The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts= 4p - 1
Explanation:
Amount per pound of walnut = $4
Amount of coupon = $1
The cost of 4 pounds of walnuts:
[tex]\text{Cost = 4 }\times5=\text{ \$20}[/tex]The amount Andrew have to pay to buy 4 pounds of walnuts:
Amount = cost - coupon
Amount = $20 - $1
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts:
let number of pounds = p
Cost for p pounds of walnut = Amount per walnut * number of walnut
Cost for p pounds of walnut = $4 * p
= $4p
The expression for the cost to buy p pounds of walnuts= cost for p - coupon
= 4p - 1
May you hello me and why did yall start making people pay?
Answer:
53.76
Explanation:
The volume of the triangular prism is given by
[tex]V=\frac{1}{2}\cdot h\cdot b\cdot l[/tex]where h is the height, b is the base, and l is the length of the prism.
Now in our case h = 3.2 m, b = 4.8 m, and l = 7m; therefore, the above equation gives
[tex]V=\frac{1}{2}\cdot3.2\cdot4.8\cdot7[/tex][tex]V=53.76\: m^3[/tex]which is our answer!
Hence, the volume of the triangular prism is 53.76 cubic meters.
The perimeter of a triangle is 14.x - 4. If two of the sides measure 3.x - 2 and 5x + 3, then how long is the third side?
Given :
The perimeter of a triangle is, P = 14x - 4.
The sides are, a = 3x-2 and b = 5x + 3.
The perimeter of a triangle with sides a, b and c can be expressed as,
[tex]P=a+b+c[/tex]Substituting the values, we get,
[tex]\begin{gathered} 14x-4=3x-2+5x+3-c \\ c=14x-4-(3x-2+5x+3) \\ c=6x-5 \end{gathered}[/tex]Thus, the correct option d.
3x + 9 ≤ 30answer the solution
Which of the following are greater than 1/443% 5/90.151/121.4
To solve this, we will need to convert all values to decimal.
First convert 1/4 to decimal:
[tex]\frac{1}{4}\text{ = 0.25}[/tex]Now convert 43% to decimal:
[tex]43\text{percent = }\frac{43}{100}\text{ = 0.43}[/tex]Simplify 5/9:
[tex]\frac{5}{9}\text{ = }0.56[/tex]0.15 is already a decimal value.
Simplify 1/12:
[tex]\frac{1}{12}\text{ = 0.083}[/tex]1.4 is already a decimal.
After simplifying, we have the following values:
0.25
0.43
0.56
0.15
0.083
1.4
We can see the values greater than 0.25 are:
0
* The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically.
Solution
f(2) = 4 and f(3) = -1
g(2) = 6 and g(-3) = 7
From the info given we can see this :
x = 2 f(2) = 4 , g(2)= 6
x= 3 f(3)= -1 , g(3)= 7
And we can calculate the slope with the following formula:
[tex]m=\frac{-1-4}{3-2}=-5[/tex][tex]m=\frac{7-6}{3-2}=1[/tex]And for this case we can conclude that the lines are neither
Since m1 is different from m2
And m1*m2 is not -1
The graph below shows the number of snowballs, y, needed to make x snowmen.
Number of Snowballs
15
10
S
(1,3)
(3,9)
(4, 12)
+
2
Number of Snowmen
3 4 5
How many snowballs are needed to make 2 snowmen?
The number of snowballs that are needed to make 2 snowmen is equal to 6.
How to write a proportional equation?Mathematically, a proportional relationship can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:
k = y/x
k = 3/1 = 9/3 = 12/4 = 3
When the number of snowmen, x = 2, the number of snowballs, y is given by:
y = kx
y = 3 × 2
y = 6.
Therefore, the ordered pair is equal to (2, 6).
Read more on proportion here: brainly.com/question/20167968
#SPJ1
0> -2x^2+4x+4Solve each inequality by graphing. Sketch it.
To solve the inequality we need to find the x-values that are the roots of the quadratic equation, let's use the quadratic formula:
[tex]\begin{gathered} \text{For an equation in the form:} \\ ax^2+bx+c=0 \\ The\text{ quadratic formula is:} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Then a=-2, b=4 and c=4} \\ x=\frac{-4\pm\sqrt[]{4^2-4(-2)(4)}}{2(-2)} \\ x=\frac{-4\pm\sqrt[]{16+32}}{-4} \\ x=\frac{-4\pm\sqrt[]{48}}{-4} \\ x=\frac{-4\pm6.93}{-4} \\ \text{Then} \\ x1=\frac{-4+6.93}{-4}=\frac{2.93}{-4}=-0.732 \\ x2=\frac{-4-6.93}{-4}=\frac{-10.93}{-4}=2.732 \end{gathered}[/tex]Now, let's try values less or greater than these roots:
If x=-1:
[tex]\begin{gathered} 0>-2(-1)^2+4(-1)+4 \\ 0>-2\cdot1-4+4 \\ 0>-2\text{ This is right, then number less than -0.732 are solutions of the inequality} \end{gathered}[/tex]Now let's try x=3:
[tex]\begin{gathered} 0>-2(3)^2+4(3)+4 \\ 0>-2\cdot9+12+4 \\ 0>-18+16 \\ 0>-2\text{ This is correct two, then the values greater that 2.732 are solutions to the inequality too} \end{gathered}[/tex]Then, the graph of the inequality is:
The red-shaded area are the solution to the inequality, then in interval notation we have:
[tex](-\infty,-0.732)\cup(2.732,\infty)[/tex]In builder notation it would be:
[tex]x|x<-0.732orx>2.732[/tex]24. A rocket is launched into the air. Its height in feet, after x seconds, is given by the equation The starting height of the rocket is h(x)=-16x’ +300x + 20 The maximum height is The rocket hits the ground after seconds.
Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall. Based on the results of his survey, he made the following claim:Two out of four middle school students visit the mall to go shopping.Explain why this claim is misleading.a. Tyrone only interviewed students in the food court.b. Tyrone did not survey enough 8th graders to draw a valid conclusion.c. Tyrone did not use a random sample of 8th graders.d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.
Tyrone randomly interviewed 55 8th graders at the Westwood Mall Saturday afternoon to determine their reason for going to the mall.
Based on the results he made the following claim.
"Two out of four middle school students visit the mall to go shopping".
Let us analyze each of the given options.
a. Tyrone only interviewed students in the food court.
There is no evidence that suggests the interview was conducted at the food court so this is not the correct answer.
b. Tyrone did not survey enough 8th graders to draw a valid conclusion
He interviewed 55 8th graders which are more than enough students so this is not misleading.
c. Tyrone did not use a random sample of 8th graders
It is given in the question that he used a random sample so this is not misleading.
d. Since Tyrone surveyed only 8th graders, his sample is not representative of all middle school students.
If you notice closely, Tyrone interviewed only 8th graders whereas the claim was about all middle school students.
So this is clearly misleading, 8th graders do not represent all middle school students.
Therefore, option d is correct.
answer yes or no and explain why or why not.if a/5 = 8 + 9, does a/5 + 9 = 8 + 9?
Equations
We are given the following equation:
a/5 = 8+ 9
Adding 9 to both sides of the equation we have:
a/5 + 9 = 8 + 9 + 9
It's evident that a/5 + 9 is not equal to 8 + 9, but to 8+9+9 instead.
Answer: No
Help pleas Which statement best completes the diagram.
The statement which best completes the cause and effect diagram is that: A. British leaders limit the ability of colonists to expand westward.
What is a cause and effect graphic organizer?A cause and effect graphic organizer is also referred to as cause and effect diagram and it can be defined as a type of chart which highlights and shows the relationship between two things, phenomenon, or events in which an occurrence of one (cause) typically leads to the occurrence of another (effect).
During the late 18th to mid 19th centuries, the United States of America began to grow westward and this led to the emigration of Native American tribes who had in this geographical region for thousands of years before the arrival of European colonists.
Consequently, conflict developed between them which was known as "The French and Indian War" and this caused British leaders to limit the ability of many European colonists to continue expanding westward.
Read more on colonists here: https://brainly.com/question/18306385
#SPJ1
Complete Question:
Which statement best completes the diagram?
A. British leaders limit the ability of colonists to expand westward.
B. British merchants refuse to buy raw materials from the colonies.
C. British military forces are ordered to leave North America.
D. British leaders end policies that strictly controlled the colonies.
A model of a dinosaur skeleton was made using a scale of 1 in : 15 in in a museum. If the size of the dinosaur’s tail in the model is 8 in, then find the actual length of dinosaur’s tail.
The length of the real dinosaur's tail is 120 inches.
How to find the actual length of the tail?We know that the scale of the model is 1in : 15in, this means that each inch in the model represents 15 inches of the actual dinosaur.
So, if the tail of the model has a length of 8 inches, the length of the real tail will have 15 times that, so the length is given by the product:
8in*15 = 120in
Learn more about scale models.
https://brainly.com/question/25722260
#SPJ1
Which description is paired with its correct expression?
O seven less than the quotient of two and a number squared, increased by six;
Onine times the difference of a number cubed and three, 9(n²-3)
7-+8
O eight more than the quotient of a number squared and four, decreased by seven;
Otwice the difference of a number cubed and eight, 27³-8
8+/-7
Answer:
seven less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
nine times the difference of a number cubed and three; 9(n³-3)
eight more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
twice the difference of a number cubed and eight; 2 n³- 8
Step-by-step explanation:
The mean mass of 8 men is 82.4 kg. What is the total mass of the 8 men?
Given:
The mean mass of 8 men is 82.4 kg.
Required:
To find the total mass of 8 men.
Explanation:
Let the total mass be x.
Now,
[tex]\begin{gathered} \frac{x}{8}=82.4 \\ \\ x=82.4\times8 \\ \\ x=659.2 \end{gathered}[/tex]Final Answer:
The total mass of 8 men is 659.2.
if you could please answer quickly my brainly app keeps crashing
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram:
circle and chords
Step 02:
congruent chords:
Congruent chords are equidistant from the center of a circle.
x = 7 + 7
x = 14
The answer is:
x = 14
Find the average rate of change of the following equation on the given interval. y=3x+1 on [45,48]
Given:
The equation is given as,
[tex]y=3x+1[/tex]The interval is given as,
[tex]\lbrack a,b\rbrack=\lbrack45,48\rbrack[/tex]The objective is to find the average rate of change.
Explanation:
The general formula to find the average rate of change is,
[tex]A=\frac{f(b)-f(a)}{b-a}\text{ . . . . (1)}[/tex]On plugging the function in the equation (1),
[tex]A=\frac{(3(48)+1)-(3(45)+1)}{48-45}[/tex]On further solving the above equation,
[tex]\begin{gathered} A=\frac{145-136}{3} \\ =\frac{9}{3} \\ =3 \end{gathered}[/tex]Hence, the average rate of change is 3.
A house casts a shadow that is 12 feet tall. A woman who is 5.5 feet tall casts a shadow that is 3 feet tall.
What is the height of the house?
A. 22 ft.
B. 55 ft.
C. 5.5 ft.
D.220 ft.
The Brock family uses up a
1
2
-gallon jug of milk every 3 days. At what rate do they drink milk?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The rate at which the Brock family drinks milk is 4 gallon per day.
According to the question,
We have the following information:
The Brock family uses 12 gallon jug of milk every 3 days.
Now, in order to find the rate at which they drink milk, we will have to divide the amount of milk by the total number of days.
So, we have the following expression:
Rate at which they drink milk = 12/3 galloon per day
Rate at which they drink milk = 4 galloon per day
Now, this the simplified answer because this is a whole number and we can not solve it further.
Hence, the rate at which they drink milk is 4 galloon per day.
To know more about rate here
https://brainly.com/question/7098666
#SPJ1
25, -34, -2, 56, 8,-7 greatest to least
To arrange this from the greatest to the least
we will first look out for the positive numbers
Among the positive numbers, 56 comes first
then 25 and finally 8
Then we move to the negative numbers
-2 comes first
then -7 and then -34
Hence
56, 25, 8, -2, -7, -34
What’s the correct answer answer asap for brainlist
The sentence in B uses the underlined word incorrectly. The kirt was clever in concocting a story about hossatye zot in trouble.
What is adjective ?An adjective is a word that generally modifies or describes a noun or noun phrase. Its semantic role is to alter the information provided by the noun.Here the word,
Ingenious means smart and clever, whereas ingenuous means innocent and naïve. The clever villain in your favorite comic book series may devise devious plots, while the clever heroine is completely unaware.Despite the fact that the adjective ingenious is more closely related to the noun engine than to the word genius, a genius is more likely to have ingenious ideas. Ingenious invention of a self-cleaning house. So is calculating the math required to launch a rocket to the moon.So here option B is vocabulary incorrect .
To learn more about adjective refer to :
https://brainly.com/question/550822
#SPJ13
An item is regularly priced at $35. Lena bought it on sale for 20% off the regular price. How much did Lena pay?
An item is regularly priced at $35.
Cost price of item = $35
Lena bought it on sale for 20% off the regular price
i.e. 20% of 35 is off in the item of cost $35
So, The amount Leena will paid = $35- 20% of 35
[tex]\begin{gathered} \text{Amount L}eena\text{ will pay =}35-20\text{ \%of35} \\ \text{Amount L}eena\text{ will pay}=35-\frac{20\times35}{100} \\ \text{Amount L}eena\text{ will pay}=35-7 \\ \text{Amount L}eena\text{ will pay}=28\text{ dollars} \end{gathered}[/tex]So, Leena will pay $28
Answer: $28
9. As a speed skater, Kyle cycles between sprinting and recovering on the 111.12-meter short track during practice every day for 50 minutes. Let t be the time in hours that Kyle sprints during a practice. A. Write the unsimplified expression to represent the total distance Kyle skates. It may help you to make a verbal model to represent the total distance Kyle skates. Be sure to use compatible units.
SOLUTIONS
As a speed skater, Kyle cycles between sprinting and recovering on the 111.12 meter short track during practice every day for 50 minutes.
Let t be the time in hours that Kyle sprints during practice.
Sprint Speed: 48 km/hr
Recovery: 18 km/hr
(a)
Write an unsimplified expression to represent the total distance Kyle skates.
[tex]speed=\frac{distance}{time}[/tex]If t= time sprinting then (50-t)= time recovering
Distance = rate x time= t(48) + (50-t)18
Distance = 111.2m
(c) Simplifying the expression
Write and solve the equation that has been modeled below.
Solution
[tex]\begin{gathered} x+x+1+1+1+1+1+1+1=1+1+1+1+1+1+1+1+1 \\ 2x+7=9 \\ \text{Separate similar terms} \\ 2x=9-7 \\ 2x=2 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{2}{2} \\ \\ x=1 \end{gathered}[/tex]The final answer
[tex]x=1[/tex]I’ve been working on these similar questions but coming to this question. I found myself being stuck.
Solution:
If the variation in pressure is P pounds per square inch, then the Loudness L in decibels is;
[tex]L=20\log _{10}(121.3P)[/tex]When L=115 decibels;
[tex]\begin{gathered} 115=20\log _{10}(121.3P) \\ \text{Divide both sides by 20;} \\ \frac{115}{20}=\frac{20\log_{10}(121.3P)}{20} \\ \log _{10}(121.3P)=5.75 \end{gathered}[/tex]But from the logarithmic law, we have;
[tex]\log _ba=c\leftrightarrow a=b^c[/tex]Thus,
[tex]\begin{gathered} \log _{10}(121.3P)=5.75 \\ 121.3P=10^{5.75} \\ 121.3P=562341.33 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by 121.3;} \\ \frac{121.3P}{121.3}=\frac{562341.33}{121.3} \\ P\cong4635.95 \end{gathered}[/tex]FINAL ANSWER:
[tex]4636.0\text{ pounds per square inch.}[/tex]What is the vertex and intercept form for the equation y=x²-2x-3? What is the standard form and intercept form for the equation y-5= -2(x+1)?What is the vertex and standard form for the equation y= (x+2)(x-3)?
Let's find the vertex for the following equation:
y = x² - 2x - 3
As you can see, we found graphically that (1, -4) is the vertex for this equation.
Now, let's find the intercept form, as follows:
x-intercept:
0 = -1² -2 * - 1 - 3
0 = 1 + 2 - 3
Then, (-1, 0)
0 = 3² - 2 * 3 - 3
0 = 9 - 6 - 3
Then (3, 0)
y-intercept:
yy
Sally Sue had spent all day preparing for the prom. All the glitz and the glamour of the evening fell apart as she stepped out of the limousine and her heel broke and she fell to the ground. Within minutes, news of her crashing fall had spread to the 550 people already at the prom. The function, p(t) = 550(1-e^-0.039t) where t represents the number of minutes after the fall, models the number of people who were already at the prom who heard the news.How many minutes does it take before all 550 people already at the prom hear the news ofthe great fall? Show your work.
We have the function
[tex]p(t)=550(1-e^{-0.039t})[/tex]Therefore we want to determine when we have
[tex]p(t_0)=550[/tex]It means that the term
[tex]e^{-0.039t}[/tex]Must go to zero, then let's forget the rest of the function for a sec and focus only on this term
[tex]e^{-0.039t}\rightarrow0[/tex]But for which value of t? When we have a decreasing exponential, it's interesting to input values that are multiples of the exponential coefficient, if we have 0.039 in the exponential, let's define that
[tex]\alpha=\frac{1}{0.039}[/tex]The inverse of the number, but why do that? look what happens when we do t = α
[tex]e^{-0.039t}\Rightarrow e^{-0.039\alpha}\Rightarrow e^{-1}=\frac{1}{e}[/tex]And when t = 2α
[tex]e^{-0.039t}\Rightarrow e^{-0.039\cdot2\alpha}\Rightarrow e^{-2}=\frac{1}{e^2}[/tex]We can write it in terms of e only.
And we can find for which value of α we have a small value that satisfies
[tex]e^{-0.039t}\approx0[/tex]Only using powers of e
Let's write some inverse powers of e:
[tex]\begin{gathered} \frac{1}{e}=0.368 \\ \\ \frac{1}{e^2}=0.135 \\ \\ \frac{1}{e^3}=0.05 \\ \\ \frac{1}{e^4}=0.02 \\ \\ \frac{1}{e^5}=0.006 \end{gathered}[/tex]See that at t = 5α we have a small value already, then if we input p(5α) we can get
[tex]\begin{gathered} p(5\alpha)=550(1-e^{-0.039\cdot5\alpha}) \\ \\ p(5\alpha)=550(1-0.006) \\ \\ p(5\alpha)=550(1-0.006) \\ \\ p(5\alpha)=550\cdot0.994 \\ \\ p(5\alpha)\approx547 \end{gathered}[/tex]That's already very close to 550, if we want a better approximation we can use t = 8α, which will result in 549.81, which is basically 550.
Therefore, we can use t = 5α and say that 3 people are not important for our case, and say that it's basically 550, or use t = 8α and get a very close value.
In both cases, the decimal answers would be
[tex]\begin{gathered} 5\alpha=\frac{5}{0.039}=128.2\text{ minutes (good approx)} \\ \\ 8\alpha=\frac{8}{0.039}=205.13\text{ minutes (even better approx)} \end{gathered}[/tex]Zachary is designing a new board game, and is trying to figure out allthe possible outcomes. How many different possible outcomes arethere if he spins a spinner with three equal-sized sections labeledWalk, Run, Stop, spins a spinner with four equal-sized sections labeledRed, Green, Blue, Orange, and spins a spinner with 5 equal-sizedsections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
ANSWER
60 possible outcomes
EXPLANATION
If he spins the 3-section spinner, there are 3 possible outcomes: Walk, Run, Stop.
If he spins the 4-section spinner, there are 4 possible outcomes: red, green, blue, orange.
If he spins the 5-section spinner, there are 5 possible outcomes: Monday, Tuesday, Wednesday, Thursday, Friday.
If he has to spin the three spinners, the total possible outcomes is the product of the possible outcomes of each spinner: 3x4x5 = 60.
Find the equation of the line though the point (-3, -2) and perpendicular to the line y = 2/3x-2.Write your answer in the form y=mx+b.
For this question we know that we have a point (-3,-2) and we want to find an equation perpendicular to the line
y=2/3x-2.
Since both lines are perpendicular we need to satisfy this:
[tex]m_1\cdot m_2=-1[/tex]With m1= 2/3. If we solve for m2 we got:
[tex]m_2=\frac{-1}{m_1}=\frac{-1}{\frac{2}{3}}=-\frac{3}{2}[/tex]And then we can find the intercept for the new line using the point given with x=-3 and y=-2 and we got this:
[tex]-2=-\frac{3}{2}(-3)+b[/tex]And solving for b we got:
[tex]b=-\frac{9}{2}-2=-\frac{13}{2}[/tex]And then our final answer would be:
[tex]y=-\frac{3}{2}x-\frac{13}{2}[/tex]12*pi=pi*12Name the property that the following statement illustratesA. Identify property of multiplicationB. Associative property of multiplication C. Commutative property of additionD. Commutative property of multiplication E. Identity property of additionF. Associative property of addition
The commutative law says that we can swap the position of numbers when we add or multiply and still get the same result
The commutative property of multiplication can be expressed as
ab = ba
The commutative property of addition can be expressed as
a + b = b + a
Looking at the given expression,
12 and pi were swapped and the sign involved is multiplication. Thus, the correct option is
D. Commutative property of multiplication
As Mars revolves around the sun, it travels at a rate of approximately 15 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mars travel in 3 minutes? Do not round your answers. Rate:mi/minDistance traveled in 3 minutes:mi
We have:
1 minute = 60 seconds
Then, 15 miles per second to miles per minute is:
[tex]15\frac{miles}{second}\times\frac{60\text{ seconds}}{1\text{ minute}}=15\times60=900\frac{miles}{minute}[/tex]Next, Distance traveled in 3 minutes is given by:
[tex]distance=900\times3=2700\text{ miles}[/tex]Answer:
rate = 900 mi/min
distance = 2700 miles
