The composite function f(x). g(x) is represented as 3x² - 17x + 10
How to find composite function?The composite function can be solved as follows:
f(x) = 3x - 2
g(x) = x - 5
Therefore, the composite function f(x). g(x) is as follows:
f(x). g(x) = f(x) × g(x)
Hence,
f(x) × g(x) = (3x - 2)(x - 5)
f(x) × g(x) = 3x² - 15x - 2x + 10
f(x) × g(x) = 3x² - 17x + 10
Therefore, the function f(x) × g(x) = 3x² - 17x + 10
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on a recent holiday weekend, a sample of 500 drivers was stopped by the police. 300 drivers were under 30 years of age. a total of 250 were under the influence of alcohol. of the drivers under 30 years of age, 175 were under the influence of alcohol. what is the probability that a driver selected at random from the sample of 500 is under 30 and not under the influence of alcohol?
P(A). P(Y)= 0.5*0.6=0.3
Probability: - Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Number of cases of A, N(A)= 250,
So,
P(A)=250/500 =0.5
and
N(Y)= 300, so P(Y)=300/500 =0.6
N(A and Y)= 175 so P(A and Y)= 175/500=0.35
A and Y are mutually exclusive implies A and Y donot have any elements in common, but here there are 175 people who are below 30 years and under the influence of alcohol, So they are not mutually exclusive!!
For A and Y to be independent, the Probability of A intersection Y should be equal to the product of their respective probabilities,
in this case P(A). P(Y)= 0.5*0.6=0.3 which is not equal to P( A intersection Y) (0.35)
So, A and Y are not mutually Independent also.
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Tammy’s take-home pay is $800 a month. She spends 7% on her take-home pay on her cell phone bill. How much is Tammy’s monthly cell phone bill?
Answer:744
Step-by-step explanation:
800-7%=744
Answer:
$56
Step-by-step explanation:
Simplify to a single power of 3:
3^{6}\cdot 3^{5}
3
6
⋅3
5 this isnt an abc choice you have to find the small number????
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
Given,
The exponents; 3^6 and 3^5.
We have to simplify this into a single power of 3.
In multiplication;
For exponents with same base, simply add the exponents.That is,
aᵇ . aⁿ = a^(b + n)
For exponents with different base, multiply the base and add the exponents.a^b . c^d = a x c ^ (b + d) = ac^bd
So,
3⁶ . 3⁵ = 3^(6 + 5) = 3¹¹
That is,
The simplified form of 3^6 . 3^5 to a single power of 3 is 3^11.
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You have 900 feet of fencing to enclose a rectangular plot that borders on
a river. If you do not fence the side along the river, find the length and
width of the plot that will maximize the area. What is the largest area that
can be enclosed?
The width, labeled x in the figure, is
(Type an integer or decimal.)
feet.
X
River
900-2x
x
Answer:
A = 101250 meter²
Step-by-step explanation:
Answer:
Maximum area enclosed will be 101250 meter².
Step-by-step explanation:
Let the length of the rectangular plot is x meters and the width is y meters.
900 meters is the length of the fence which represents the length of the three sides of the plot.
Therefore,
x + 2y = 900
y =  meters
Now the area of the rectangular plot will be
A = Length × Width
= (x)(y)
= 
= 450x - 
We know for the maximum area we will differentiate the area and equalize it t the zero.

= 450 - x
For the maximum area, 
Therefore, 450 - x = 0
x = 450
and y = 
y = 
y = 450 - 225
= 225 meters
Now the area enclosed A = 450 × 225
A = 101250 meter²
30. A certain test track for new car models is 6,720 meters long. If a car is currently of the way down
the track, how many more kilometers must it travel
to reach the end?
E. 2.24
F. 4.48
met
G. 6.72
H. 10.0
Answer: E. 2.24
Step-by-step explanation:
6720 - 6720 x 2/3
6720 - 4480
= 2,240
1 kilo = 1000 meters
2240 ÷ 1000
= 2.24
The birth weights ( to the nearest pound) of a sample of 27 newborn babies at a certain hospital are given in the following table, along with the number of babies at each birth weight. Find the mean birth weight of these 27 babies. Round your answer to at least on decimal point
Given
The table,
The sample size is 27.
To find:
The mean weight of these 27 babies.
Explanation:
It is given that,
That implies,
The mean weight of 27 babies is,
[tex]\begin{gathered} Mean=\frac{\sum_^x_if_i}{\sum_^f_i} \\ =\frac{4\times5+6\times10+7\times12}{5+10+12} \\ =\frac{20+60+84}{27} \\ =\frac{164}{27} \\ =6.07 \\ =6.1pounds \end{gathered}[/tex]Hence, the mean weight of 27 babies is 6.1 pounds.
-12/7 = 6w solve for w and simplify your answer as much as possible
Danny measured a house and its lot and made a scale drawing. The scale of the drawing was 1 inch : 5 feet. The houses driveway is 20 feet widein real life. How wide is the driveway in the drawing?
The width of the house driveway in the scale drawing is 4 inches.
What is scale drawing?Scale drawing is drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale).
Therefore, he measured a house and its lot and made a scale drawing.
The scale of the drawing was 1 inch : 5 feet.
The houses driveway is 20 feet wide in real life.
Therefore,
5 feet = 1 inch
20 feet = ?
cross multiply
Therefore,
width of the driveway on the scale drawing = 20 × 1 / 5
width of the driveway on the scale drawing = 20 / 5
width of the driveway on the scale drawing = 4 inches.
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Provide the name and classification and parent equation for each one.
The amount of gas that a helicopter uses is directly
proportional to the number of hours spent flying. The
helicopter flies for 2 hours and Uses 26 gallons of fuel.
Find the number of gallons of fuel that the helicopter uses
to fly for 5 hours.
Answer:
65
Step-by-step explanation:
2:26
1:x
26/2 = x = 13
The heli uses 13 gallons per hour.
5:y
13x5 = y = 65
Hope that helps
Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
Slope of the line graph here is undefined.
When a line is vertical, its slope is ambiguous. A vertical line lacks the horizontal distance required for a positive, negative, or zero slop to exist. Since there is no horizontal change, there is no slope for vertical lines because 0 cannot be divided into any integer.
It is obvious that the x-coordinates are the same if we have a pair of coordinates, (x1, y1) and (x1, y2) through which a line passes. They are the same vertical line's points. As a result, the slope of such a line will be ambiguous.
Examples of undefined slope in real-world situations include elevators that only go up and down, and a mountain cliff that is vertical for a certain amount of height but impossible for climbers to scale.
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AThe formula for the circumference of a circle is C = 2tr. Find the circumference of acircle with a diameter of 4 ft.
Given the formula for the circumference of a circle:
C = 2πr
Let's find the circumference of a circle with a diameter of 4 ft.
Where r is the radius.
To find the radius, we have:
[tex]\text{radius}=\frac{\text{diameter}}{2}=\frac{4}{2}=2ft[/tex]The radius of the circle is 2 ft.
Take π = 3.14
Hence, to find the circumference of the circle, C, substitute 2 for r, 3.14 for π, and evaluate.
Thus, we have:
[tex]\begin{gathered} C=2\pi r \\ \\ C=2\ast3.14\ast2 \\ \\ C=12.56\text{ ft} \end{gathered}[/tex]Therefore, the circumference of the circle is 12.56 ft
ANSWER:
C. 12.56 ft
Question ♀️ 2The function p(t) = 2(3)^t represents the population of a certain type of bacteria after t days. What is the population of the bacteria after 7 days?
Explanation
Given the function;
[tex]p(t)=2(3)^t[/tex]We are asked to find the population of the bacteria after 7 days.
Given that t represents the number of days, we can find the population by substituting 7 into the formula. This can be seen below.
[tex]\begin{gathered} p(t)=2(3)^7 \\ =2\times2187=4374 \end{gathered}[/tex]Answer: 4374
Iris's checking account pays simple interest at 3% per year. She has $185 in
her account. Write a linear function to model the amount of money in her
checking account at any time t.
The linear function to model the amount of money in her checking account at any time t is 185 + 5.55t.
What is an interest?An interest simply means the extra amount that's borrowed when one borrows money or when one saves.
In this case, the checking account pays simple interest at 3% per year. She has $185 in her account.
The amount of money in the account at anytime will be:
= 185 + (PRT/100)
P = principal
R = rate
T = time
= 185 + [(185 × 3 × t)/100]
= 185 + 5.55t
The function is 185 + 5.55t.
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Members of a lacrosse team raised $2863.50 to go to a tournament. They rented a
bus for $1087.50 and budgeted $74 per player for meals. Which equation or tape
diagram could be used to represent the context if a represents the number of players
the team can bring to the tournament?
Linear equations - The team can bring its 24 players
What do you mean by linear equations with one variable?
A linear equation with one variable is one that can be written as ax+b = 0, where a and b are two integers, and x is a variable. This type of problem only has one solution. For instance, the linear equation 4x+4=8 only has one variable.
We are given that,
the total money raised by the lacrosse team is given to be $2863.50
bus rented at a cost of $1087.50
meal budget per person is calculated to be $74
let us assume the number of players the team can bring to the tournament to be "x".
bus rent + (meal budget * number of players) = total money raised
= 1087.50 + (74*x) = 2863.50
= 1087.50 + 74x = 2863.50
= 74x = 2863.50 - 1087.50
= 74x = 1776
= x = 1776 ÷ 74
= x = 24
Thus the team can bring its 24 players.
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Mr. Giordano's drove 4.5 miles in 5 minutes. Mr. Baras drove 6.3 miles in 8 minutes. Who drove faster? Explain using unit rates for both teachers.
If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras
The distance traveled by Mr. Giordano = 4.5 miles
The time taken = 5 minutes
Speed = Distance / Time
Substitute the values in the equation
Speed = 4.5/5
= 0.9 miles per minutes
The distance traveled by Mr. Baras = 6.3 miles
The time taken = 8 minutes
Speed = Distance / Time
Substitute the values in the equation
Speed = 6.3/8
= 0.78 miles per minutes
Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras
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Find the values of the ratios
(red to blue) of the
perimeters and areas of the
similar figures. Write the
ratios as fractions in
simplest form.
5
8
The ratio of the perimeters is
The ratio of the areas is
Answer:
perimeter: 5/8area: 25/64Step-by-step explanation:
You want the ratios (red to blue), of perimeter and area, given that corresponding sides have the ratio red to blue = 5 to 8.
Perimeter ratioThe ratio of perimeters is the ratio of corresponding side lengths:
red to blue = 5 / 8
Area ratioThe ratio of areas is the square of the ratio of corresponding side lengths:
red to blue = (5 to 8)² = 25 / 64
__
Additional comment
Ratios are customarily expressed in any of three equivalent forms:
5 to 85:85/8 "fraction" formPLEASE HELP DUE IN 3-5 MINUTES, THANK YOU!!
Answer:
In second week there is percentage limit (-ve sign) of 20% in people traveling examine to first week.
In 0.33 week there is proportion increase of 50% in human beings traveling compare to 2nd week.
In fourth week there is share limit of 75% in humans visiting evaluate to 1/3 week.
HELP ME PLEASE!!!!! will give brainlist
Answer:
y=3x+3
Step-by-step explanation:
i use point (-1,0) and (0,3) then 3-0/0-(-1)=3/1=3 so (0,3) 3 is the y intercept plug in so y=3x+3is the equation
Answer:
See below
Step-by-step explanation:
Find two convenient points to calculate the slope:
0,3 and -1,0 slope = m = (3-0) / ( 0 - -1) = 3
and the y axis intercept = 3 (from looking at graph)
line equation is y = mx + b ( where b is the y-axis intercept)
y = 3x + 3
-9- -8x2= -209 Solve this equation by taking square roots
The value of the quadratic equation given as -9- -8x^2= -209 is 5
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to solve the quadratic equation?The quadratic equation is given as
-9- -8x^2= -209
Add 9 to all sides of the equation
So, we have
-8x^2= -200
Divide both sides of the equation by -8
x^2= 25
Take the square roots
x = 5
Hence, the solution of the equation is 5
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Melanie invests $3,000 at 12% simple interest for 1 year. How much is in the account at the end of the 1 year period?
We have the following:
We must apply the simple interest formula which is the following:
[tex]A=P\cdot(1+rt)[/tex]Where, P is the principal 3000
r is the interest rate 0.12
t is time in years
A is the total value
replacing:
[tex]\begin{gathered} A=3000\cdot(1+0.12\cdot1) \\ A=3000\cdot1.12 \\ A=3360 \end{gathered}[/tex]The answer is $3360 at the end of the 1 year period
John and Nelly are cleaning their house, Nelly takes 3 hours longer than John if she cleans alone, If they can do the cleaning together in 2 hours, how long can John clean all b yh himself
Answer: 3 hours
Let john take x hours to finish the work
Let nelly take y hours to finish the work
given, y =x+3
Portion of work done by john alone in one hour = 1/x
Portion of work done by Nelly alone in one hour = 1/y
∴Portion of work done by both john and nelly in one hour = 1/x + 1/y
[tex]= \frac{1}{x} + \frac{1}{x+3}\\=\frac{x+3+x}{x*(x+3)}\\=\frac{2x+3}{x^2+3x}[/tex]
Total time taken by John and nelly to finish the work = 2 hours
[tex]\therefore [2(2x+3)]/[x^2 + 3x] = 1\\= > 4x + 6 = x^2 + 3x\\= > x^2 -x -6 =0\\= > x^2 - 3x + 2x -6 =0\\= > x(x-3) + 2(x-3)=0\\= > (x+2)(x-3)=0[/tex]
Hence either x = -2 or x = 3
Since x is time taken, it cannot be negative, hence x = 3
∴Time taken by john to finish the work = 3 hours
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Mr. Jonas took out a loan of $12,400. The interest rate is 3% per year, and the interest is not compounded. How much amount will Mr. Jonas have to repay after 4 years?
Jonas have to repay $13888 after 4 years.
Given
Principle amount of loan (P) = $12,400
Rate of interest (R) = 3%
Time period (T) = 4 years
Also the interest is not compounded, hence it is simple interest.
The formula for simple interest is (PTR)/100
Where,
P = Principle amount
T = time period
R = rate of interest
By substituting the values in the formula we get,
Simple interest = (12400 x 4 x 3) / 100
Simple interest = 1488
Hence adding this interest to Principle sum we get
12400 + 1488 = 13888
Jonas has to repay $13888 after 4 years.
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For what values of b is the difference between the fractions [tex]\frac{2b-1}{2}[/tex] and [tex]\frac{1+5b}{4}[/tex] negative? (for 25 points) i will give you brainlyiest or smthing if u give answer
The value of b for which the difference between the fractions
(2b - 1) / 2 and (1 + 5b) / 4 negative will be;
⇒ b < -3
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
Two fractions are,
⇒ (2b - 1) / 2 and (1 + 5b) / 4
Since, The difference between the fractions (2b - 1) / 2 and (1 + 5b) / 4 negative.
So, we can formulate;
⇒ (1 + 5b) / 4 - (2b - 1) / 2 < 0
Solve for b, as;
⇒ 1 + 5b - 2 (2b - 1) < 0 x 4
⇒ 1 + 5b - 4b + 2 < 0
⇒ b + 3 < 0
Subtract 3 both side;
⇒ b + 3 - 3 < 0 - 3
⇒ b < -3
Therefore, The value of b for which the difference between the fractions (2b - 1) / 2 and (1 + 5b) / 4 negative will be;
⇒ b < -3
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is -48=48 have no solution or infinite solutions?
What is the shaded area???
Step-by-step explanation:
[tex]area \: of \: circle = \pi\:r^{2} \\ \pi \times6.5^{2} - \pi \times {2.3}^{2} = 36.96\pi = 116.113... {cm}^{2} [/tex]
Answer:
116.129 cm²
Step-by-step explanation:
Area of circle:[tex]\boxed{\bf Area \ of \ circle = \pi r^2}[/tex]
Area of outer circle:
R = 6.5 cm
Area =3.142 * 6.5 * 6.5
= 132.75 cm²
Area of inner circle:
r = 2.3 cm
Area of inner circle =3.142 * 2.3 *2.3
= 16.621 cm²
Area of shaded area = area of outer circle - area of inner circle
= 132.75 - 16.621
= 116.129 cm²
Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
After four years, the investment is worth £8934.34.
How does compound interest work?The interest you earn on interest is known as compound interest. For instance, if you start with $100 and it generates 5% interest annually, you will conclude the first year with $105 in your account. You'll have $110.25 after the second year is over.
We employ the formula approach to determine the entire amount,
A = P(1+r)^n
The amount invested, or principal(P), is £8,000.
Interest rate r is 2.8%, or 0.028.
n = 4 years have passed.
Now, immediately enter these values into the formula, A = P(1+r)n.
A = 8000 * (1 + 0.028) ^ 4
= 8000 * 1.028 ^ 4
= 8934.34
Consequently, the investment's value after four years is £8934.34.
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A committee of 3 members is selected from a club made up of junior members and senior members. What is the expected number of juniors in the committee?.
The expected number of juniors in the committee is 1.3
The question is incomplete, the complete question is given below:
A committee of 3 members is selected from a club made up of 13 juniors members and 17 senior members. What is the expected number of juniors in the committee?
The expected number of juniors in the committee is computed here as:
Juniors in the committee=13
Seniors in the committee=17
Total number of members=(13+17)=30
Fraction of juniors in total members=13/30
So expected number of juniors in the committee:
=Fraction of juniors in total members*Total number of members to be selected
=(13/30)*3
=1.3
Therefore 1.30 is the expected number of juniors in the committee
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Lana’s Linoleum Luxuries makes rectangular kitchen tiles with an area of t square inches.
The area in square inches of the tile is 9 / 4 t .
How to find the area of a rectangle?She makes rectangular kitchen tiles with an area of t square inches.
Therefore,
area of the rectangular kitchen tiles = lw
t = lw
l = t / w
w = t / l
Therefore, the tile is 3 / 4 as long and 3 times wide as her kitchen tiles.
Hence,
area of the tile = 3 / 4 t / w × 3(t / l)
area of the tile = 9 / 4 × t² / lw
where
lw = t
Hence,
area of the tile = 9 / 4 × t² / t
area of the tile = 9 / 4 × t
Therefore,
area of the tile = 9 / 4 t
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ms. Torres has a box of scraps of wood. She measures the length of each scrap of wood to the nearest half inch results are represented on the line plot below.
The length of the scraps of wood when placed side by side is 53 inches.
What is the length of the scraps of wood?A line plot is a graph that is made up of a number line and check marks above the numbers on the number line. The check marks above the number line represents the frequency of the data. For example, there are two checkmarks above 7. This means that there are two scraps of woods that measure 7 inches.
In order to determine the approximate length of the scraps of wood if they are placed side by side, add the length of each scrap of wood together.
Addition is a mathematical operation that is used to determine the sum of two or more numbers. The sign that is used to denote addition is +.
[tex]5\frac{1}{2} + 6 + (6\frac{1}{2}. 3) + (7. 2) + 8[/tex] =
[tex]5\frac{1}{2} + 6 + 19\frac{1}{2} + 14 + 8[/tex] = 53 inches
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