Choose the graph that represents the time for which the velocity of the ball will be between –90 and –58 ft/s.
Answers
The answer is c because t must be less than 2.5 and more than 1.5.
Find this by separating the inequality into:
-90 < -32t - 10
&
-32t - 10 < -58
Simplify and you get 2.5 and 1.5
Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have:
The velocity of the ball will be between –90 and –58 ft/s.
Let v be the velocity of the ball:
v lies between -90 and -58
-90 < v < -58
The above expression represents the inequality:
Or
-90 < -32t - 10
t < 2.5
And
-32t - 10 < -58
t > 1.5
The number line will be:
Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.
Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
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Related Questions
what are two functions, f(x) and g(x), that would result in a rational function?
Answers
Lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin
Answers
4 x 12 x 4 x 4 x 12 x 4= 40 cm.
Hope this helps!!
HELPPPPPPPPPPP WITH CACULAS
Answers
7) As x goes to 1, we have that the function itself is getting closer and closer to the value 4. It is important for this calculation to notice that we do not care about f(4) but rather the value of the function as x is around 4. This function could have been discontinuous at 4 (have a hole there or not be defined) but we would still have that [tex] \lim_{x \to 1} f(x)=4 [/tex] .
8) The value of the investment after 1 year will be equal to 400*(1.051); after 2 years the value will be equal to (400*1.051)*1.051 (the quantity after one year times (1+interest)) and after n years: [tex]400*1.051^n[/tex]. Substituting n=5 we get: 512.95$.
Now for the other part: [tex]400*1.051^n=1000[/tex] (We need to solve for n)
[tex]1.051^n=2.5[/tex] Taking logs each side:
[tex]n*log1.051=log2.5[/tex]
This yields n=18.42 years.
9) Let us take the cost: it has a fixed component of 350$ and a variable component of 20c=0.2$ per serving. Hence C(x)=350+0.2*x
The revenue function has only a variable component, 70 cents per serving. Similarly, R=0.7*x where x is the number of servings.
One has that P(x)=R(x)-C(x)=0.7*x-(350+0.2*x)=0.5x-350
Finally, if the Society breaks even, we have that P(x)=0. Solving that equation, we have: 0=0.5x-350 hence 0.5x=350 hence x=700; thus, 700 servings are needed in order for the society to break even.
10) Let us assume that q=a*p+b (general linear relationship). We have that a and b satisfy:
5000=a*60+b and 3500=a*75+b. We need to solve that system of equations to get the coefficient of our function. Subtracting both equations, we get that 1500=-15*a hence a=-100. Substituting back in the first equation, 5000=-100*60+b, yielding that b=11000. Hence the linear model that we were seeking is q=-100*p+11000.
11) If there is no surplus or shortage, we have that the price is chosen so that supply and demand are equal. Hence -3p+400=7p-500. 10p=900, hence p=90$. The required price is at 90$.
Where is the vertex of the quadratic y = (x -7)2 + 9
Answers
rule: common equation for a parabola is y=ax²+bx+c. If to re-write this equation in the form y=(x+m)²+n, then point (-m;n) is vertex of this parabola.
According to the described rule vertex is (7;9).
The graph of this function is in the attachment.
Final answer:
The vertex of the quadratic function y = (x -7)² + 9 is at the point (7, 9).
Explanation:
Vertex of a quadratic function is the highest or lowest point on the graph of the function. In this case, the quadratic function is in the form y = (x -7)² + 9.
To find the vertex, we notice that the function is in the form y = (x - h)² + k, where (h, k) represents the vertex. Therefore, the vertex of the given quadratic function is at (7, 9).
Brooke earns $7 an hour at her job now. She can represent the total she makes in a week using the expression 7r. Brooke has asked for a $1 an hour raise. Which expressing would represent the amount Brooke would make in a week after the raise?
Answers
(7 + 1) = 8 $ / h
Therefore we must now rewrite the weekly expression of your earnings.
Rewriting we have:
(7 + 1) r =
8r
Answer:
the amount Brooke would make in a week after the raise is:
8r
8R
Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:
Month
Texts
1
120
2
237
3
354
4
471
The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?
Answers
It should be the additional texts per month or D
Answer:
The number of texts he sends per month
Step-by-step explanation:
The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.
In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).
In other words, it tells how many texts he sends per month.
Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m
A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees
Answers
so W= 90 Y=90 X+Z= 180 . so 90+180+90 =360 degrees. B.
anyone free to help with this?
Mildred Lost bought two (2) radial tires at $49.95 each and two (2) seat cushions at $16.99 each. The sales tax where she lives is 6 percent. What was the total amount of the purchase?
Answers
The total amount of Mildred's purchase was $141.91.
_____
amount + 6%×amount = amount*(1 +.06)
Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?
Answers
number of pots = p + 25
Explanation:
On weekends, Noah makes 11 pots more than the normal weekdays.
We are given that the equation representing the number of pots is:
number of pots = p + 11
Now, Noah made 14 pots more that his usual numbers, this means that we will add 14 to the usual number of pots that he makes.
Therefore, the equation will become:
number of pots = p + 14 + 11
number of pots = p + 25
Hope this helps :)
Find the equation of the plane in xyzxyz-space through the point p=(5,5,3)p=(5,5,3) and perpendicular to the vector n=(1,2,5)
Answers
Given that the plane passes through point (5,5,3), the equation of the plane is therefore:
Π : 1(x-5)+2(y-5)+5(z-3)=0
on simplifying, x-5+2y-10+5z-15=0
Π : x+2y+5z=30
The equation of the plane in xyz-space that passes through the point p=(5,5,3) and is perpendicular to the vector n=(1,2,5) is x + 2y + 5z = 30.
Explanation:In mathematics, the equation of the plane can be found using the plane equation Ax + By + Cz = D. Given that the plane goes through point p=(5,5,3) and is perpendicular to vector n=(1,2,5). The vector n actually gives us the coefficients A, B, and C. Meaning A=1, B=2, and C=5. We get D by substituting the given point into the equation (Ax + By + Cz = D) as follows D = Ax + By + Cz = (1*5) + (2*5) + (5*3) = 5 + 10 + 15 = 30. Thus, the equation of the plane is x + 2y + 5z = 30.
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A moving company charges $0.60 per pound for a move from New York to Florida. A family estimates that their belongings weigh about 6 tons. About how much would it cost the family to move from New York to Florida?
Answers
so 6 tons would be 12,000
because we multiply 6x 2,000
So now we need to find the cost 12,000 Ibs.
0.60*2,000=1,200
1,200*6
=$7,200
Which of the following would NOT be a deduction from a paycheck?
Select the best answer from the choices provided.
taxes
FICA
hourly wages
health insurance
Answers
Use signed numbers to solve. A helicopter descended 1200 feet, rose 800 feet, and then descended 450 feet. What was the net gain or loss in altitude? A. lost 2450 ft B. lost 850 ft C. gained 850 ft D. gained 2450 ft
Answers
First the helicopter descended 1200 feet. So the change in altitude will be -1200 feet.
Then the helicopter rose by 800 feet. So the change in altitude will be 800 feet.
Finally the helicopter descended by 450 feet. So the change in altitude will be -450 feet.
The net change in altitude will be the sum of all the above 3 changes.
Change in altitude = -1200 + 800 - 450 = -850 feet
The negative sign indicates a descend i.e. loss in altitude. So the net change in altitude was a loss of 850 feet.
Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of the polynomial being subtracted?
Answers
We have then, that according with the coment below:
(3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab)
the additive inverse is:
(3a2 - 2b2 - 8ab) Note that is the same expression that
(-3a2 + 2b2 + 8ab)
but with different signs.
Answer:
the additive inverse of the polynomial being subtracted is
(3a2 - 2b2 - 8ab)
Answer:
Option 3
Step-by-step explanation:
edge 2020
Find the banker's interest to the nearest cent. Principal: $2,500; Rate: 9%; Time: 180 days: Interest: ? (based on a 365 day year).
Answers
I=PxRxT
I: Simple Interest.
P: Principal.
R: Rate
T: Time (It must be expressed in years or a fraction of years).
You have:
P=$2500
R=9%=0.09
T=180 days=180/365
When you substitute these values into the formula, you obtain:
I=PxRxT
I=($2500)(0.09)(180/365)
I=$110.959
Final answer:
The banker's interest rounded to the nearest cent is approximately $110.60.
Explanation:
To calculate the banker's interest on a principal of $2,500 at a rate of 9% for 180 days, you would apply the formula for simple interest:
Interest = Principal × rate × time
Since time needs to be expressed in years and the rate as a decimal, convert 180 days into a fraction of a year by dividing by 365:
Time (in years) = 180 / 365 ≈ 0.4932
Convert the rate to a decimal:
Rate (as a decimal) = 9% = 0.09
Now calculate the interest:
Interest = $2,500 × 0.09 × 0.4932 ≈ $110.595
Thus, the banker's interest rounded to the nearest cent is approximately $110.60.
find the difference of the least common multiple and the greatest common factor of 12 and 32 show your work please
Answers
6*2. 8*4
3*2*2. 4*2 2*2
2*2*2*2*2
Do the rest of the math yourself lol
PLEASE ANSWER FAST PLEASE!!!!!!
1. Beatrice decides she wants to babysit a few children at the same time to earn the money faster. She tells parents that if they allow her to babysit their children at her house, she will eliminate her automatic $5 tip and will give them an additional $5 discount.
(a) Write an equation showing the total cost for each client. Identify all variables.
(b) Four parents bring their children to Beatrice’s house at the same time for babysitting. Beatrice wants to find out how many hours she must babysit the 4 children to earn exactly the $100 she needs in order to buy the present for her mother. Write and solve an equation to find the number of hours. Justify each step in the solution.
(c) One parent decides not to drop off her child. The remaining 3 parents drop their children off at 9 a.m. Two of the parents say they will be back at 1 p.m. The third parent says she will pick up her child at 2 p.m. At noon, Beatrice realizes she needs help feeding the 3 children at the same time. She tells her little sister that she will pay her if she helps feed the children. How much can Beatrice pay her little sister and still make sure she has enough money to buy her mother a $100 present? Show your work and justify your answer.
Answers
Let B be the amount Beatrice charges per hour per child
Let x be the number of hours
Let n be the number of children
a)total amount Beatrice charges = T = B*x*n - 10
b)n =4 and T = 100
100 = B*x*4 -40
x = 35/B
c)Let S be the amount she has t o pay to her sister
n = 3 and x = (4+4+5) = 13
so, 13*B*3 -30 -S = 100
S = 39B - 130
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answers
Answer:
900
Step-by-step explanation:
Khan academy
Which of these is a point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7)
A. y+7=4(x-3)
B. y-7= -1/4(x+3)
C. y+7= -1/4(x-3)
D. y-7= -4x(x+3)
Answers
1. rule: if y+a₁=k₁(x+b₁) ⊥ y+a₂=k₂(x+b₂), then k₁*k₂= -1.
for unknown line k= -1/4.
2. substituting the coordinates (-3;7) into the equations, it is possible to find that 'y-7' and 'x+3'.
3. at the end, if to make up the equation: y-7= -1/4(x+3).
Answer: B
The point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7) is:
B. [tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
The slope intercept form is y=mx+b where m is slope.
We have given perpendicular line as:
y-3=4(x-10)
y-3=4x-40
y=4x-37
The slope intercept form of the given line is
y=4x-37
Slope of this line is m=4
Now, as we know the two perpendicular lines have negative reciprocal slope.
Thus the other line have slope [tex]m=-\frac{1}{4}[/tex]
Now. the equation of line passing through point (-3,7) and having slope [tex]\frac{-1}{4}[/tex] is:
[tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
Therefore the correct option is B.
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Assuming boys and girls are equally likely, find the probability of a couple having a baby boyboy when their sixthsixth child is born, given that the first fivefive children were all boysall boys.
Answers
Answer:
50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.
Step-by-step explanation:
For each child, there are only two possible outcomes. Either it is a boy, or it is a girl. The probability of a child being a boy or a girl is independent of the other children. So we use the binomial probability distribution to solve this question.
The conditional probability formula is also used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Find the probability of a couple having a baby boyboy when their sixth child is born, given that the first five children were all boys.
Event A: First five children being boys.
Event B: Sixth children being a boy.
P(A):
First five children being boys.
P(X = 5) when n = 5.
Equally likely to be boy or girl, so p = 0.5.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(A) = P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
Intersection:
Intersection between the first five children being boys and the sixth also being a boy, so [tex]P(X = 6)[/tex] when n = 6.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(A \cap B) = P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.015625[/tex]
Probability:
[tex]P(B|A) = \frac{0.015625}{0.03125} = 0.5[/tex]
50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.
NEED HELP ASAP!! WILL GIVE BRAINLIEST
5. Marco wrote the equation below.
cos(-pi/2)=cos(3pi/2)
which statement best describes marcos equation?
a. it is true because the cosine function is odd
b. it is false because the cosine function is even
c. it is true because the cosine function has a period of 2pi
d. it is false because the cosine function has a period of pi.
Answers
The given equation is represented below:
cos(-pi/2)=cos(3pi/2)
The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0
Further a function is defined as an even function if f(x) = f(-x)
Cosine function is an even function.
Therefore it is true and the correct option is c
It is true because the cosine function has a period of 2pi
Hope it helps ..!!
Answer:
Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].
Step-by-step explanation:
Given : Marco wrote the equation below.
[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]
To find : Which statement best describes Macro equation?
Solution :
Since, the period of the given cos function is 360°
So, it holds the property of trigonometric :
[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.
Taking [tex]\theta =-\frac{\pi}{2}[/tex]
Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]
So, the given function is a even function in a period of [tex]2\pi[/tex].
Therefore, Option C is correct.
It is true because the cosine function has a period of [tex]2\pi[/tex].
Workers in france average 5 fewer days of vacation a year than italians. americans average 24 fewer vacation days than the french. if the italians average 42 vacation days each year (the most in the world), how many does the average american worker have a year?
Answers
The average american worker has 13 vacation days per year.
if m ABC = 116 degrees what is ABC
Answers
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
Answers
Answer:
The height of the pole is 322.75 feet.
Step-by-step explanation:
Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole
Length between the point of attachment of wire from base of the pole = BC = 137 feet
Angle of elevation to the pole = θ = 67°
We have to find the length of the pole that is AB Let the height of pole be h feet.
According to trigonometry :
[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]
Here, C = 67° , perpendicular = AB = h , base = BC = 137
Substitute the values,
[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]
[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]
[tex]h=\tan 67^{\circ} \times 137[/tex]
[tex]h=322.75[/tex]
Thus, the height of the pole is 322.75 feet.
Answer:60.1
Step-by-step explanation:
cos
Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?
Answers
Kens turtle competed in a 0.50- meter race. His turtle had traveled 49/100 meter when the winning turtle crossed the finish line. What is 49/100 written as a decimal
Answers
There are a couple ways we can convert a fraction to a decimal, but I'll use a simple way.
To convert 49/100 to a decimal, we must divide the numerator (top of the fraction, 49) by the denominator (bottom of the fraction, 100).
49 ÷ 100 = 0.49
So, 49/100 is written as 0.49 as a decimal.
Well, to make it simple it's 0.49. Hope it helps!
An Native American tepee is a conical tent. Find the number of cubic feet of air in a teepee 10 ft. in diameter and 12 ft. high. 100 cu. ft. 300 cu. ft. 400 cu. ft.
Answers
V = ((pi) * (r ^ 2) * (h)) / (3)
Remembering that:
r = d / 2
Substituting the values:
V = ((pi) * ((d / 2) ^ 2) * (h)) / (3)
V = ((pi) * (((10) / 2) ^ 2) * (12)) / (3)
V = 314.16 ft ^ 3
Answer:
V = 314.16 ft ^ 3
The nearest option is:
300 cu. ft
Answer:
100 pi cubic feet
Step-by-step explanation:
Help Me Plzzzzzzzzzźzź
Answers
So for the first one, it would be 4 • 500/1 • 5
2000/5 = 400.
This is the answer.
y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.
Answers
Answer:
2
0
two real solutions
Step-by-step explanation:
from edge!!
To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.
Explanation:The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:
x = −b ± √(b² − 4ac) / (2a)
For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.
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Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.
Step 1: (6x4 – 8x2) + (3x2 + 4)
Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Falyn should factor out a negative from one of the groups so the binomials will be the same.
Answers
Answer:
Faelyn should realize that her work shows that the polynomial is prime.
Explanation:
The only difference between her factors in Step 2 is that the 4 in the first group is negative, while the 4 in the second group is positive.
Rearranging the polynomial to factor it will not change the end result.
Factoring out a negative will make not only one, but both terms, in one of the binomials the opposite sign; this will not make the factors the same.
Factoring only 2x out of the first group will result in having (3x³+4x); this is not the same either.
She should realize that when this happens, her polynomial is prime.
The precision of what Faelyn should do is that Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
How to find the factors of polynomial?Factors of the polynomial which are multiplied to produce the original polynomial.
The polynomial which can not be factored is known as prime polynomial.
The standard form of the polynomial with highest power of 2 can be given as,
Given information-
The given polynomial equitation in the problem is,
[tex]6x^4 -8x^2 + 3x^2 + 4[/tex]
1) First step of Faelyn is[tex](6x^4- 8x^2) + (3x^2 + 4)[/tex]
2) Second step of Faelyn is[tex]2x^2(3x^2 - 4) + 1(3x^2 + 4)[/tex]
Faelyn noticed that she does not have a common factor. The polynomial which can not be factored is known as prime polynomial.
Thus Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
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