Answer:
a. 1/10
b. 4/10
c. 20
Step-by-step explanation:
There are 10 equal sections.
a. 1 section is labeled "Large Prize", so the probability of winning a large prize is 1/10.
b. 1 section is labeled "Large Prize" and 3 sections are labeled "Small Prize", so there's 4 prize section. Therefore, the probability of winning a prize is 4/10.
c. Each person has a 4/10 chance of winning a prize. So if there are 50 people, we would expect 4/10 × 50 = 20 people to win a prize.
What is the measure of ∠x?
Jeffery has run 3/8 of the race what fraction of the race do Jeffery have left
Answer:5/8
Step-by-step explanation:
sharice bought 8 songs that cost 0.79 each. She also bought an album. The total price of these items was 15.21 what was the price of the album?
Answer:
Step-by-step explanation:
0.79 x 8 =
6.72
15.21 - 6.72 =
Answer =
8.49
Please help me on this math question please
Answer:
here is the answer, out of all my experience i'm not too good on these word problems. You should check number two but if you agree than yay.
Step-by-step explanation:
f(3)=5(3)^2-7(4(3)+3)
Answer:
[tex]f(3)=-60[/tex]
Step-by-step explanation:
[tex]f(3)=5(3)^2-7(4(3)+3)\\\\f(3)=5(3)^2-7(12+3)\\\\f(3)=5(3)^2-7(15)\\\\f(3)=5\times 9-7\times 15\\\\f(3)=45-105\\\\f(3)=-60[/tex]
Lisa spots the mother bird on a branch above the nest. She
measures an angle of elevation to the bird of 67degrees. Find how
high the mother bird is above the ground, to the nearest foot.
To complete the calculations, more data is needed. We only have the angle of elevation of the mother bird, we need one relevant data, as for example, the distance from Lisa to the tree. We'll assume it to be 20 feet.
Answer:
The mother bird is 47 feet above the ground
Step-by-step explanation:
Right Triangles
They are a special type of triangles that have an internal angle of 90°. In such conditions, the following trigonometric relationship is valid:
[tex]\displaystyle tan\theta=\frac{y}{x}[/tex]
Where [tex]\theta[/tex] is the angle of elevation, y is the height of the triangle and x is the horizontal distance to the vertical leg
We can easily find the height of the tree by solving for y
[tex]y=xtan\theta[/tex]
[tex]y=20tan67^o[/tex]
[tex]y=47\ feet[/tex]
The mother bird is 47 feet above the ground
John, Sally, and Natalie would all like to save some money. John decides that it
would be best to save money in a jar in his closet every single month. He decides
to start with $300, and then save $100 each month. Sally has $6000 and decides
to put her money in the bank in an account that has a 7% interest rate that is
compounded annually. Natalie has $5000 and decides to put her money in the
bank in an account that has a 10% interest rate that is compounded continuously.
How much money have after 2 years?
How much money will sally have in 10 years?
What type of exponential model is Natalie’s situation?
Write the model equation for Natalie’s situation
How much money will Natalie have after 2 years?
How much money will Natalie have after 10 years
Answer:
Part 1) John’s situation is modeled by a linear equation (see the explanation)
Part 2) [tex]y=100x+300[/tex]
Part 3) [tex]\$12,300[/tex]
Part 4) [tex]\$2,700[/tex]
Part 5) Is a exponential growth function
Part 6) [tex]A=6,000(1.07)^{t}[/tex]
Part 7) [tex]\$11,802.91[/tex]
Part 8) [tex]\$6,869.40[/tex]
Part 9) Is a exponential growth function
Part 10) [tex]A=5,000(e)^{0.10t}[/tex] or [tex]A=5,000(1.1052)^{t}[/tex]
Part 11) [tex]\$13,591.41[/tex]
Part 12) [tex]\$6,107.01[/tex]
Part 13) Natalie has the most money after 10 years
Part 14) Sally has the most money after 2 years
Step-by-step explanation:
Part 1) What type of equation models John’s situation?
Let
y ----> the total money saved in a jar
x ---> the time in months
The linear equation in slope intercept form
y=mx+b
The slope is equal to
[tex]m=\$100\ per\ month[/tex]
The y-intercept or initial value is
[tex]b=\$300[/tex]
so
[tex]y=100x+300[/tex]
therefore
John’s situation is modeled by a linear equation
Part 2) Write the model equation for John’s situation
see part 1)
Part 3) How much money will John have after 10 years?
Remember that
1 year is equal to 12 months
so
[tex]10\ years=10(12)=120 months[/tex]
For x=120 months
substitute in the linear equation
[tex]y=100(120)+300=\$12,300[/tex]
Part 4) How much money will John have after 2 years?
Remember that
1 year is equal to 12 months
so
[tex]2\ years=2(12)=24\ months[/tex]
For x=24 months
substitute in the linear equation
[tex]y=100(24)+300=\$2,700[/tex]
Part 5) What type of exponential model is Sally’s situation?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]P=\$6,000\\ r=7\%=0.07\\n=1[/tex]
substitute in the formula above
[tex]A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}[/tex]
therefore
Is a exponential growth function
Part 6) Write the model equation for Sally’s situation
see the Part 5)
Part 7) How much money will Sally have after 10 years?
For t=10 years
substitute the value of t in the exponential growth function
[tex]A=6,000(1.07)^{10}=\$11,802.91[/tex]
Part 8) How much money will Sally have after 2 years?
For t=2 years
substitute the value of t in the exponential growth function
[tex]A=6,000(1.07)^{2}=\$6,869.40[/tex]
Part 9) What type of exponential model is Natalie’s situation?
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{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 in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]P=\$5,000\\r=10\%=0.10[/tex]
substitute in the formula above
[tex]A=5,000(e)^{0.10t}[/tex]
Applying property of exponents
[tex]A=5,000(1.1052)^{t}[/tex]
therefore
Is a exponential growth function
Part 10) Write the model equation for Natalie’s situation
[tex]A=5,000(e)^{0.10t}[/tex] or [tex]A=5,000(1.1052)^{t}[/tex]
see Part 9)
Part 11) How much money will Natalie have after 10 years?
For t=10 years
substitute
[tex]A=5,000(e)^{0.10*10}=\$13,591.41[/tex]
Part 12) How much money will Natalie have after 2 years?
For t=2 years
substitute
[tex]A=5,000(e)^{0.10*2}=\$6,107.01[/tex]
Part 13) Who will have the most money after 10 years?
Compare the final investment after 10 years of John, Sally, and Natalie
Natalie has the most money after 10 years
Part 14) Who will have the most money after 2 years?
Compare the final investment after 2 years of John, Sally, and Natalie
Sally has the most money after 2 years
H=-16t^2+ 64+60, Where T is the elapsed time, in seconds
Answer:
The given equation is H = -16t^2 + 64t + 60, where t is the elapsed time in seconds. This equation represents the height, H, of an object thrown upward from the ground with an initial velocity of 64 ft/s.
Step-by-step explanation:
1. The term -16t^2 represents the effect of gravity on the object. Since the coefficient is negative, it indicates that the object is moving upward against the force of gravity. The square of the time, t^2, shows that the effect of gravity increases as time passes. 2. The term 64t represents the initial velocity of the object. The coefficient 64 indicates that the object was thrown upward with an initial velocity of 64 ft/s. The time, t, shows the effect of the initial velocity on the height. 3. The constant term 60 represents any additional height above the ground at the start. It could be the height from which the object was thrown or any elevation from the ground. By plugging different values of t into the equation, you can find the corresponding heights at different times. For example, if you substitute t = 0, the equation becomes H = -16(0)^2 + 64(0) + 60 = 60. This means that at the start (t = 0), the object is at a height of 60 feet above the ground. To find the maximum height reached by the object, we need to determine the vertex of the parabolic equation. The vertex is given by the formula t = -b/(2a), where a and b are the coefficients of t^2 and t, respectively. In this case, a = -16 and b = 64. Substituting these values into the formula, we get t = -64/(2(-16)) = 2 seconds. This means that the object reaches its maximum height after 2 seconds. To find the maximum height, substitute t = 2 into the equation: H = -16(2)^2 + 64(2) + 60 = 64 feet. Therefore, the object reaches a maximum height of 64 feet above the ground after 2 seconds. I hope this explanation helps you understand the meaning of the given equation and how to interpret it in the context of elapsed time and height. Let me know if this helped!
Which polygon appears to be regular
Figure A
Figure B
Figure C
Figure D
Answer:
The answer is figure a :-)
The reason why is because all sides of figure A are equivalent.
Answer:
_____________________________________________
Step-by-step explanation:
How is b the answer???
B
Step-by-step explanation:
(1)Area of triangle= 1/2 x height (7cm) x base (8cm)
= 56/2
= 28
(2)Area of circle = (Pi)r^2
= (Pi)4cm^2
= 50.26548....
Since the circle is half divide the above by 2
= 25.132741.....
Round the answer to the nearest hundredth
= 25.13
(1) + (2)
28+25.13= 53.13
Hope this helps! :)
y= 15/2 when x = -5
Write direct variation that relates x and y
Answer:
[tex]y=-1.5x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem we have
y=15/2 when x=-5
Find the constant of proportionality k
[tex]k=\frac{y}{x}[/tex]
substitute the given values
[tex]k=\frac{(15/2)}{-5}=-1.5[/tex]
therefore
The linear equation that relates x and y is equal to
[tex]y=-1.5x[/tex]
If you have $11 and you spend $7 on a sandwich, drink, and chips, what fraction of your money did you spend?
Answer:
Step-by-step explanation:
u had 11 and u spent 7
7/11 <=== the fraction of money u spent is 7 out of 11
List all the factors of 56
Answer:
1*56 8*7 ECT
Step-by-step explanation:
56 one time=56. 7 8 times = 56
what is 3 1/3, 2 5/6, and 2 3/4 added in simplest form?
1) Turn everything into improper fractions: 10/3, 17/6, and 11/4
2) Find LCM of 3, 6, and 4: 12
3) Fix improper fractions to match the new denominator: 40/12, 34/12, and 33/12
4) Add them all up: 40/12+34/12+33/12=107/12=8 11/12
So your final answer is 8 11/12
Hope this helped and please mark as brainliest!
3. If d=rt, where d is distance, ris rate,
and t is time, how long, in hours, will
it take Derron to drive 180 miles at
an average rate of 45 miles per hour?
Answer:
Step-by-step explanation:
D=rt
180miles = 45mph* times
180miles/45mph =time
Time = 4hours
What is the value of x?
X=
Triangle: 9cm, 3x-20cm, 72cm, and 56cm
In this problem, we use the Triangle Inequality Theorem to find that the minimum value for x, which would yield a valid triangle, is 27.67.
Explanation:In this Mathematics problem, we're given a triangle with sides 9cm, 3x-20cm, 72cm, and 56cm. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By doing this, we can set up an inequality to solve for x:
The two smaller sides must be greater than the third side: 9cm + (3x - 20cm) > 72cm.Then, simplify to: 3x - 11 > 72.Next, bring 11 to the right side: 3x > 83.Finally, divide by 3 on both sides: x > 27.67.So, the minimum value for x that would yield a valid triangle is 27.67.
Learn more about Triangle Inequality Theorem here:https://brainly.com/question/30956177
#SPJ12
maria says that dividing 1/4 by 3 is the same as multiplying 1/2 by 1/3 do you agree or disagree
Answer:No
Step-by-step explanation:
Martha needs 28 strawberries for every 4 smoothies she makes. Complete the table using equivalent ratios.
answer: 28: 4
21: 3
70: 10
step-by-step explanation:
divide 28 by 4, and of course, do to the bottom what you do to the top. 4 divided by 4 is 1, and 28 divided by 4 is 7.
7: 4.
then, multiply by the number of smoothies.
for 3, it's 21: 3.
for 10, it's 70: 10.
How to get 813 with exponents parentheses in three different operations
Answer:
813 = 800 + 10 + 3 = (8 [tex]\times 10^{2}[/tex] ) + ( 1[tex]\times 10^1[/tex] ) + ( 3 [tex]\times 10^0[/tex] )
Step-by-step explanation:
i) 813 = 800 + 10 + 3 = (8 [tex]\times 10^{2}[/tex] ) + ( 1[tex]\times 10^1[/tex] ) + ( 3 [tex]\times 10^0[/tex] )
what is the value of the expression 2(3/4 - 1) + 0.35
Answer:
-.15
Step-by-step explanation:
you first do whats in the parantheses (3/4 - 1) which equals -.25, then multiply by 2 which gives you -.5, now add .35 and your total is -.15
Answer:
0.85
Step-by-step explanation:
2(3/4-1)+0.35
=(1.5-1)+0.35
=0.5+0.35
=0.85
What is the decay factor of the exponential function represented by the table?
1/3
2/3
2
6
Answer: 1/3
Answer:
Option 2 (B) 2/3
Step-by-step explanation:
Got it correct
Rita finds the quotient of 584 divide by 17
to be 33 R23. Explain why her answer
is not correct. Then find the correct answer.
answer.
Answer:
Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.
Step-by-step explanation:
Quotient is the required answer if 584 is divided by 17
584 will be the dividend and 17 is the divisor.
To calculate 584/17, 17 will go in 58 3times with 7 as remainder. This remainder 7 will combine with 4 to make 74, 17 will also go in 74 4times with remainder of 6.
The final answer by combining the number of times 17 goes in 584 which is 34 with final remainder of 6. This means that;
584/17 = 34 remainder 6 i.e 34R6
This shows that Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.
What is 21 over 4 written as a whole number
Answer:7
Step-by-step explanation:
Answer:
Technically, since it's an improper fraction, turning it into a whole number is not possible.
Step-by-step explanation:
21/4 as a decimal is 5.25
5.25 as a mixed number would be 5 1/4. Therefore, the closest 21/4 can get to a "whole number" is 5.
Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborhood. What is the total number of fliers they gave out
Answer:
The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Amount of fliers the volunteers gave for a political campaign = 21/38
Remaining 612 were given out in another neighborhood
2. What is the total number of fliers they gave out?
x = Total of fliers
21x/38 = Fliers given out in the first neighborhood
612 = Fliers given out in the second neighborhood
Let's solve for x, this way:
x - 21x/38 = 612
38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)
17x = 23,256
x = 23,256/17
x = 1,368
The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.
What is 17 equals 5y - 3
Will make brainliest if answered correctly
Answer:
C(g) = 2.19g ; 2.5
Step-by-step explanation:
Question 1
Since the cost is $2.19 per gallon. For every gallon, the cost will increase by $2.19. Hence, the cost per gallon C(g) is 2.19g.
Question 2
f(1.5) = 3(1.5) - 2
= 4.5 - 2
= 2.5
Answer:
1. C(g) = 2.98g
2. 2.5
Step-by-step explanation:
1. 1 gallon cost $2.98
Therefore y gallon will cost = y2.98 ie C(g) = 2.98g
2. F(x) = 3x — 2
F(1.5) = 3x1.5 — 2 = 4.5 — 2 = 2.5
I need help please! Thank you
Answer:
We also know that If two angles are complementary then their sum is equal to 90°. So, two angles ∠1 & ∠2 are complementary.
Step-by-step explanation:
As BA is perpendicular to BC. So, angle ∠ABC is 90°.
We also know that If two angles are complementary then their sum is equal to 90°. As ∠ABC is the sum of the ∠1 & ∠2. In other words, ∠1 & ∠2 are complementary. So, two angles ∠1 & ∠2 are complementary.
Lets prove this.
Given: BA ⊥ BC
Prove: ∠1 & ∠2 are complementary.
Statement Reasons
1. ∠1 & ∠2 are complementary 1. Given
2. ∠1 + ∠2 = 90° 2. Def. of complementary angles
8.
A company manufactures cell phones. In August, a random sample
of 125 cell phones was inspected nd 3 phones were found to be
defective. The company manufactured 8,000 cell phones in August.
Based on the results from the sample, about how many cell phones
are expected to be defective?
@ 64 cell phones
B 192 cell phones
© 2,667 cell phones
D 3,360 cell phones
Answer:
b
Step-by-step explanation:
2x exponent 2 times -4
Answer:
[tex]-16x^2[/tex]
Step-by-step explanation:
[tex](2x)^2 * -4\\=4x^2*-4\\=-16x^2[/tex]
Answer:
0
Step-by-step explanation:
An exponent multiply's that number by that amount of the exponent.
EX : 2^3 where ^ represents exponent
You would write it out like :2*2*2=8
Your problem asks us to multiply the number 2 by itself twice, equaling 4
and 4 subtracted by 4 is zero .
Pretend you are teaching a friend how to find the circumference of a circle. Your friend isn’t even sure they know what circumference is. Write a narrative of what you would say to your friend to explain what circumference is and how you find it.
The circumference of a circle is the distance around the Outside of the circle.
The circumference of found by multiplying PI by the diameter of the circle.