Answer:
The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.
Step-by-step explanation:
Given:
A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.
The sales tax on each rental is 16%.
The group has $2,500 available to spend on ski and snowboard rentals.
If the ratio of pairs of skis to snowboards is 7:3.
Now, to find the greatest number of pairs of skis and snowboards rentals.
So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]
And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]
So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:
[tex]318.50 + 330 = 648.50.[/tex]
Now, to get the rental amount after sales tax:
648.50 + 16% of $648.50.
[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]
[tex]=648.50+103.76[/tex]
[tex]=\$752.26.[/tex]
The total rental amount after sales tax = $752.26.
As the group has available $2,500.
So, the sets according to the given ratio:
[tex]2500\div 752.26 = 3.32.[/tex]
[tex]=3\ sets.[/tex]
Thus, there are 3 sets of the ratio 7:3.
So, the rental price according to sets are:
The rent of Skis:
[tex]7\times 3 = 21[/tex]
[tex]21\times 45.50= 955.50[/tex]
The rent of snowboards:
[tex]3\times 3 = 9[/tex]
[tex]9\times 110 = 990[/tex]
So. the total rental amount of skis and snowboards according to sets are:
[tex]955.50 + 990 = 1,945.50[/tex]
Now, the amount of rent after sales tax:
$1945.50 + 16% of $1945.50.
[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]
[tex]=1945.50+311.28=\$2256.78.[/tex]
Thus, the total cost = $2256.78.
Now, to get the greatest number of pairs of skis to snowboards that can be rent:
[tex]2,500 - 2,256.78 = 243.22[/tex]
The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.
Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.
Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.
(8,-3) and (8,4)
Linear functions
Answer:
[tex]\displaystyle x = 8[/tex]
Step-by-step explanation:
Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.
I am joyous to assist you anytime.
Solve both equations.
Equation 1:
Answer:
x = 1.22
Step-by-step explanation:
[tex]\frac{5x-1}{8} -\frac{5-7x}{2} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{2(5x-1) - 8(5-7x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(10x-2) - (40-56x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(10x-2-40+56x)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(66x-42)}{16} = \frac{3(6-x)}{6}[/tex]
[tex]\frac{(66x-42)}{16} = \frac{(18-3x)}{6}[/tex]
[tex](66x-42) \times 6 = (18-3x) \times 16[/tex]
[tex](396x-252) = (288-48x)[/tex]
[tex](396x +48x) = (288+252)[/tex]
[tex]444x = (540)[/tex]
[tex]x = \frac{540}{444}[/tex]
x = 1.22
Equation 2:
Answer:
x = -13.97
Step-by-step explanation:
[tex]\frac{x}{3} - \frac{7(x-2)}{9} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-3(7(x-2))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-3(7x-14))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-(21x-42))}{27} = 4- \frac{2x-5}{6}[/tex]
[tex]\frac{9x-(21x-42)}{27} = \frac{24 - (2x-5)}{6}[/tex]
[tex]\frac{-12x+42}{27} = \frac{-2x+29}{6}[/tex]
[tex](-12x+42) \times 6 = (-2x+29) \times 27[/tex]
[tex](-72x+252) = (-34x+783) [/tex]
[tex](252-783) = (-34x +72x) [/tex]
[tex](-531) = (38x) [/tex]
[tex]x =\frac {-531}{38}[/tex]
x = -13.97
How long did the sound take(in seconds) from the rocket motors at Time=0 to reach the people 500 meters away.
The speed of sound in early mornomg temperatures is 339.5 meters per second.
Sound will generally obey the basic equation of distance=rate×time
Answer:
It takes approximately 1.5 seconds to reach the people 500 metres away
Step-by-step explanation:
Since ; distance=rate×time
time= distance/ rate
Distance= 500 metres ,rate= 339.5 m/s
Time= 500/339.5
Time= 1.5 seconds
10. What is the distance between (8,7) and (3,-5)?
Answer:
distance between points=13 units
Step-by-step explanation:
distance between points=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
put [tex](x_1,x_2)[/tex]=(8,7) and [tex](y_1,y_2)[/tex]=(3,-5)
distance between points=[tex]\sqrt{(3-8)^2+(-5-7)^2}[/tex]
distance between points=[tex]\sqrt{(-5)^2+(-12)^2}[/tex]
distance between points=[tex]\sqrt{25+144}[/tex]
distance between points=[tex]\sqrt{169}[/tex]
distance between points=13 units answer
find the x- intercept and y- intercept from the following linear equation
-9x+4y+=36
please help ????
Answer:
x intercept- (-4,0) y intercept- (0, 9)
Step-by-step explanation:
Subsitute 0 for x to get y = 9. That is your y intercept. Subsitute 0 for y and get -4 for your x intercept
What decimal is bigger 0.33 or 0.34
To determine which decimal is bigger between 0.33 and 0.34, we compare the digits after the decimal point. Since the hundredths place in 0.34 is 4 and in 0.33 is 3, 0.34 is the larger decimal.
Explanation:The question is asking to compare two decimals to determine which is larger. To compare 0.33 and 0.34, you look at the digits from left to right. Both numbers have a 0 before the decimal point, so you compare the digits after the decimal point. First, you compare the tenths place, the digit immediately after the decimal point. In both numbers, this digit is 3, so they are equal up to this point. Next, you look at the hundredths place, the next digit to the right. In 0.33, the digit is 3, while in 0.34, the digit is 4. Because 4 is greater than 3, 0.34 is the larger decimal.
Final answer:
0.34 is larger than 0.33 because the digit in the hundredths place is greater for 0.34.
Explanation:
When comparing two decimals, 0.33 and 0.34, we can determine which is larger by examining the digits from left to right. Here, both numbers have 0 before the decimal point and a '3' in the tenths place, but they differ in the hundredths place. Since 4 is greater than 3, the decimal 0.34 is larger than 0.33. To compare 0.33 and 0.34, we can look at the digits to the right of the decimal point. In this case, 0.34 has a larger digit than 0.33, so it is bigger.
find the diamter of a circle if its area is 706.9mm²
Answer:
30 mmStep-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have
[tex]A=706.9\ mm^2[/tex]
Substitute:
[tex]\pi r^2=706.9[/tex] divide both sides by π
[tex]r^2=\dfrac{706.9}{\pi}[/tex] use π ≈ 3.14
[tex]r^2\approx\dfrac{706.9}{3.14}\\\\r^2\approx225\to r=\sqrt{225}\\\\r= 15\ mm[/tex]
The diameter d = 2r.
Therefore
[tex]d=2(15)=30\ mm[/tex]
Answer:
30mm
Step-by-step explanation:
A=[tex]\pi[/tex][tex]r^{2}[/tex]
Substitute 706.9 for A and [tex]\pi[/tex] for 3.14
706.9= 3.14[tex]r^{2}[/tex] divided both sides by 706.9
when you divided 3.14 by 3.14 it will cross and when you divide 706.9 by 3.14 it will give you 225.
[tex]\sqrt{225}[/tex]
15 times 15 is 225
radius= 15
d=2r
multiply 15 by 2
the answer is 30.
The temperature falls from 0 degrees to Negative 12 and one-fourth degrees in 3 and one-half hours. Which expression finds the change in temperature per hour? HURRY I ONLY HAVE 20 MIN PLEASE PLEASEEEEEEE
Answer:
-3.5 degrees per hour
[tex] - 3.5t[/tex]
Step-by-step explanation:
The total change is temperature is -12.25 degrees.
The total time is 3.5 hours.
This means that temperature changes by -3.5 degrees per hour (-12.25 degrees ÷ 3.5 hours).
As an expression of hours, simple multiply the coefficient by a variable. I'm assuming the letter t for time (where t is the number of hours):
[tex] - 3.5t[/tex]
7. Destiny made 47 out of 70 free throws in her basketball season. What percent of free
throws did she make a Round io the nearest tenth of a percent.
Help please!!!
Answer:
72.3%
Step-by-step explanation:
hey guys
im new here
please solve this for me with steps!
ill mark as the best answer
Answer:
The factors of [tex]2(x+y)^2-9(x+y)-5[/tex] is ((x+y)-5)(2x+2y+1)
Step-by-step explanation:
Given polynomial
=>[tex]2(x+y)^2-9(x+y)-5[/tex]
To Find:
The factors of the polynomial =?
Solution:
Lets assume k = (x+y)
Then [tex]2(x+y)^2-9(x+y)-5[/tex] can be written as [tex]2k^2-9k-5[/tex]
Now by using quadratic formula
k =[tex]\frac{-b\pm\sqrt{(b^2-4ac}}{2a}[/tex]
where
a= 2
b= -9
c= -5
Substituting the values, we get
k =[tex]\frac{-b\pm\sqrt{(b^2-4ac)}}{2a}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{((-9)^2-4(2)(-5)}}{2(2))}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{(81+40)}}{4}[/tex]
k =[tex]\frac{-(-9) \pm \sqrt{(121)}}{4}[/tex]
k =[tex]\frac{-(-9) \pm 11}}{4}[/tex]
k= [tex]\frac{ 9 \pm 11}{4}[/tex]
k = [tex]\frac{20}{4}[/tex] k = [tex]\frac{-2}{4}[/tex]
[tex]k_1 =5[/tex] [tex]k_2 = -\frac{1}{2}[/tex]
[tex]2k^2-9k-5= 2(k-5)(k+\frac{1}{2})[/tex]
Solving the RHS we get
[tex]\frac{2}{2}(k-5)(2k+1)[/tex]
[tex](k-5)(2k+1)[/tex]
Substituting k = x+y
[tex]((x+y)-5)(2(x+y+1)[/tex]
[tex]((x+y)-5)(2x+2y+1)[/tex]
PLEASE PLEASE HELP ME PLEASE I AM SO DUM I DONT KNOW THE ANSWER PLEASE JUST HELP ME
Scientists studied two animal populations. Function f(x) = 830(0.8)x models a bear population in a given region x years after the study began. The table models the cougar population in the same region.Use the table of data to interpret a linear function.
In the year the study began, how many more bears than cougars were in the given region?
Answer:
Cougar population was 790 at the beginning
830-790=40
There are 14 boys and 12 girls in Mateo's homework class. Which ratio correctly describes the students in the class?
A) The ratio of boys to girls is 7:6
B) The ratio of girls to boys is 6:8
C) The ratio of boys to all students is 14:28
D) The ratio of girls to all students is 6:7
Answer:A should be the best answer to this problem
Step-by-step explanation:
Answer:
The ratio of boys to girls is 7:6
Step-by-step explanation:
1/2 of 14 is 7. So the boys would be equal to 7. 1/2 of 12 is 6.
So the girls would be equal to 6. If you put that in a ratio it would be 7(boys):6(girls) = 7:6
Therefore your answer is A: The ratio of boys to girls is 7:6
Hope this helped! Please mark Brainliest! :)
The function f(x) = 37x + 20 models the total cost for Rachel to be a member at a gym for x months. What can be interpreted from the y-intercept of the function?
A Rachel must pay $37 per month to use the gym.
B. Rachel must pay $20 per month to use the gym
C. Rachel must pay a $37 membership fee to join the gym.
D. Rachel must pay a $20 membership fee to join the gym.
" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function ⇒ D
Step-by-step explanation:
The form of the linear function is f(x) = mx + b, where
m is the slope (rate of change) of the functionb is the y-intercept (initial amount) of the function∵ f(x) = 37 x + 20 models the total cost for Rachel to be a member
at a gym for x months
∵ f(x) = m x + b
∴ m = 37 and b = 20
∵ m represents the rate of change
- That means she must to pay 37 per month for x months
∴ Rachel must pay $37 per month to use the gym
∵ b represents the initial amount
- That means she pays a fixed amount one time
∴ Rachel must pay a $20 membership fee to join the gym
" Rachel must pay a $20 membership fee to join the gym " can be interpreted from the y-intercept of the function
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Solve for y 9x - y = -6x + 4y
Answer:
y = 3x
Step-by-step explanation:
Given
9x - y = - 6x + 4y ( subtract 4y from both sides )
9x - 5y = - 6x ( subtract 9x from both sides )
- 5y = - 15x ( divide both sides by - 5 )
y = 3x
is y=2/7x proportional?
In the equation y=2/7x, y is directly proportional to x.
To determine if the equation y = (2/7)x represents a proportional relationship, you can check if it fits the criteria for proportionality. In a proportional relationship, the ratio between y and x should remain constant. This means that if you double x, y should also double, and so on.
In the equation y = (2/7)x, the coefficient 2/7 is a constant, and it is the same for all values of x.
Therefore, this equation represents a proportional relationship.
In this case, if you double the value of x, the value of y will also double, and if you triple x, y will also become three times its original value, and so on. This is a key characteristic of a proportional relationship.
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What is the measure of angle A?
Each member of the school chess team receives a chess set and clock. The total cost of these items for 5 members is $125. Jenna knows that a chess set costs $10, but she does not know how much a clock costs. She sets up the equation below to solve for the cost of a clock, represented in her equation by x.
The question deals with setting up and solving an equation to find the cost of a clock, when the total cost for a chess set and clock is given. The cost of a clock is found to be $15.
Explanation:The subject of this question is Mathematics, specifically dealing with setting up and solving an equation. The total cost of the chess set and clock for each member is $125/5 = $25. Jenna knows that the chess set costs $10. So, the cost of a clock would be $25 - $10 = $15. Therefore, the cost of a clock is $15.
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Circles!! Need help
Answer:
[tex]x_{123} x^{2} \sqrt{x} \neq \sqrt{x} \sqrt{x} \geq \neq \pi \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] x^{2} \pi[/tex]
Step-by-step explanation:
because im smart
Answer:
see explanation
Step-by-step explanation:
The measure of arc AE is
AE = 360° - (100 + 40 + 60)° = 360° - 200° = 160°
∠ BCD = 0.5( m arc AE - m arc BD ), that is
x = 0.5(160 - 40) = 0.5 × 120 = 60
i need answersssss y<-2x+4
The expression (x−3)(x+3)(3x) represents the volume of a rectangular prism, where x−3 is the width, x+3 is the length, and 3x is the height.
The value of x is tripled. Which statement must be true about the new prism?
A
The volume is tripled.
B
The width is tripled.
C
The length is tripled.
D
The height is tripled
Answer:
width = (x-1)
Step-by-step explanation:
The volume of the prisms is defined in the problem as
Volume = x^3 + 9x^2 + 6x − 16
Volume = width*height* length
And we know that,
length = (x+2)
height = (x+8)
We can find the roots of the equation, which happen to be
x = -8
x = -2
x = 1
(See image below)
This means that the volume can be represented as
Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)
Therefore,
The width = (x-1)
Step-by-step explanation:
If you awnser please iclude work
Answer:
B and D
Step-by-step explanation:
The graph of a proportional relationship is a straight line graph which must pass through the origin.
The only straight line graphs which pass through the origin are B and D
Identify the given item as probability distribution, continuous random variable, or discrete random variable. The number of oranges purchased in a grocery store.
Answer:
Discrete random variable
Step-by-step explanation:
We are given the following in the question:
x is the number of number of oranges purchased in a grocery store.
Thus, it have the following properties.
The number of oranges can always be counted and not measured.They will always have a finite value.They will have discrete values.They cannot take any value within an interval.Thus, it is a discrete random variable
What is another way to write 101 - 13.7x = 73.6
Answer:
x=2
Step-by-step explanation:
101-13.7x=73.6
13.7x=101-73.6
13.7x=27.4
x=27.4/13.7
x=2
Answer:
Step-by-step explanation:
well....there's a few
101 - 13.7x = 73.6
can be written like :
101 - 73.6 = 13.7x
or
- 13.7x = - 101 + 73.6
or
27.4 = 13.7x
or
27.4 / 13.7 = x
Is that what you mean ?
Help me to prove the given below. Thank you in advance
Answer:
Construct MO, where O is the midpoint of CG. (As shown in the attached figure)
(1) LM = MG //given, CM is the median to the hypotenuse
(2) CO = OG // construction
(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment
(4) MO // LC //triangle mid-segment theorem
(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)
(6) m∠LCO=90° //given, ΔLCG is a right triangle
(7) m∠MOG=90° //(5), (6), definition of congruent angles
(8) m∠MOC=180° – 90° = 90° // linear pair
(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles
(10) MO=MO //common side, reflexive property of equality
(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate
(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)
(13) MG= ½LG // Given, CM is the median to the hypotenuse
(15) MC = ½LG //(12) , (13), substitution
a 168 cm tall barrel has a circumference of 69.08 cm. what is the volume of the barrel using the formula for the volume of a cylinder as an estimate. round to the nearest hundredth of a cubic centimeter
Answer:
[tex]V=63,829.92\ cm^3[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=69.08\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]69.08=2(3.14)r[/tex]
solve for r
[tex]69.08=6.28r[/tex]
[tex]r=69.08/6.28[/tex]
[tex]r=11\ cm[/tex]
step 2
Find the volume of the cylinder
we know that
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]h=168\ cm[/tex]
[tex]r=11\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]V=(3.14)(11)^{2}(168)[/tex]
[tex]V=63,829.92\ cm^3[/tex]
A parabola has its vertex at (2, 1) and crosses the x-axis at (1,0) anu al l
the equations below has this parabola for its graph? (TEKS A2.4B-R)
ui...
Ay=1-(x - 2)^2
C y = -1 - (x + 2)^2
Dy= -1 - (x - 2)^2
B
y = 1 + (x + 2)^2
Answer:
A
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (2, 1), thus
y = a(x - 2)² + 1
To find a substitute (1, 0) into the equation
0 = a(1 - 2)² + 1
0 = a + 1 ( subtract 1 from both sides )
a = - 1
Hence
y = - (x - 2)² + 1 or
y = 1 - (x - 2)² → A
The equation of the parabola with its vertex at (2, 1) and that crosses the x-axis at (1, 0) is y=1-(x - 2)^2.
Explanation:The vertex form of a parabola's equation is y=a(x-h)^2+k where (h, k) is the vertex. Here, the vertex is given as (2, 1). Also, it crosses the x-axis at (1,0), which makes it a downward-facing parabola(as y=0 when x=1), and hence, 'a' is negative. Now, we can compare the given options with these details.
Option A: y=1-(x - 2)^2 perfectly matches our requirements, because it's in the correct vertex form, and 'a' is negative (-1) which corresponds to a downward parabola.
So, the equation of the parabola with its vertex at (2,1) and that crosses the x-axis at (1,0) is y=1-(x - 2)^2.
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A local college offers scholarships to students who graduate in the top 1% of their high school classes according to GPA. If a high school has 400 students graduating one year , how many students from that high school would be eligible for these scholarships.
Answer:
4 students would be eligible for the scholarships
Step-by-step explanation:
Final answer:
In a high school with 400 graduating students, only 4 students would be eligible for scholarships that are offered to students in the top 1% of their class by GPA.
Explanation:
To determine how many students from a high school with 400 graduating students would be eligible for scholarships offered to those in the top 1% of their class, we simply need to calculate 1% of 400. Mathematically, this is represented as:
400 students * 1% = 400 students * 0.01 = 4 students
Therefore, in a high school graduating class of 400 students, only 4 students would be eligible for these scholarships based on being in the top 1% of their class according to GPA.
Choose the point-slope form of the line passing through (3.5) with a slope of -3.
O y– 3 = -3 (x – 5)
o =3(y – 5) = 2-3
O y - 5 = -3 (2-3)
o 30 – 5y = -3
Answer:
y-5=-3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-3(x-3)
Which of the following is equivalent to i^33?
Answer:
i
Step-by-step explanation:
(10 points) Using this graph, how can I graph y=x
Answer:
You would graph a point at the origin with a slope of 1
Step-by-step explanation:
Y=x means whatever the y value is, the x is the same.
Answer:
1
Step-by-step explanation:
The equation for graphing is y=mx+b and if it’s y=x then it means y=1x because when x is left alone it equals to 1