane is 3,055 feet and angle of elevation is 71 degrees, find the airplane’s altitude.
Answer: 10,472.36 feet
Step-by-step explanation:
- Observe the diagram attached (It is not drawn to scale).
- Calculate the height between helicopter and airplane (h), as following:
[tex]tan\alpha=\frac{opposite}{adjacent}\\\\tan(71\°)=\frac{h}{3,055}[/tex]
Solve for h:
[tex]h=(3,055)(tan(71\°))\\h=8,872.36ft[/tex]
- Therefore, the altitude of the plane is:
[tex]altitude=1,600ft+8,872.36ft\\altitude=10,472.36ft[/tex]
You can use the tangent ratio to find the airplane's altitude.
The altitude of the airplane in the given condition is 10,471.72 ft
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
What is tangent ratio?In a right angled triangle(triangle with one of the angles as right angle which is 90 degrees), seeing from perspective of an angle, the tangent ratio is the ratio of the side opposite to that angle and the side which is perpendicular to that opposite side.
How to find the airplane's altitude if angle of elevation is given?Refer to the attached figure.
The altitude of the plane is the length of the line segment CE.
We have the rectangle ABDE, thus, AD = BE in terms of length.
(remember that |AB| means length of line segment AB).
Thus,
|CE| = |CB| + |BE| = |CB| + 1600 ft
Using the tangent ratio for triangle ABC from angle A, we get:
[tex]tan(A) = \dfrac{|CB|}{|AB|} = \dfrac{|CB|}{3055}\\\\tan(71) \approx 2.904 = \dfrac{|CB|}{3055}\\\\|CB| = 3055 \times 2.904 = 8.871.72 \: \rm ft[/tex]
Thus,
|CE| = |CB| + 1600 = 8871.72 + 1600 = 10,471.72 ft.
Thus,
The altitude of the airplane in the given condition is 10,471.72 ft
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PLEASE HELP!
What is the measure of angle C?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
[tex] R = 10.39^\circ [/tex]
Step-by-step explanation:
Since you have the lengths of all the sides, you can use sine, cosine, or tangent to find the answer. Let's use the tangent ratio.
For angle C, AB is the opposite leg, and BC is the adjacent leg.
[tex] \tan C = \dfrac{opp}{adj} [/tex]
[tex] \tan C = \dfrac{22}{120} [/tex]
[tex] C = \tan^{-1} \dfrac{22}{120} [/tex]
[tex] C = 10.39^\circ [/tex]
Applying the tangent ratio (tan ∅ = opposite length/adjacent length), the measure of angle C, to the nearest hundreth, is: 10.39°
What is the Tangent Ratio?In a given right triangle, the tangent ratio is given as, tan ∅ = opposite length/adjacent length.
Given the following:
∅ = ∠COpposite = 22Adjacent = 120Applying the tangent ratio:
tan C = 22/120
m∠C = tan^(-1)(22/120)
m∠C = 10.39° (nearest hundreth)
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There are x boys playing in the park. The number of girls playing in the park is equal to the square root of the number of boys. If the total number of boys and girls playing in the park is 42, find the number of boys. A. 36 B. 6 C. 49 D. 7
Answer:
Option A. 36
Step-by-step explanation:
Let
x-------> the number of boys
y------> the number of girls
we know that
[tex]x+y=42[/tex] -----> equation A
[tex]y=\sqrt{x}[/tex] -----> equation B
using a graphing tool to solve the system of equations
Remember that the solution is the intersection point both graphs
The solution is the point (36,6)
see the attached figure
therefore
The number of boys is 36
Fill in the blanks to complete the following statements. Bold left parenthesis a right parenthesis For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1minusp)greater than or equals______. Bold left parenthesis b right parenthesis Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals______. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
For the shape of the distribution of the sample proportion to be approximately normal, it is required that np (1 -p ) greater than or equals 10.
Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals0.35.
Step-by-step explanation:
Normal distribution is the shape data takes as a symmetrical bell shaped curve. Normal approximation can only be taken when np or np(1-p) greater than 10.
Fill in the blanks to complete the following statements:
For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1 - p)greater than or equals__10____. Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals__0.35____.The first blank should be filled with '5' as per the npq rule for approximation using normal distribution and the second statement's blank is filled with '0.35', which is the population proportion.
Explanation:To complete your statements:
np(1-p) greater than or equals 5 - This is a common guideline when checking if we can use a normal distribution to approximate a binomial distribution, also referred to as the 'npq rule'. The mean of the sampling distribution with a population proportion of 0.35 (p) is 0.35. This is true based on the formula for the mean of a sampling distribution for proportions, which equals the population proportion (p).
It's essential to remember that in hypothesis testing of a single population proportion, the binomial distribution's shape needs to be similar to a normal distribution. The terms 'np' and 'nq' refer to the conditions for this binomial distribution. Here 'n' is the number of trials, 'p' is the probability of success, and 'q=1-p' is the probability of failure, both must be more significant than five for the approximation to be acceptable.
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I’ll give brainliest!! Help!! Paige has $213.84 deducted from her paycheck for her 401(k). Her gross paycheck amount is $1944. What percent of her gross paycheck amount does she have deducted for her 401(k)
9%
11%
13%
Answer:
11 %
Step-by-step explanation:
Percent = Amount deducted/original amount × 100 %
= 213.84/1944 × 100 %
= 11.00 %
Paige has 11.00 % of her paycheck deducted for her 401(k).
Answer:
11%
Step-by-step explanation:
The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels . one day , she counts 15 seats and 22 wheels. The equation repesenting the total number of seats is u + b = 15 where u is the number of unicycles and b is the number of bicycles
Answer:
Step-by-step explanation:
U+b=15
7+8=15
What are the zeros of the function? f(x)=x(x−2)(x+6)
Select each correct answer.
−6
−2
0
2
6
Answer:
-6,0,2
Step-by-step explanation:
f(x)=x(x−2)(x+6)
To find the zeros of the function, set the function equal to zero
0 =x(x−2)(x+6)
Using the zero product property
x=0 x-2 =0 x+6=0
Solve each equation
x=0 x=2 x=-6
There are three zero's
-6,0,2
A quadrilateral has all sides the same length and no right angels.What is the name of the quadrilateral
I think it's possibly a rhombus
Which is NOT a major expense category?A) housingb) transportationc) electricityd) food???
Answer: the one that is not a magor epense catgortuy is c : transportation
Step-by-step explanation:
the answer is: C) transportation
A potter works 4 days a week, makes 14 pots per day on average, and charges $24 a pot. Money per 4-day workweek?
To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by zα/2, (b) find the critical value t Subscript alpha divided by tα/2, or (c) state that neither the normal nor the t distribution applies.?
95 % ; n=100; σ = unknown; population appears to be skewed
Choose the correct answer below.
A. tα/2 =2.626
B. zα/2 = 1.96
C. tα/2 =1.984
D. zα/2 = 2.575
E. Neither the normal nor the t distribution applies
To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by zα/2, (b) find the critical value t Subscript alpha divided by tα/2, or (c) state that neither the normal nor the t distribution applies.?
98 % ; n= 19; σ = 21.4; population appears to be normally distributed
A. zα/2 = 2.33
B. tα/2 = 2.214
C. zα/2 = 2.552
D. zα/2 = 2.055
E. Neither normal nor t distribution applies
Answer:
1: z = 1.96
2: t = 2.552
Step-by-step explanation:
1: When you don't know the population standard deviation and the sample size is large, you can still use a z test because many large samples are relatively normally distributed. A 95% confidence interval uses a z-score of 1.96
2. We are told that n < 30, so we use t distribution. Use the degrees of freedom, which is one less than the population, and the column that has 0.02 in the area of 2 tails.
In constructing a confidence interval, if the standard deviation is unknown and the population appears skewed, we typically use the t-distribution. However, without enough information given, the answer to the first problem tends towards 'Neither normal nor t distribution applies'. For the second problem, the standard deviation is given and the population appears normally distributed, hence answer is 'zα/2 = 2.33' from the z-table.
Explanation:The relevant subject matter here is Statistics, specifically, confidence intervals. The construction of a confidence interval depends on the knowledge of the standard deviation and whether the population is normally distributed or not.
For the first problem, since the standard deviation (σ) is unknown and the population appears to be skewed, student's t-distribution applies here. This would involve using tα/2 with degree of freedom (n-1) in place of the unavailable standard deviation. However, without enough data provided in the question, it is difficult to correctly compute tα/2. The answer therefore likely tends towards option E: 'Neither the normal nor the t distribution applies'.
For the second problem, the standard deviation (σ) is given and the population appears to be normally distributed. This suggests the normal distribution applies, hence you would compute zα/2, the critical value for the z-score at a 98% confidence level. Referring to a standard z-table at a 98% confidence level gives a z-score of approximately 2.33. So, the answer for this scenario is A: zα/2 = 2.33.
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1. the domain set of C = {( 2, 5), (2, 6), (2, 7)} {2} 2. the range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)} domain = range = {all real numbers} 3. the range and domain of F = {(x, y ) | x + y =10} domain = {all real numbers}: range = {y: y = 3} 4. the range and domain of P = {(x, y ) | y = 3} {3, 4, 5, 6}
For the given sets, the domain of set C is {2}, and its range is {5, 6, 7}. Set E has both domain and range as {3, 4, 5, 6}.
A set of ordered pairs is defined as a relation. The domain of a relation is the set of all the first elements of the ordered pairs, and the range is the set of all the second elements. Let's look at the listed sets and determine their domains and ranges.
For set C = {( 2, 5), (2, 6), (2, 7)}, the domain is {2}, because 2 is the only first element in all the pairs. The range for set C is {5, 6, 7} since those are all the second elements in the pairs.The range of set E = {(3, 3), (4, 4), (5, 5), (6, 6)} is the set of y-values or second elements of the ordered pairs, which is {3, 4, 5, 6}. Since each pair has the same x and y values, the domain of E is also {3, 4, 5, 6}.For the relation F = {(x, y) | x + y = 10}, if the domain is all real numbers, then the range must also include all real numbers that can be paired with a number from the domain to sum up to 10.For relation P = {(x, y ) | y = 3}, regardless of the x values, if y is always 3, then the range is {3}. The domain can include any real number as x, but the specific domain provided is {3, 4, 5, 6}.A function is a special type of relation where each element of the domain is associated with exactly one element in the range. This condition is also known as the vertical line test when graphing the relation on a coordinate plane.
△ABC is a right triangle with right angle at ∠B . AB=34 cm AC=55 cm What is the measure of ∠C , to the nearest degree? Enter your answer in the box.
Answer:
38°
Step-by-step explanation:
One side length is 34cm and the hypotenuse is 55cm. Used SOH-CAH-TOA to find what trig function to use. You have the opposite side and the hypotenuse, so use sine. SinC = 34/55. You can input this into a calculator as 34/55 and press sin^-1 to get the angle value, which is approximately 38°.
Answer:
△ABC is a right triangle with right angle at ∠B.
AB=34 cm
AC=55 cm
What is the measure of ∠C, to the nearest degree?
Enter your answer in the box.
38°
Step-by-step explanation:
Yadira's mom is buying hot dogs and hot dog buns for the family barbecue. Hot dogs come in packs of 1 and hot dog buns come in packs of 9. The store does not sell parts of a pack and Yadira's mom wants the same number of hot dogs as hot dog buns. What is the smallest total number of hot dogs that Yadira's mom can purchase?
Answer:
Nine
Step-by-step explanation:
The smallest number of buns is one pack or 9 buns.
If there is one hot dog per bun, the smallest number of hot dogs is nine.
Answer:
36 hotdogs
Step-by-step explanation:
Mathematically, we say that 36 is the least common multiple of 12 and 9. In math notation this looks like:
lcm of 9 and 12 is 36
The smallest total number of hot dogs that Yadira's mom can purchase is , 36.
If an object is propelled upward from a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation h = -16t^2+vt+s, where h is in feet. If the object is propelled from a height of 12 feet with an initial velocity of 64 feet per second, it's height h is given by the equation h = -16t^2+64t+12. After how many seconds is the height 72 feet?
Answer:
The object first reaches 72 feet after 1.5 seconds; it is this height again after 2.5 seconds.
Step-by-step explanation:
To find the amount of time it takes to reach 72 feet, we solve the equation
72 = -16t² + 64t + 12
To solve this, we will set it equal to 0 by subtracting 72 from each side:
72-72 = -16t² + 64t + 12 - 72
0 = -16t² + 64t - 60
Next we will use the quadratic formula to solve this:
By setting up and solving the required quadratic equation, it is determined that an object propelled from a height of 12 feet with an initial velocity of 64 feet per second will take 3.75 seconds to reach a height of 72 feet.
Explanation:The height h of the object is given by the equation h = -16t^2 + 64t + 12. We need to solve for time t, where the height h is 72 feet. By setting the equation equal to 72, we get 72 = -16t^2 + 64t + 12.
Moving -16t^2 and 64t to the other side, we get 16t^2 - 64t + (72 - 12) = 0. This simplifies to 16t^2 - 64t + 60 = 0. Divide every term in the equation by four to get: 4t^2 - 16t + 15 = 0. This equation must now be solved using the quadratic formula: t = [-b +/- sqrt(b^2 - 4ac)] / (2a).
Plugging in the values a=4, b=-16, and c=15, we get two possible solutions: t = 1 and t = 3.75 seconds. As the object is propelled up and comes down, we take the larger value, t=3.75 seconds, because that's the actual duration for the object to reach the height of 72 feet.
Learn more about Projectile Motion here:https://brainly.com/question/20627626
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