Please help, need it so much!
[9.06] Jacob kicks a soccer ball off the ground and in the air with an initial velocity of 33 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?
15.1 feet
16.5 feet
17.0 feet
18.2 feet
Answer:
C. 17.0 feet
Step-by-step explanation:
We have been given that Jacob kicks a soccer ball off the ground and in the air with an initial velocity of 33 feet per second. We are asked to find the maximum height the soccer ball using formula [tex]H(t)=-16t^2+vt+s[/tex].
First of all, we will substitute [tex]v=33[/tex] in our given formula.
[tex]H(t)=-16t^2+33t+0[/tex]
Since our given parabola has a negative leading coefficient, so it will be downward opening parabola. The maximum height of the ball will be y-coordinate of the vertex of parabola.
Let us find x-coordinate of parabola as:
[tex]\frac{-b}{2a}=\frac{-33}{2\times -16}=\frac{-33}{-32}=\frac{33}{32}[/tex]
Now, we will substitute [tex]x=\frac{33}{32}[/tex] in our formula to find y-coordinate of vertex.
[tex]H(\frac{33}{32})=-16(\frac{33}{32})^2+33(\frac{33}{32})+0[/tex]
[tex]H(\frac{33}{32})=-16*\frac{1089}{1024}+\frac{1089}{32}[/tex]
[tex]H(\frac{33}{32})=-16*1.0634765625+34.03125[/tex]
[tex]H(\frac{33}{32})=-17.015625+34.03125[/tex]
[tex]H(\frac{33}{32})=17.015625[/tex]
[tex]H(\frac{33}{32})\approx 17.0[/tex]
Therefore, the ball reached the maximum height of 17.0 feet and option C is the correct choice.
59 pounds to 35 pounds increase or decrease
Comparing 59 pounds to 35 pounds shows a decrease of 24 pounds, which can be calculated by subtracting the smaller number from the larger number.
Explanation:If we are considering the transition from 59 pounds to 35 pounds, we need to determine whether this change represents an increase or a decrease. Comparing the two numbers, we can observe that 35 pounds is less than 59 pounds. Therefore, moving from a higher number to a lower number indicates a decrease. To calculate the decrease, we subtract the smaller number (35 pounds) from the larger number (59 pounds) which equals 24 pounds. So, there is a decrease of 24 pounds.
Using the example parameters given in the hypothetical experiment on weight perception, we've applied similar reasoning. If someone in the experiment stepped down from lifting 20 pounds to lifting weights less than this, it would also be considered a decrease in weight. If they stepped up from lifting a weight of 20 pounds to a heavier weight, it would be termed an increase. This example underscores the importance of difference detection, which is often studied in sensory experiments within psychology.
What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?
The length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches. What is the width?
If w=the width of the rectangle, which of the following expressions represents the length of the rectangle?
1. 2w+3
2. 2(w+3)
3. 3(2w)
That makes no sense, what DO you get?
The correct answer is, A, or question 1, or 2w + 3.
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How many times does the graph of the function below intersect or touch the x-axis? y=-3x^2+x+4 ...?
Answer:
The answer is 2 times.
which rule describes the transformation that was used to form parallelogram A'B'C'D'
Transformation involves changing the position of a shape
The transformation rule is: [tex](x-10,y-3)[/tex]
From the attachment, we have:
[tex]A = (4,7)[/tex]
[tex]A' = (-6,4)[/tex]
The translation rule from ABCD to A'B'C'D' is calculated as follows:
[tex](x,y) = A' - A[/tex]
This gives:
[tex](x,y) = (-6,4) - (4,7)[/tex]
Rewrite as:
[tex](x,y) = (-6- 4,4-7)[/tex]
[tex](x,y) = (-10,-3)[/tex]
Hence, the transformation rule is:
[tex](x-10,y-3)[/tex]
Read more about transformations at:
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What is the function rule for (1,6) (2,24) and (3,54)?
Find the zeros of g(x)=x2+5x−24g
What integer is equivalent to 9^3/2?
Answer:
27
Step-by-step explanation:
Convert the fraction in the exponent to a root, to simplify the expression and make the calculation easier.
[tex]9^{\frac{3}{2}}\\=\sqrt{9^{3} } \\=\sqrt{729} \\=27[/tex]
Therefore the integer which is equivalent to [tex]9^{\frac{3}{2} }[/tex] is 27.
What is the x-intercept of the line with this equation −2r+1/2 y=18?
Enter your answer in the box.
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how many grams of O2 are in 5.0 mol of the element? Can someone tell me if I have this right please.? 1 mole of O2 = molecular wt of 32
so 5 mol = 32 *5=160 g ...?
Answer:
160g
Step-by-step explanation:
How do you simplify cscx*secx-tanx?
HELP!! Which of the following is not a possible value for a probability?
A. 0.001
B. 1/16
C. 0.82
D. 5/4
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we know that
Probability is the giving the possibility of given outcome or any certain events.
Probability is the number of ways of achieving the success.
Probability of event that certain to happen is 1.
Probability of event that is impossible is 0.
Sum of probabilities of all likelihood occurring events is 1.
So, Probability of any event can exceed 1.
But,
[tex]\frac{5}{4}=1.25\text{ which is greater than 1}\\[/tex]
Hence, it is not possible value for a probability .
Therefore, Option 'D' is correct.
Final answer:
The value 5/4 is not a valid probability, as probabilities must be between 0 and 1 inclusive. The correct answer is D.
Explanation:
The question that needs assistance asks about which value is not a possible value for a probability. By definition, probabilities can range from 0 (the event will not occur) to 1 (the event is certain to occur). So, looking at the options given, A (0.001), B (1/16), and C (0.82) are all between 0 and 1, which means they are valid probabilities. However, option D (5/4) is greater than 1, which makes it an invalid probability. The correct answer is D: 5/4 is not a possible value for a probability.
Find the dimensions of a right-circular cylinder that is open on the top and closed on the bottom, so that the can holds 1 liter and uses the least amount of material? ...?
The dimensions of the right-circular cylinder, which has a volume of 1 liter and uses the least amount of material, are such that the radius and twice the height are equal to the cube root of the volume divided by π, i.e., (0.001/π)^(1/3).
Explanation:In Mathematics, given the volume of a right-circular cylinder (an open top can), we can find its optimal dimensions that would use the least amount of material. These dimensions correspond to the minimum surface area of the cylinder, which includes its closed bottom but not the open top.
Since the volume V of a right-circular cylinder is given by V=πr²h, where r is the radius and h is the height. We know that the volume equals 1 liter or 0.001 m³. Rearranging the volume equation for h gives us h=V/(πr²).
Next, the surface area A of the cylinder with closed bottom is A=2πrh+πr². Substituting h=V/(πr²) into the surface area gives A=2r(V/r)+(πr²) which simplifies to A=2V/r+πr². For the surface area to be minimum, the derivative of A with respect to r must be equal to zero. The first derivative of A is A'=-2V/r²+2πr. Set A'=0 we solve for r we find r=(V/(π))^(1/3). Substituting this value back into the equation for h gives us h=2*(V/(π))^(1/3).
Hence, for a right-circular cylinder of 1 liter volume (0.001 m³) to use the least amount of material, it should have a radius and twice the height equal to the cube root of the volume divided by π, i.e., (0.001/π)^(1/3).
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Lynn and dawn tossed a coin 60 times and got heads 33 times what is the experimental probability of tossing heads using Lynn and dawns results
Answer: Experimental probability of tossing head is [tex]\frac{11}{20}[/tex]
Step-by-step explanation:
Since we have given that
Number of times Lynn tossed a coin = 60 times
Number of times head comes = 33
Experimental probability of tossing heads using Lynn and drawn results is given by
[tex]\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\\\\=\frac{33}{60}\\\\=\frac{11}{20}[/tex]
Hence, Experimental probability of tossing head is [tex]\frac{11}{20}[/tex].
Answer:
experimental probability of tossing heads using Lynn and dawns results is [tex]\frac{11}{20}[/tex].
Step-by-step explanation:
Given :Lynn and dawn tossed a coin 60 times and got heads 33 times
To find : what is the experimental probability of tossing heads using Lynn and dawns results.
Solution : We have given that
Number of times Lynn tossed a coin = 60 times.
Number of times head comes = 33.
Probability of tossing heads using Lynn and drawn results is given by:
= N[tex]\frac{number of favouable outcome }{total possible outcome}[/tex]
= [tex]\frac{33}{60}[/tex].
On simplification
=[tex]\frac{11}{20}[/tex].
Therefore, experimental probability of tossing heads using Lynn and dawns results is [tex]\frac{11}{20}[/tex].
solve this problem 2-(-8)+(-3)=
Answer:
7Step-by-step explanation:
(-)(-) = (+)
(-)(+) = (+)(-) = (-)
(+)(+) = (+)
2 - (-8) + (-3) = (*)
-(-8) = 8
+(-3) = -3
(*) = 2 + 8 - 3 = 10 - 3 = 7
A triangle has three sides and a pentagon has five sides. true false
Find P(Not a 2).
X 1 2 3 4
P(X) 0.30 0.40 0.15 0.15
A. 0.70
B. 0.60
C. 0.30
D. 0.40
Answer:
Option B is correct.
Step-by-step explanation:
We have been given the different probabilities at different point we need to find the probability of not of 2
We know that sum of probabilities is 1
[tex]P(a_2)+P(not a_2)=1[/tex]
Here, the probability that is P(a 2)=0.40
Hence, the required probability is 1-0.40=0.60
Therefore, option B is correct.
what is the base salary for the Bit Labs?
Hours of training Monthly salary
10 1250
20 1400
30 1550
40 1700
50 1850
60 2000
70 2150
What is the correct radical form of this expression? (32a^10b^5/2)^2/5
A(r) is a function that gives the area of a circle with radius r. It can be written in equation form as A(r) = 3.14r2. What is the value of A(3)? A(r) is a function that gives the area of a circle with radius r. It can be written in equation form as A(r) = 3.14r2. What is the value of A(3)?
find the HCF of 140,210,315
The triangular region shows the number of possible raisins, x, and number of possible chocolate chips, y, a baker can use in a recipe.
Which combination of raisins and chocolate chips can the baker use?
A. 28 raisins and 20 chocolate chips
B. 33 raisins and 25 chocolate chips
C. 45 raisins and 10 chocolate chips
D. 55 raisins and 12 chocolate chips
we will proceed to verify each of the cases to determine the solution of the problem
we know that
The combination of raisins and chocolate chips that can the baker use, must be inside the triangular region
so
we're graphing each of the cases
Let
x--------> the number of possible raisins
y--------> the number of possible chocolate chips
case A
Let
[tex]A(28,20)[/tex]
using a graphing tool
see the attached figure
The point [tex]A(28,20)[/tex] is include inside the triangular region
therefore
The case A is a solution
case B
Let
[tex]B(33,25)[/tex]
using a graphing tool
see the attached figure
The point [tex]B(33,25)[/tex] is not include inside the triangular region
therefore
The case B is not a solution
case C
Let
[tex]C(45,10)[/tex]
using a graphing tool
see the attached figure
The point [tex]C(45,10)[/tex] is not include inside the triangular region
therefore
The case C is not a solution
case D
Let
[tex]D(55,12)[/tex]
using a graphing tool
see the attached figure
The point [tex]D(55,12)[/tex] is not include inside the triangular region
therefore
The case D is not a solution
the answer is the option A
[tex](28,20)[/tex]
The product of some negative number and 4 less than twice that number = 336. find the number
Nicole deposits $2,136 in a savings account paying 5.36% interest. To the nearest dollar, how much money does Nicole have in total after nine years? a. $213 b. $1,030 c. $1,272 d. $3,166
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=9\ years\\ P=\$2,136\\ A=?\\r=0.0536[/tex]
substitute in the formula above
[tex]A=2,136(1+0.0536*9)[/tex]
[tex]A=2,136(1.4824)[/tex]
[tex]A=\$3,166.41[/tex]
Round to the nearest dollar
[tex]A=\$3,166[/tex]
therefore
the answer is the option D
[tex]\$3,166[/tex]
How can an expression written in either radical form or rational exponent form be rewritten to fit the other form?
An expression when written in either radical form or rational exponent form be rewritten to fit the other form as well.
When we write in different forms the Denominator defines as the Index and the Numerator defines as Power on the variable.
For Example:-We can write [tex]4^{\frac{2}{3}[/tex] as [tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]
Again, vice versa,
For example:-We can write [tex]\sqrt[5]{x^4}[/tex] as [tex]x^{\frac{4}{5}[/tex]
Therefore , we can written in other forms as well to fit .
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To convert from radical form to rational exponent form, use [tex]\( \sqrt[n]{a} = a^{1/n} \),[/tex] and vice versa for conversion.
An expression written in radical form can be rewritten in rational exponent form and vice versa using the following conversions:
1. From Radical Form to Rational Exponent Form:
- For a radical expression [tex]\( \sqrt[n]{a} \), where \( n \)[/tex] is the index and [tex]\( a \)[/tex] is the radicand:
- The equivalent expression in rational exponent form is [tex]\( a^{1/n} \)[/tex].
2. From Rational Exponent Form to Radical Form:
- For an expression [tex]\( a^{m/n} \)[/tex], where [tex]\( a \)[/tex] is the base, [tex]\( m \)[/tex] is the numerator, and [tex]\( n \)[/tex] is the denominator:
- The equivalent expression in radical form is [tex]\( \sqrt[n]{a^m} \).[/tex]
These conversions allow us to switch between radical form and rational exponent form easily. It's important to remember that the index of the radical corresponds to the denominator of the rational exponent, and the exponent of the base corresponds to the numerator of the rational exponent.
whats the slope intercept for x-8y=-6
Brown has own bakery he baked 5 cakes per day due to occasional christmas story to be in the whole christmas week how many cakes will he bake
14/5 the fraction as a percentage
Answer:
The fraction 14/5 can be expressed as 280 percent.
A salad bar offers 8 choices of toppings for lettuce. In how many ways can you choose 4 or 5 toppings? ...?