Answer
Using speed formula:
[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]
Let y represents the distance in miles and x represents the time in hours.
As per the given statement:
Andrew drove 55 mph on his trip.
Using formula;
we have;
[tex]55 = \frac{y}{x}[/tex]
Multiply both sides by x we have;
[tex]y = 55x[/tex]
Therefore, the equation best represents the distance he drove is [tex]y = 55x[/tex]
On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for adults and $3 for children. The total revenue from ticket sales on Sunday was $1750. The system of equations below represents the number of people and total sales for the county fair on Sunday, where x represents the number of child tickets and y represents the number of adult tickets.
Use synthetic division and the Remainder Theorem to find P(a)
P(x)=x^4+3x^3-6x^2-10x+8 ; a=2
28
–16
2
4
Using synthetic division and the Remainder Theorem, we find that P(a) for P(x) when a=2 is P(2)=4, which is the remainder of the synthetic division.
To find P(a) for the given polynomial P(x)=x⁴+3x³-6x²-10x+8 when a=2, we can use synthetic division. The Remainder Theorem states that the remainder of the division of a polynomial by a linear divisor (x - a) is equal to P(a).
Let's perform the synthetic division:
Write down the coefficients of P(x): 1, 3, -6, -10, 8.Write the value of a below the synthetic division bar: 2.Bring down the leading coefficient: 1.Multiply this coefficient by a and write the result below the next coefficient: 1 * 2 = 2. Add this to the next coefficient: 3 + 2 = 5.Repeat this process for all coefficients.The synthetic division should look like this:
2 | 1 3 -6 -10 8The final number in the bottom row is the remainder, which is also P(2). So, P(2)=4.
Q10 Q6.) Find a set of parametric equations for the line that passes through the given points
What is the change in temperature between -8°c and 3°c ?
what is the product of r and t if R equals 5.33 and T equals 0.5
A quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.
The quadratic equation 3x² − 15x + 20 = 0 has a radicand of -15, indicating no real solutions. The equation 3x² + 5x − 8 = 0 can be solved using the quadratic formula, yielding solutions of x = 1 and x = -8/3.
For the quadratic equation 3x² − 15x + 20 = 0, the radicand can be found as part of the quadratic formula process, which is b^2 - 4ac. Here, a=3, b= -15, and c=20. Substituting these values in, we get the radicand as (-15)² - 4(3)(20) = 225 - 240 = -15. Since the radicand is negative, this indicates that the equation has no real solutions; the solutions are complex numbers.
To solve the equation 3x² + 5x − 8 = 0, we will use the quadratic formula, x = −b ± √(b^2 - 4ac) / (2a), since we have a quadratic with a, b, and c all non-zero. Substituting a=3, b=5, and c= -8, we find the radicand to be (5)² - 4(3)(-8) = 25 + 96 = 121. Calculating further, x = (-5 ± √121) / 6, which simplifies to x = (-5 ± 11) / 6. Thus, we have two solutions: x = (11 - 5) / 6 = 1 and x = (-5 - 11) / 6 = -16/6 = -8/3.
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Mr. Morris left work at 5:53 P.M. and drove 47 minutes to his home. What time did he arrive?
Answer:
6:40
Step-by-step explanation:
please help with this word problem
The exponential function y = 2(3)x grows by a factor of 9 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7?
Answer:
9
Step-by-step explanation:
A die is tossed. find the odds against rolling a number greater than 11.
Unsaved If you are studying the effects of UV rays on eyesight and you group 10 people together and make them wear sunglasses for 10 weeks and see if their eyesight is affected and then take another group and do not give them sunglasses and test their vision after 10 weeks, what is the treatment ? note this is not an ethical study.
sunglasses.
10 weeks.
eyesight.
vision test.
Answer:
Sunglasses
Step-by-step explanation:
What is the null hypothesis if we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2? h0: µ1 = 0?
No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:
Hₐ: µ₁ > µ₂
Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.
Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.
Therefore, the null hypothesis would be:
H₀: µ₁ - µ₂ = 0
where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.
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Graph the parabola 3x^2+6x-24
Determine the number of possible solutions for a triangle with A= 30 a=20 and b=16
There is a unique solution for a triangle with A=30 degrees, a=20 units, and b=16 units. By using the Law of Sines, sin(B) is computed as 0.4. Since there is no obtuse angle with the same sine, there is only one possible angle B, leading to one possible triangle.
To determine the number of possible solutions for a triangle with A=30 degrees, a=20 units (side opposite angle A), and b=16 units (another side), we need to apply the Law of Sines and explore the possible cases. According to the Law of Sines:
a/sin(A) = b/sin(B)
For the given values, we have:
20/sin(30 degrees) = 16/sin(B)
Calculating sin(B) gives us:
sin(B) = 16 * sin(30 degrees) / 20 = 8/20 = 0.4
Now, if sin(B) is less than 1, which it is in our case, there are two possible scenarios:
B is acute: There will be one solution for B, meaning B could be angle whose sine is 0.4.
B is obtuse: We must also check if there is a possible obtuse angle that also has a sine of 0.4. However, since the sine function is positive and less than or equal to 1 for angles between 0 and 180 degrees and it's symmetric with respect to 90 degrees, there can't be an obtuse angle with the same sine value as an acute angle.
Therefore, we only have one possible angle B, which implies we have a unique solution for the triangle.
Additionally, we should check whether side b is larger than the altitude from A; otherwise, there would be no solution for the triangle. To do this, we can use the extended Law of Sines to calculate the diameter (D) of the triangle's circumcircle:
D = a / sin(A)
And thus, the altitude (h) from A would be:
h = D * sin(B)
If b > h, we have a valid triangle and a unique solution.
There is exactly one possible solution for a triangle with the given side lengths a = 20, b = 16, and angle A = 30°.
To determine the number of possible solutions for a triangle given the side lengths a, b, and the angle A, we can use the Law of Sines. The Law of Sines states:
[tex]\[\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\][/tex]
where:
a, b, c - side lengths of the triangle
A, B, C - angles opposite to the respective sides
Given:
A = 30°
a = 20
b = 16
We can find the angle B using the Law of Sines:[tex]\[\frac{a}{\sin(A)} = \frac{b}{\sin(B)}\][/tex]
[tex]\[\frac{20}{\sin(30^\circ)} = \frac{16}{\sin(B)}\][/tex]
sin (B) = [tex]\frac{16 \times \sin(30^\circ)}{20}[/tex]
= [tex]\frac{16 \times 0.5}{20}[/tex]sin
= [tex]\frac{8}{20}[/tex]
= 0.4
To find the angle B, we take the inverse sine:
B = [tex]\sin^{-1}(0.4)[/tex]
B = 23.58°
Now, we can find angle C since the sum of angles in a triangle is 180°:C = 180° - A - B
C = 180° - 30° - 23.58°
C = 126.42°
Now, let's check if the side lengths satisfy the triangle inequality theorem:
a + b > c
20 + 16 >
36 > c
Since 36 is greater than c, the triangle inequality theorem is satisfied.
So, there is exactly one possible solution for a triangle with the given side lengths a = 20, b = 16, and angle A = 30°.
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a student is a boy with red hair? (round to nearest hundredth)
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Answer:
0.05
Step-by-step explanation:
Given :
Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
Solution :
Since ware required to find the probability that a student is a boy with red hair.
Total no. of boys with red hair = 2
Total no. of students = 4+4+10+2+5+6+8+1=40
Thus the probability that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]
⇒[tex]\frac{2}{40}[/tex]
⇒[tex]\frac{1}{20}[/tex]
⇒[tex]0.05[/tex]
Hence the probability that a student is a boy with red hair is 0.05
The period if a function is 4pi
How many cycles of the function occur in a horizontal length of 12pi?
(answer was 3)
QUESTION: Which type of transformation of the parent function would be shown by the graph?
Answer:
She's right the answer is a horizontal stretch.
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Two events are independent when the following is true:
a. the outcome of one event determines the outcome of the other event
b. there is no correlation between the two events
c. the outcome of one event does NOT determine the outcome of the other event
d. The outcome of the event is determined by the theoretical probability of the event
Solution:
Independent Events:
Consider an experiment of Rolling a die, then getting an even number and multiple of 3.
Total favorable outcome = {1,2,3,4,5,6}=6
A=Even number = {2,4,6}
B=Multiple of 3 = {3,6}
A ∩ B={6}
P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]
P(A ∩ B)=[tex]\frac{1}{6}[/tex]
So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)
Hence two events A and B are independent.
Option (c). the outcome of one event does NOT determine the outcome of the other event
Answer:
C on edge or the outcome of one event does NOT determine the outcome of the other event
Step-by-step explanation:
A cirlce with a radius of 8 cm rotates 30 degrees in one second. Determine the angle of rotation in radians.
Angle:___ w:___ v:___
BRAINLIEST!!!
Which statement about a dilation with a scale factor of 3 is true?
The statement which is true about the dilation is:
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
Step-by-step explanation:We know that the dilation transformation changes the size of the original figure but the shape is preserved.
The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.
The ratio of the corresponding sides of the two figure are equal.
i.e.
[tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]
What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?
Answer:
The zeros to the quadratic equation are:
[tex]x= -4+\sqrt{\frac{41}{2}}\\\\x= -4-\sqrt{\frac{41}{2}}[/tex]
Step-by-step explanation:
A quadratic function is one of the form [tex]f(x) = ax^2 + bx + c[/tex], where a, b, and c are numbers with a not equal to zero.
The zeros of a quadratic function are the two values of x when [tex]f(x) = 0[/tex] or [tex]ax^2 + bx +c = 0[/tex].
To find the zeros of the quadratic function [tex]f(x)= 2x^2 + 16x -9[/tex] , we set [tex]f(x) = 0[/tex], and solve the equation.
[tex]2x^2+16x\:-9=0[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=2,\:b=16,\:c=-9:\quad x_{1,\:2}=\frac{-16\pm \sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}\\\\x=\frac{-16+\sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}= -4+\sqrt{\frac{41}{2}}\\\\x=\frac{-16-\sqrt{16^2-4\cdot \:2\left(-9\right)}}{2\cdot \:2}= -4-\sqrt{\frac{41}{2}}[/tex]
A drink contains 20% cranberry juice and the rest is apple juice. What is the ratio of cranberry juice to apple juice? A.1:20 B.1:4 C.4:1 D.20:1
Write an equation of the line with the given slope, m, and y-intercept (0,b) m=-3/5 b=7/10
The equation of the line with a slope of -3/5 and a y-intercept of 7/10 is y = (-3/5)x + (7/10).
Explanation:To write an equation of a line with a given slope (m) and y-intercept (0,b), we use the slope-intercept form of a linear equation which is y = mx + b. In this case, the slope is -3/5 and the y-intercept is 7/10.
Substituting these values into the slope-intercept formula, the equation of the line is y = (-3/5)x + (7/10).
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If you have 2500 to invest at 6 interest compounded quarterly. For how many years will the money need to be invested for that amount to triple?
Evaluate: 18.4 ÷ 2.3 × 3.4 + 13.812 =
Yanis fires pottery in a kiln. He decides to measure the rate of change of temperature of the pottery over time. What would be an appropriate unit for Yanis's purpose?
Answer with explanation:
Pottery is on a Kiln.
Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).
Unit of time is second, minute and hour.
Rate of change of temperature of the pottery over time can be written as
[tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]
Internationally , Kelvin is used as S.I unit of Temperature.
So,Yanin can use
[tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]
as Rate of change of temperature of the pottery over time.
help me out with this
what is The desired outcomes of a specified event.
Answer:
Favorable Outcomes
Step-by-step explanation:
I had 42 ounces of rice. On Monday I bought 58 more ounces of rice. Then I divided all the rice into 10 equal-sized portions for dinner with friends. How many ounces of rice were in each portion? ounces
The student initially had 42 ounces of rice, bought 58 more for a total of 100 ounces. These were divided into 10 portions, so each portion will contain 10 ounces of rice.
Explanation:This problem is a basic arithmetic question. The student starts with 42 ounces of rice and then adds 58 more ounces, for a total of 100 ounces. She then divides these 100 ounces into 10 equal portions. The key here is to understand the concept of division, which basically means splitting up a total amount (100 ounces) evenly into a certain number of parts (10 portions). To do this, simply use the operation of division: 100 divided by 10 equals 10. Thus, each portion will contain 10 ounces of rice.
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