Answers
Answer:
B)
Step-by-step explanation:
exponential function given by:
[tex] \displaystyle f(x )= a \cdot{b}^{x} [/tex]
where:
a is the y-interceptb can be any numbersince the function crosses y-axis at (0,4) point
[tex]a = 4[/tex]to find a we can consider (1,8) point it tells us when x is 1 then y is 8 thus:
[tex] \displaystyle 8= 4 \cdot{b}^{1} [/tex]
[tex] \displaystyle 8= 4 \cdot{b}^{} [/tex]
divide both sides by 4:
[tex] \displaystyle \boxed{b = 2}[/tex]
altogether substitute:
[tex] \displaystyle f(x)= 4 \cdot{2}^{x} [/tex]
hence our answer is B)
Related Questions
Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)
Answers
Answer:
(x, y) = (5,8)
Step-by-step explanation:
Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8
At a gas station during a road trip, Gerard has $32.00 to spend on fuel and windshield washer fluid for his car. Fuel costs $2.75 per gallon, and each bottle of windshield washer fluid costs $3.00. The car's average fuel efficiency is 38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles, what is the maximum number of bottles of windshield washer fluid Gerard can buy? (Note: all prices include taxes.)
Answers
Answer:
Step-by-step explanation:
Total amount with Gerald = $32
Cost of fuel per gallon = $2.75
Cost of each bottle of windshield = $3
38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,
Total gallons of fuel = 250 miles / 38 miles
= 6.5789473684210 gallons
Total cost of fuel = Total gallons of fuel × cost per gallon
= 6.5789473684210 × $2.75
= $18.1
Amount left for windshield = Total amount with Gerald - Total cost of fuel
= $32 - $18.1
= $13.9
what is the maximum number of bottles of windshield washer fluid Gerard can buy?
= Amount left for windshield / Cost of each bottle of windshield
= $13.9 / $3
= 4.6333333333333 bottles
Maximum number of bottles =
4 bottles
please help she wont go to the next aswer
Answers
Answer:
$9.04 /gal
Step-by-step explanation:
1 gallon = 128 oz
8 * 4.23 oz = 33.84 oz
$2.39 /33.84 oz = .0707 $/oz
.0707 $/oz * 128 = $9.04 $/gal
can someone help me make these into square root graphs? i thought i knew how, but trying it is confusing me
Answers
Answer:
Step-by-step explanation:
Use trigonometric identities to solve each equation within the given domain.
–sin2(x) = cos(2x) from [–π, π]. PLEASE SHOW WORK!!!
Answers
It looks like the equation is
-sin²(x) = cos(2x)
Recall the half-angle identity for sine:
sin²(x) = (1 - cos(2x))/2
Then the equation can be written as
-(1 - cos(2x))/2 = cos(2x)
Solve for cos(2x):
-1/2 + 1/2 cos(2x) = cos(2x)
-1/2 = 1/2 cos(2x)
cos(2x) = -1
On the unit circle, cos(y) = -1 when y = arccos(-1) = π. Since cosine has a period of 2π, more generally we have cos(y) = -1 for y = π + 2nπ where n is any integer. Then
2x = π + 2nπ
x = π/2 + nπ
In the interval [-π, π], you get two solutions x = -π/2 and x = π/2.
A reporter announces that there is an 80% chance of a thunderstorm tomorrow, and if the thunderstorm materializes, there is a 14% chance that it will produce a tornado.What is the probability that there will be a tornado tomorrow? What is the probability that there is a storm, but does not produce a tornado?
Answers
Answer & Step-by-step explanation:
We will only get a tornado if there is already a thunderstorm materializing
0.80 * 0.14 = 0.112
Probability of a tornado = 11.2%
There is a 100 - 14 = 86% chance of a tornado not being produced.
0.80 * 0.86 = 0.688
Probability of a storm and no tornado = 68.8%
Please i need help lllll
Answers
Answer:
C
Step-by-step explanation:
A function x values must correspond to one y values.
One y values can correspond to two different x values.
C shows this isn't a function
2. Dentre as formas de representar um número decimal, a mais comum é a que utiliza vírgula. Valor como 0,25 está presente nos comércios, nos hospitais, nas lanchonetes e em muitos outros lugares. Esse valor também pode ser representado por A. ( ) 25/10 B. ( ) 1/4 C. ( )1/25 D. ( ) 1/25
Answers
Answer:
B: 0.25 = 1/4
Step-by-step explanation:
Queremos encontrar otra representación del número 0.25
Notar que hay dos decimales luego de la coma, por lo que podemos multiplicar este número y dividir por 100.
0.25 = 0.25*1 = 0.25*(100/100) = (0.25*100)/(100) = 25/100
Ahora tenemos el número escrito como una fracción, la cual debemos simplificar.
25/100
Podemos ver que tanto el numerador como el denominador son multiplos de 5, por lo que podemos dividir ambos por 5:
25/100 = (25/5)/(100/5) = 5/20
Nuevamente, ambos son multiplos de 5, por lo que podemos dividir ambos por 5.
5/20 = (5/5)/(20/5) = 1/4
así tenemos:
0.25 = 25/100 = 5/20 = 1/4
0.25 = 1/4
La opción correcta es B.
A rectangle is 12 feet long and 5 feet wide. If the length of the rectangle is increased by 25% and the width is decreased by 20%, what is the change in the area of the rectangle? The change in the area of the rectangle is
Answers
Answer:
no change in area
Step-by-step explanation:
The original area is
A = 12*5 = 60 ft^2
The new length and width
l = 12 + .25 (12) = 12+3 =15
w = 5 - .2 (5) =5-1 = 4
The new area is
A = l*w =15*4 = 60 ft^2
The area is the same
Consecutive numbers are whole numbers that follow in order such as 7, 8, 9, 10, and so forth. Suppose the average of 15 consecutive numbers is 15. What is the average of the first five numbers of the set?
Answers
Answer:
10
Step-by-step explanation:
First, we need to find the sum of the 15 consecutive numbers. The formula to finding the average of a set of numbers is the sum of the terms divided by the number of terms. So to find the sum, you do 15x15 because the average is 15 and there are 15 numbers. 15x15=225, so you know the sum of the consecutive numbers is 225. Let X be equal to the first consecutive number of the 15 consecutive numbers.
X+(X+1)+(X+2)+(X+3)....+(X+14)=225
=15X+(105)=225
=15X=225-105
=15X=120
=X=8
So the first consecutive number of the 15 is 8. Therefore, the second consecutive number is 9, the third is 10, and so on. The question asks for the average of the first five numbers, which is 8, 9, 10, 11, and 12.
The summation formula is [tex]S=(\alpha_{1}+\alpha_{n})\frac{n}{2\\}[/tex].
[tex]S=(\alpha_{1}+\alpha_{n})\frac{n}{2\\}\\ S=(8+12)\frac{5}{2}\\ S=(20)2.5\\ S=50[/tex]
So the sum of the first five consecutive numbers is 50. Since there are 5 numbers, you do 50÷5=10. Therefore, the answer is 10.
A student survey was conducted at a major university. Data were collected from a random sample of 206 undergraduate students, and the information that was collected included physical characteristics (such as height and handedness), study habits, academic performance and attitudes, and social behaviors. In this exercise we will focus on exploring relationships between some of those variables. The variables are:
Answers
Answer:
Students Major
Cheat reporting response
Number of Alcohols taken
Student's Height
Step-by-step explanation:
The Variables are the following:
Categorical variables
1. Major – The student's majors -
Arts & Social Science or STEM
2. Cheat - Response about reporting cheating - Yes or No
Quantitative Variables
3. Alcohol - Number of alcoholic beverages consumed in a typical week
4. Height - Self-reported height (in inches)
match the absolute value functions with their vertices
Answers
Vertex: (5, 2/3) - > f(x) = 3/5 |x - 5| + 2/3
Vertex: (-1, -3/7) - > f(x) = 1/2 |x + 1| - 3/7
Vertex: (0, -4/5) - > f(x) = 1/2 |x| - 4/5
Vertex: (2/5, 5/3) - > f(x) = 3/2 |x - 2/5| + 5/3
Step-by-step explanation:
Hi, I need help with this!!! I don’t understand this :-(
Answers
Answer: See image and explanation below
Step-by-step explanation:
The problem gives us 6 points to draw into the sketch.
The first and second point gives the domain and range of the sketch. The last 4 points tell us the coordinates.
Let's do the first two points. This tells us that the sketch should not go further (-3,0) and (3,0) of the x-axis, and should not go further (0,0) and (0,4) of the y-axis.
For the last 4 points, we can convert them to coordinates and graph them. The points would be (-2,3), (1,2), (-3,0), (3,0), and (0,4).
After we draw the 5 points listed above onto the graph, we can connect the points.
In the image I attached, the lines are straight, but when you draw it out, you should make your lines more curved.
Please help me solve this problem
Answers
Help anyone can help me do this question,I will mark brainlest.
Answers
Answer:
Answer is in attached image
I hope it help...
Tulio will invest $1,000,000 at 5% annual interest. Determine how much money will Tulio have after 10 years if the interest is calculated using the following methods.
Answers
Answer:
$1,500,000
Step-by-step explanation:
Given
Principal = $1,000,000
Rate = 5%
Time = 10years
Interest = PRT/100
Interest = 1000000*5*10/100
Interest = 100000*5
Interest = $500,000
Amount after 10years = $1,000,000+ $500,000
Amount after 10years = $1,500,000
The height, h, in metres, of a rocket t seconds after it is launched is approximately modelled by the quadratic relation h = 80t - 16t2. To the nearest second, how long is the rocket in the air?
Answers
Answer: 5 s
Step-by-step explanation:
Given
Height of the rocket can be modelled as [tex]h=80-16t^2[/tex]
Rocket will land on earth when it's height becomes 0
[tex]\Rightarrow 80t-16t^2=0\\\Rightarrow t(80-16t)=0\\\\\Rightarrow t=0\ \text{or}\ t=\dfrac{80}{16}=5\ s[/tex]
Neglecting 0 value
Thus, rocket remains in air for 5 s.
help me with this math question
Answers
Answer:3
Step-by-step explanation:
Just count from -1 to positive 2 the dot doesn’t move
What’s the answer? I don’t understand the question and I came to see if you all can help
Answers
Answer:
15/2 that is the answer man
When a coin and die are tossed together find the probability of getting:
a)coin with head and die with prime number
b)coin with head and die with composite number
c)coin with tail and die with even prime number
Answers
Answer:
a) 1/4
b) 1/6
c) 1/12
Step-by-step explanation:
Let S be the sample space.
S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}
n(s) =12
Events
A: coin with head and die with prime number .
B:coin with head and die with composite number.
C:coin with tail and die with even prime number.
a) A={H2,H3,H5}
n(A) = 3
P(A) =n(A)/n(S)
=3/12
= 1/4
b) B={H4,H6}
n(B)= 2
P(B) = n(B)/n(S)
= 2/12
= 1/6
c) C ={T2}
n(C) = 1
P(C) = n(C)/n(S)
= 1/12
Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?
Answers
Given:
The recursive formulae.
To find:
The correct explicit formulae for the given recursive formulae.
Solution:
If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].
If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:
[tex]f(n)=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:
[tex]f(n)=5+(n-1)5[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:
[tex]f(n)=5+(n-1)3[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].
How to find a parallel sides of trapezium length 7.3mm and 5.3mm ,and it's height is 5mm calculate the area of a trapezium
Answers
Answer:
31.50 mm²
Step-by-step explanation:
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices and edges
If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
1/2 x ( 7.3 + 5.3) x 5 = 31.50 mm²
How far apart are -14 1/2 and 2 on the number line
Answers
Which of the following will simplify to the
correct solutions of y = 2x2 + 5x - 7?
-5+ 25 - 56 525-56
A
с
4
4
-5 + 25 +56 5+25+ 56
B
D
4
4
Answers
Answer:
f the answer to the question is A
Answer:b
Step-by-step explanation:
Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is −34?
Parallel Perpendicular Neither
Line M, with slope3/4 Line N, with slope 4/3 Line P, with slope -4/3 Line Q, with slope -3/4
Answers
Given:
The slope of a line is [tex]-\dfrac{3}{4}[/tex].
To find:
The lines in the options are parallel, perpendicular or neither parallel nor perpendicular to the given line.
Solution:
We know that the slopes of parallel lines are equal.
The slope of line Q and the slope of given line are same, i.e., [tex]-\dfrac{3}{4}[/tex]. So, the line Q is parallel to the given line.
The slope of a perpendicular line is the opposite reciprocal of the slope of the line because the product of slopes of two perpendicular lines is -1.
The slope of a line is [tex]-\dfrac{3}{4}[/tex]. It means the slope of the perpendicular line must be [tex]\dfrac{4}{3}[/tex]. So, the line N is perpendicular to the given line.
The slopes of line M and P are neither equal to the slope of the given line nor opposite reciprocal of the slope of the line.
Therefore, the lines M and P are neither parallel nor perpendicular.
Will Mark brainlest !please help. (The probabilty of germenating a new flower seed is found to be 0.92,if you sow a packet of 500 seeds in the field ,how many seeds will you expect to be germinated)
Answers
Answer: 0. 92 = 92%
100% = 500
92% = 500 × 92/100 = 460
Step-by-step explanation:
The table below gives the distribution of milk
chocolate M&M's
Color
Brown
Red
Yellow
Green
Orange
Blue
Probability
0.13
0.13
0.14
0.16
0.20
0.24
If a candy is drawn at random, what is the probability
that it is not orange or red?
PLZ HELP!!!!!
Answers
Explanation:
The probability of picking red is 0.13
The probability of picking orange is 0.20
The probability of picking either of these is 0.13+0.20 = 0.33
So the probability of picking neither of them is 1 - 0.33 = 0.67
There's a 67% of this happening.
Answer:
0.34
Step-by-step explanation:
because the probability of red is 20 and the probability of orange is 14 20 + 14 is 34.
What should be done so that the expression will have a value of 28?
6 + 2 + 32 × 2
Answers
Answer:
6+2+(32×2)
6+2+(64)
8+64
72
difference between 72 and 28
72-28
=44
add 44 to make the value 28
stuck on a maths question please help with an explanation thank you stay safe :)
Answers
======================================================
Explanation:
He answered 5/7 of the 35 short-answer questions correctly. So he got (5/7)*35 = 25 of those questions correct. At 2 marks each for these questions, he earned 25*2 = 50 points from this group alone.
There are 35 short-answer questions and 15 long-answer questions. That's 35+15 = 50 questions total.
We're told that he answered 60% of all the questions correctly. So he answered 0.60*50 = 30 questions correctly.
Earlier we found that he answered 25 short-answer questions, which must mean he got 30-25 = 5 long-answer questions done correctly. At 4 marks a piece, Keith earns 5*4 = 20 points in this group.
So overall, he earned 50+20 = 70 points from both types of questions.
---------------------
If he got all answers correct, then he would earn 35*2 = 70 points from the short-answer questions and 15*4 = 60 points from the long-answer questions. That's a total of 70+60 = 130 points to get a perfect score.
The ratio of his score to the perfect score is 70:130 which reduces to 7:13 when dividing both parts by the GCF 10.
9514 1404 393
Answer:
70/130 . . . . reduces to 7/13
Step-by-step explanation:
StrategyThe problem statement describes 2 kinds of quiz questions, and different relations regarding the numbers of questions answered correctly. The problem asks for the number of marks Keith had relative to the total number of marks.
This means you need to find Keith's marks and the available marks for each question type (4 numbers).
Because of the way the problem tells you the number of long-answer questions answered, additional computations are required to find the total number of questions Keith answered and the number of short-answer questions Keith answered. (The difference of these is the number of long-answer questions answered.) That's 3 more computations.
You have to keep in mind the purpose of each computation and how it fits in to the final result. This is why we label the intermediate results.
SolutionShort Answer Marks
There were 35 short-answer questions for 2 marks each. That's a total of ...
(35)(2) = 70 . . . . marks for all short-answer questions
Keith got 5/7 of those, so got ...
(5/7)×70 = 50 . . . . Keith's marks for short-answer questions.
__
Long Answer Marks
There were 15 long-answer questions for 4 marks each. That's a total of ...
(15)(4) = 60 . . . . marks for all long-answer questions
The total number of questions on the quiz was 35 +15 = 50. Keith answered 60% of them, so answered ...
0.60×50 = 30 . . . . total number of questions Keith answered
We know Keith answered (5/7)(35) = 25 short-answer questions, so must have answered 30-25 = 5 long-answer questions. His marks for those were ...
(5)(4) = 20 . . . . Keith's marks for long-answer questions
__
Total Marks
Then the total number of marks for all answers on the quiz is ...
short marks + long marks = 70 +60 = 130 . . . available marks
And Keith's overall score was ...
(Keith's short marks + Keith's long marks)/(available marks)
= (50 +20)/130 = 70/130 . . . . Keith's score ratio for the quiz
You need to design a rectangle with a perimeter of 11 cm. The length must be 2.8 cm. What is the width of the rectangle? (You might want to draw a picture.)
a) Let w = the width of the rectangle. Write the equation you would use to solve this problem.
Answers
Step-by-step explanation:
p = 2×( l+w)
p = 2×l + 2×w
=> 2×w = p - 2×l
w = (p - 2×l) / 2
w = (11 - (2×2.8))/2
= (11- 5.6)/2
= 5.4 /2
= 2.7 cm
