The gymnast would pay a total of $50 per month for his membership to the yoga studio if he attends 3 classes per month.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
The equation y = 20 + 10x represents the total amount the gymnast pays per month for his membership to the yoga studio, where:
y is the total cost per month, in dollars
x is the number of classes the gymnast attends per month
The equation has two parts:
The constant 20 represents the fixed monthly fee the gymnast pays, regardless of how many classes he attends.
The term 10x represents the additional fee the gymnast pays for each class he attends. Since the coefficient of x is 10, the gymnast pays $10 for each class he attends.
Therefore, if the gymnast attends x classes per month, his total monthly cost would be:
Total Cost = Monthly Fee + Cost per Class * Number of Classes
y = 20 + 10x
For example, if the gymnast attends 3 classes per month, his total monthly cost would be:
y = 20 + 10(3)
y = 20 + 30
y = 50
Therefore, the gymnast would pay a total of $50 per month for his membership to the yoga studio if he attends 3 classes per month.
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A student mows lawns on the weekends. It takes him 120 min to mow 4 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 30 hours to mow 12 lawns.
It will take him 9 hours to mow 12 lawns.
It will take him 6 hours to mow 12 lawns.
It will take him 3 hours to mow 12 lawns.
Answer: It will take him 6 hours
Step-by-step explanation: 4 lawns = 120 min
1 lawn = 30 min
12 lawn = 360 min = 6 hours
To mow 12 lawns, the student will spend 6 hours.
Explanation:To predict the time the student will spend mowing 12 lawns, we can use the information given in the question. The student takes 120 minutes to mow 4 lawns. We can calculate the time the student will take to mow 1 lawn by dividing 120 minutes by 4, which equals 30 minutes per lawn. Since the student has 12 lawns to mow, we multiply 30 minutes by 12 to get the total time. The student will spend 360 minutes, or 6 hours, mowing 12 lawns.
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An airline can sell no more than 155 tickets for a flight. So far 97 tickets
have been sold. Denzel made this number line to show the number of
tickets the airline is still able to sell.
Answer:
Step-by-step explanation:
Tammy must run more than 63 miles total to reach your fitness goals. She has already ran 31 miles and runs for miles per day which of the following inequalities could be used to solve for X the number of days Tammy still needs to run to reach your fitness goals.
Answer:
[tex]31+4x > 63[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
Step-by-step explanation:
She has already run 31 miles and runs 4 miles per day:
This means that after x days, the distance she will have run is:
[tex]D(x)=31+4x[/tex]
Tammy must run more than 63 miles total to reach her fitness goals.
This means that:
[tex]D(x) > 63[/tex]
[tex]31+4x > 63[/tex]
The inequality is:
[tex]31+4x > 63[/tex]
Solution:
[tex]4x > 32[/tex]
[tex]x > \dfrac{32}{4}[/tex]
[tex]x > 8[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
The height after t seconds of a projectile that is launched upward with a velocity of 64 feet per second from the top of a 45 foot building is given by. When will the projectile attain a height of 85 feet?
The projectile will attain a height of 85 feet at approximately 0.775 seconds or 3.225 seconds.
Calculating the Time to reach a certain heightGiven that
Velocity = 64 feet per second --- v
Initial height = 45 feet --- h
The height function can be represented as
h(t) = -16t² + vt + h
So, we have
h(t) = -16t² + 64t + 45
where h is the height in feet and t is the time in seconds.
To find when the projectile will attain a height of 85 feet, we need to solve the equation for t
So, we have
-16t² + 64t + 45 = 85
-16t² + 64t - 40 = 0
Using a graphing tool, we have
t = 0.775 and t = 3.225
Therefore, the projectile will attain a height of 85 feet at approximately t = 0.775 seconds or t = 3.225 seconds.
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I need to find the maximum revenue!
The revenue is maximized for a value p = 100, and the maximum revenue is:
R = 23,500
How to maximize the revenue?We know that the number of items sold for a prize p is:
-2.35p + 470
Then the revenue will be:
R = (-2.35p + 470)*p
So we need to find the value of p that maximizes that quadratic equation, we can see that the maximum will be at the vertex, then let's write:
R = -2.35p² + 470p
The vertex is at:
p = -470/(2*2.35)
p = 100
Finally, the maximum revenue is:
R = -2.35*100² + 470*100
R = 23,500
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Eight times a number, x, is one-third the sum of the number and two. Which answer represents this situation? Responses 8x=13x+2 8 x equals 1 third x plus 2 8x=13(x+2) 8 x equals 1 third open parentheses x plus 2 close parentheses 8x+13(x+2) 8 x plus 1 third open parentheses x plus 2 close parentheses 8x+13x+2
The problem can be translated into an equation as follows: 8x = (1/3)(x+2)
the answer that represents this situation is: 8x = (1/3)(x+2)
Simplifying the right side of the equation:
8x = (1/3)x + (2/3)
Multiplying both sides of the equation by 3 to eliminate the fraction:
24x = x + 2
Subtracting x from both sides of the equation:
23x = 2
Dividing both sides of the equation by 23:
x = 2/23
Therefore, the answer that represents this situation is:
8x = (1/3)(x+2)
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I need help with these 3 questions.
a. The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.
What is the statistics
b.the pressure to build to its highest point (75/264).
c. Sample statistic's value is 0.2835.
d. Estimate's standard error is 0.0255.
e. Its highest level, the 95% confidence interval, is (0.2326, 0.3344).
A subfield of mathematics called statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.
Several disciplines, including business, economics, sociology, psychology, epidemiology, and public health, employ it. Statistic uses a variety of techniques to gather and analyse data to better understand.
(A) The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.
(b) The sample statistic, given as p, is the percentage of subjects that allowed the pressure to build to its highest point (75/264).
(c) The sample statistic's value is 0.2835.
(d) The estimate's standard error is 0.0255.
(e) For the percentage of people who would permit the pressure to reach its highest level, the 95% confidence interval is (0.2326, 0.3344).
Therefore, Overall, the findings of this study indicate that a significant majority of high school pupils will tolerate pressures up to 300 mmHg without ever complaining about the discomfort. The range of values inside the 95% confidence.
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What’s the value of a?
What is the area, in square inches, of the shaded part of the rectangle below?
72 points <3
Answer:
Step-by-step explanation:
16 × 19 = 304
1/2(19×9)=85.5
304-85.5= 218.5
The width of a rectangle measures (5v2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P = 2(11v + 5w) cm.
Explain about the perimeter of the rectangle?The perimeter of a rectangle is the length measured around the edge of the rectangle. Although a rectangle has two dimensions, its perimeter only has one and is expressed in linear distances like feet or meters.
The perimeter calculation can be used, for instance, to calculate that many ft of brick border are required overall if somehow the rectangle depicts a garden which needs a brick border.
The sum of the lengths of a rectangle's four sides is known as its perimeter.
Rectangle perimeter = 2L + 2W.
Length = (6v+7w)
width = (5v - 2w)
P = 2 (length + width)
P = 2(6v+7w + 5v - 2w)
On simplifying:
P = 2(11v + 5w)
Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P = 2(11v + 5w) cm.
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Compete question:
The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
If f(x) = -4x + 4, what is f(x) when x = 3?
f(3) = what is it
Answer:
-8
Step-by-step explanation:
f(3) = -4(3) + 4 = -12 + 4 = -8
Answer:
f(x) = -8Step-by-step explanation:
[tex]\boxed{\sf f(x) = -4x + 4 \;\: when \;\; x=3}[/tex]
For f(x) -4x+4 substitute x with 3:-
[tex]\sf f\left(3\right)\:=\:-4(3)\:+\:4[/tex]
[tex]\sf f\left(3\right)\:=\:-4\times 3\:+\:4[/tex]
[tex]\sf f(3)=-12+4[/tex]
[tex]\sf f(3)=-8[/tex]
Therefore, f(x) = -8.
______________________
Hope this helps!
1. Given the function f(x)=x^2+1, copy and complete the following table
A circle is shown. 2 radii with length 8 inches are drawn. A line connects the radii points on the circle to form a triangle. The angle between the 2 radii is 90 degrees. The area between the triangle and the outline of the circle is shaded.
What is the area of the shaded portion of the circle?
(16π – 32) in2
(16π – 8) in2
(64π – 32) in2
(64π – 8) in
The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.
What is a CircIe?A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.
The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and Area οf the TriangIe.
Area οf an Arc =(θ /360) × π r²
Area = (90/360) × π × (8)²
Area οf the arc = 16 π in²
Area οf the triangIe = (1/2) × base × height
Area οf the triangIe = (1/2) × 8 × 8 = 32 in²
Area οf the shaded pοrtiοn = (16 π -32) inch²
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Eric has 4 pounds of blueberries to make into pies. How many pies can Eric make if each pie needs the given amount of blueberries?
82. Write an expression that represents the number that
(a) is 7 more than X;
(d) exceeds X by 7;
(b) is 7 less than X;
(e) is X less than 7;
(c) is X more than 7
(f) exceeds 7 by X
Answer:
dont understand 14+14=π
Name the minor arc and find it’s measure. Then name the major arc and find it’s measure.
The minor arc in the given diagram as required to be determined is; arc TU and it's measure is; 116°.
The major arc in the given diagram as required to be determined is; arc TVU and it's measure is; 244°.
What are the measures of the minor and major arcs in the diagram?It follows from the task content that the minor and major arcs are to be named and their measures determined as required.
The minor arc in a circle is usually subtended by an angle less than 180° while the major arc is subtended by an angle greater than 180°.
Ultimately, the minor arc is; arc TU and it's measure is; 116° while the major arc is; arc TVU and it's measure is; 244°.
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A
,
B
and
C
form a triangle where
∠
B
A
C
=
90
∘
.
A
B
=
14.7
mm and
B
C
=
25.9
mm.
Find the length of
A
C
, giving your answer rounded to 1 decimal place.
To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle. the length of AC is approximately [tex]29.8 mm[/tex].
What is the square of the length of the hypotenuse?the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can use AC as the hypotenuse, so:
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]AC^2 = (14.7 mm)^2 + (25.9 mm)^2[/tex]
[tex]AC^2 = 216.09 mm^2 + 671.61 mm^2[/tex]
[tex]AC^2 = 887.7 mm^2[/tex]
Taking the square root of both sides, we get:
[tex]AC = \sqrt887.7 mm[/tex]
[tex]AC \approx 29.8 mm[/tex] (rounded to 1 decimal place)
Therefore, the length of AC is approximately [tex]29.8 mm[/tex].
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Help please, view attachment below
Which graph represents the function over the interval [−3, 3]?
f(x)=⌈x⌉−3
The correct graph is Option D - the bottom left graph.
What is the explanation for the above?Given function is f(x)=ceil(x+1)
To plot graph of f(x) in interval of(-3,3) :
ceil(x+1) is ceiling function
The output of ceil(x) is least integer greater than x
for example ceil(5.5)=6
For an interval of (-3,-2):
Take x=(-2.4)
x+1=(-1.4)
y=f(x)=ceil(x+1)=(-1)
Similarly,
For an interval of (-2,-1):
Take x=(-1.4)
x+1=(-0.4)
y=f(x)=ceil(x+1)=(0)
For an interval of (-1,0)
y=f(x)=1
For an interval of (0,1)
y=f(x)=2
For an interval of (1,2)
y=f(x)=3
For an interval of (2,3)
y=f(x)=4
Thus, The correct graph is the bottom left graph.
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The temperature in Chicago was 7 degrees Celsius. It was dropping at a steady rate of 3 degrees per hour. How many hours did it take for the temperature to drop below -5 degrees Celsius?
Write an inequality that represents the situation.
Answer:
-3x+7 < -5
Step-by-step explanation:
Lets set x as the number of hours since the time it was 7 degrees.
This means that the expression 7-3x would represent the temperature after x hours.
To find the inequality that represents when it would be below -5 degrees, we just set this less than -5:
-5 > 7-3x.
If you want, you can also rearrange this to -3x+7 < -5.
Answer:
4 hours
Step-by-step explanation:
Inequality:
[tex]7-3x < -5[/tex]
[tex]7-7-3x < -5-7[/tex]
[tex]-3x < -12[/tex]
[tex]\frac{-3x}{-3} < \frac{-12}{-3}[/tex]
[tex]x > 4[/tex]
Hope this helps
In the circle below, suppose and . Find the following.
The missing values in the figure are solved to be
angle KLI = 111
angle LIJ = 129 degrees
How to find the missing anglesThe missing angles are solved using the inscribed angle theorem and the knowledge of cyclic quadrilateral
arc KLI = 138 degrees = 2 * angle KJI (inscribed angle theorem)
angle KJI = 138 / 2
angle KJI = 69 degrees
angle KLI + angle KJI = 180 degrees (cyclic quadrilateral property)
where angle KJI = 69
angle KLI = 180 - 69
angle KLI = 111 degrees
angle LIJ + angle LKJ = 180 degrees (cyclic quadrilateral property)
angle LKJ = 51 degrees (given)
angle LIJ = 180 - 51
angle LIJ = 129 degrees
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the recipe for ellie fruit drink included 1 1/4 quarts of cranberry juice 2 2/3 quarts of apple juice and 5/8 of a quart of lemonade. The recipe makes enough for 4 people. Ellie needs to make enough fruit drink for 20 people . How much of each ingredient does she need?
Answer:
25/4 quarts of cranberry juice
40/3 quarts of apple juice
25/8 quarts of lemonade
Step-by-step explanation:
just multiply everything by 5
:)
Find the extract value of x
Answer:
25 + 5√29
Step-by-step explanation:
(I added a photo below)
First, let's find BC using the Pythagorean theorem (from ∆BCD):
[tex] {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725[/tex]
[tex]725 > 0[/tex]
[tex]bc = \sqrt{725} =5 \sqrt{29} [/tex]
Then we see, that AB = 25 + x
So, now we can find AC:
[tex] {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 [/tex]
Now we have a quadratic equation:
[tex] {x}^{2} - 50x - 100 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} [/tex]
This is a negative number and we cannot use it, since x has to be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} [/tex]
A salesman gets paid an annual salary of $35,000 plus he makes $75 for each sale. If this salesman made $46,700, how many sales did he make?
Answer: 156
Step-by-step explanation:
Annual Salary = $35, 000
Subtract anual salary from 46, 700. ---> 46,700-35,000= 11,700
One sale = $75
To find out how many sales, divide the remaining 11,700 by 75.
11,700/75= 156
156 sales.
can you solve this question?
f'(7)=?
instantaneous rate of change=?
(a) f'(7) = 9. The derivative of the function f(x) evaluated at x=7, is 9.
(b) The instantaneous rate of change of y with respect to x at x = 7 is 9.
What is the derivative of the function?
Given that the tangent line to the graph of y = f(x) at point (7, 56) has the equation y = 9x - 7, we can use the slope-intercept form of the equation of a line to find the slope of the tangent line.
The slope of the tangent line is 9. This is also equal to the derivative of the function f(x) evaluated at x=7, which gives us the answer to part (a).
The instantaneous rate of change of y with respect to x at x = 7 is also given by the derivative of the function at x=7. Therefore, the answer to part (b) is also f'(7) = 9.
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Rajan baut a book for Rs 180 and sold it to sajan at a profit of 20%. Sajan sold that book to nirajan at a lost 20%. At what price nirajan should sell the book to receive 5% profit ?
Solution,
CP for rajan=180 rs
Sp for rajan=(20%+1)×180
=216
Cp for niranjan=216
And, Sp=.8×216
=172.8
Cp for niranjan=172.8
For 5% profit,
Sp for Niranjan=(5%+1)×172.8
=181.44
Hence, for Niranjan to gain 5% profit, he must sell it for 181.44 rs
Answer - 181.44
Explanation - For Rajan,
Cost Price = Rs 180
Profit Percent = 20%
Profit Percent = (S.P - C.P/C.P)*100
20 = (S.P - 180/180) *100
S.P = Rs 216
For Sajan,
C.P = Rs 216
Loss Percent= 20%
Loss = (C.P - S.P/C.P)*100
20 = (216-S.P/216)*100
S.P = Rs 172.8
For Niranjan to Sell Book and get 5% profit,
C.P = Rs 172.8
Profit Percent = (S.P - C.P/C.P)*100
5 = (S.P-172.8/172.8)*100
S.P = 181.44
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
[tex]y=\frac{1}{2} x+2[/tex]
[tex]y=(x-h)^2+k[/tex]
[tex]y=(x+3)^2-2=x^2+6x+7[/tex]
The drop down options are “greater than”, “less than”, and “equal to”
The length of FG is equal to the length of F'G'.
The perimeter of pentagon CDEFG is equal to the perimeter of pentagon C'D'E'F'G.
What are the properties of a translated shape?The properties of a translated shape are the shape and size of the translated shape are the same as that of the original shape. The orientation of the translated shape is the same as that of the original shape. The distance between the corresponding points of the translated shape and the original shape is constant.
The area and perimeter of the translated shape are the same as that of the original shape. The interior angles of the translated shape are the same as that of the original shape. The coordinates of the vertices of the translated shape are obtained by adding a constant value to the corresponding coordinates of the vertices of the original shape.
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Image transcribed:
Pentagon CDEFG is translated 7 units up and 5 units left, resulting in pentagon C'D'E'F'G' (not shown).
Part A
Select from the drop-down menu to correctly complete this sentence:
The length of FG is ___ the length of F'G'.
Part B
The perimeter of pentagon CDEFG is ____ the perimeter of pentagon C'D'EF'G.
. Sam is 8 ft man and the length of his shadow is 10 feet. Find the height of the building casting a shadow of 200 feet. (Draw a diagram , and label, set up a proportions and solve)
The height of the building is 160 ft
Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
Types of proportion :
Direct Proportion
Inverse Proportion
Continued Proportion
Comparing the heights and shadows using ratio proportions
Sam Height = 8 ft
Sam Shadow = 10 ft
Building Height = x ft
Building Shadow = 200 ft
Sam Height/Sam Shadow = Building Height/Building Shadow
AB/BC = PQ/QR
8/10 = x/200
8*200 = 10*x
1600/10 = x
x = 160 ft
The height of the building is 160 ft
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Find the shaded area
Answer:
21.5 m^2
Step-by-step explanation:
Area of circle A = πr^2 = 3.14(10/2)^2 = 78.5
Area of square A = 10^2 = 100
Area of shaded area: 100 - 78.5 = 21.5 m^2
A contestant on a game show has a 1 in 6 chance of winning for each try at a certain game. Which probability models can be used to simulate the contestant’s chances of winning??
Select ALL of the models that can be used to simulate this event.
A) a fair six-sided number cube
B) a fair coin
C) a spinner with 7 equal sections
D) a spinner with 6 equal sections.
E) a bag of 12 black chips and 60 red chips.
The probability models that represents a probability of winning of 1/6 are given as follows:
A) a fair six-sided number cube.
D) a spinner with 6 equal sections.
E) a bag of 12 black chips and 60 red chips.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
For this problem, we want a probability of 1/6 of winning each trial, hence the events are given as follows:
A) a fair six-sided number cube. -> One out of the six numbers is equivalent to winning.
D) a spinner with 6 equal sections. -> One out of the six regions is equivalent to winning.
E) a bag of 12 black chips and 60 red chips. -> 12/(12 + 60) = 12/72 = 1/6.
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