Answer:
Their will be 2 coins in allThere were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.
Let x be the number of 50-cent coins in the bag,
And y be the number of 20-cent coins.
From the problem,
we know that y = x - 5,
Since there were 5 fewer 20-cent coins than 50-cent coins.
We can also set up an equation for the total value of the coins in the bag,
⇒ 0.5x + 0.2y = 24.20
Now we can substitute y = x - 5 into the equation,
⇒ 0.5x + 0.2(x - 5) = 24.20
Simplifying, we get,
⇒ 0.7x - 1 = 24.20
⇒ 0.7x = 25.20
⇒ x = 36
So there were 36 50-cent coins in the bag.
Using y = x - 5,
We can find that there were 31 20-cent coins.
Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).
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S 2. Let f(x) = x - k√x
a. Find a value of k such that the function has a critical point at x = 25.
b. Is the above critical point a local maximum, local minimum or neither? Show calculus to support your answer.
a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative
[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]
so that
[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]
b. Taking the second derivative, we get
[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]
At x = 25, the second derivative has a positive sign,
[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]
which means f(x) is concave upward around x = 25, so this critical point is a local minimum.
Find the area of a regular polygon with 5 sides that has a side length of 6 inches and an apothem of 9 inches.
Area = [?]in2
Answer:
see the attachment photo!
Answer: The correct answer is 135 in².
Step-by-step explanation: An area of a polygon is this:
Area = (number of sides × length of one side × apothem)/2
(5 x 6 x 9) / 2 = 135
The ________________ measures the spread of the middle 50% of the data set.
A. median
B. range
C. interquartile range
D. mode
Answer:
C. interquartile range
Step-by-step explanation:
using this to show im right
"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."
Hope This Helped
Evaluate the expression.
A family plan for a cell phone has a monthly base price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) (in $) of a family for x additional family members added is C(x)=
The linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
How to get the linear equation?
Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.
Then if there are x family members added, the cost will be:
$75 + $10.99*x
Then the linear equation that models the cost for having x additional family members added is:
c(x) = $75 + $10.99*x
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find the slope of the lined graph
Answer:
1
Step-by-step explanation:
The points go rise:1 up:1 so the slope is 1.
Answer:
hey!! we can taIk here
Step-by-step explanation:
Work out the length of
x.
Give your answer rounded to 3 significant figures.
The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The right-angle triangle is given below.
The given triangle is an isosceles right triangle.
P = B = x
Then we have
1.8² = x² + x²
2x² = 3.24
x² = 1.62
x = 1.27 cm
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What is The converse of p→q
Answer:
q→p
Step-by-step explanation:
The converse of p→q is q→p.
which means If q ,then p.
A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.
Answer:
33,75 clients(huh?)
Step-by-step explanation:
75 / 100 = 0,75(1% of all clients)
0,75 * 45 = 33,75(number of business clients)
15 ( y - 4 ) - 2 (y - 9 ) + 5 (y + 6) = 0
Answer:
y = 2/3
Step-by-step explanation:
Assuming you are looking for "y":
15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0
15y - 60 - 2y + 18 + 5y + 30 = 0
15y - 2y + 5y -60 + 18 + 30 = 0
18y = 60 - 18 - 30
18y = 12
y = 12/18
y = 2/3
What is the volume, in cubic meters of the prism below?
Answer:
1848 Cubic Meters
Step-by-step explanation:
The volume should be (7*24*22)/2
This is because this object is bascally half of a rectangular prism, so we need to divide the whole product by 2 at the end.
7*24*22 = 3696
3696/2 = 1848
HELPP PLEASE!!!
Harry is 5 years older than his sister, and the product of their
ages is 84.
Let h represent Harry's age, then h- 5 represents his
sister's age, and h (h-5) = 84 models the situation.
The equation can also be written as h² - 5h = 84.
Rewrite the equation so that it is in the form polynomial = 0.
Enter the polynomial, in standard form, in the box.
= 0
Answer:
See below
Step-by-step explanation:
h^2 - 5h = 84
h^2 - 5h - 84 = 0
help me solve this please help I will gave u brilliant answer
Answer: 1.) 3 2/3 2.) 2 9/10 3.) 9 11/15 4.) 7 11/12
B. Question 2,
My answer is reasonable, because if we round 1 7/10 to 2 and 1 1/5 to 1
2+1=3 and my answer is 2 9/10. This estimate makes sense because 2 9/10 can be rouned to 3, meaning it is reasonable.
Step-by-step explanation:
1 1/6 + 2 3/6= 3 4/6
Simplifyed=3 2/3
1 7/10 + 1 2/10 = 2 9/10
7 5/15 + 2 6/15= 9 11/15
4 8/12 + 3 3/12= 7 11/12
Jennifer serves the volleyball to Marsha with an upward velocity of 10.5 ft/s. The ball is 5 feet above the ground when she strikes it. How long does Marsha have to
react, before the volleyball hits the ground? Round your answer to two decimal
Answer:
0.98 seconds
Step-by-step explanation:
We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.
__
motion equationThe general form of the equation of height for ballistic motion is ...
[tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]
The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.
For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...
h(t) = -16t² +10.5t +5
__
reaction timeMarsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...
a = -16b = 10.5c = 5The solution is ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]
The positive solution is ...
t ≈ 0.976327 ≈ 0.98
Marsha has about 0.98 seconds to react before the volleyball hits the ground.
_____
Additional comment
After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.
a. The velocity, v, of an object is moving in a medium at time t is given by
t = √ 30² +50+2 du. Evaluate t.
+
The value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
Velocity of the object moving in the medium
The velocity of the object moving in the medium is given as;
t = ∫(3u² + 5u + 2)du
the value of t is obtained by integrating the function as follows;
t = (3u³)/3 + (5u²)/2 + 2u
t = u³ + 2.5u² + 2u
Thus, the value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
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hey can someone help me on this"in your own words describe when you should use area and when you should use volume in calculating the amount of space an object occupies.
Answer:
Normally,in calculating the amount of space an object occupies...the volume method is require due to 3 dimensional rule,vice versa an area
mohjjbn bn hjbjn hjbnm
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?
22,500 = 2 p
2 (22,500) = p
22,500 = 2 p minus 8
2 (22,500) = p minus 8
An equation is formed of two equal expressions. The correct option is A.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Therefore, the equation shows p, the price in dollars that she paid for her previous car,
Price of new car = 2 (Price of the previous car)
22,500 = 2p
Hence, the correct option is A.
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Answer: a
Step-by-step explanation:
1. Solve the quadratic function by graphing. x²-3x - 18 - 0
Answer:
that's easy all you have to do is find out what is the value of x then divided by 2 once you divide by 2 subtract 3x 18 and 0
A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets. There were more student tickets sold than adult tickets. How many adult tickets were sold?
A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets is mathematically given as
How many adult tickets were sold?Generally, the equation for a sold tickets is mathematically given as
S=x+72
Therefore
x+x+72=772
2x+72=772
2x=772-72
x=350
In conclusion, tickets sold was
x=350
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Find the measure of the remote exterior angle. m/x (198-5n)
m2y = (5n+37)
m²z = (n+7)
The measure of the remote exterior angle is 128°.
How to calculate the angle?From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)
198 - 5n = 6n + 44
Collect like terms
154 = 6n + 5n
154 = 11n
n = 154/11
n = 14
The value of angle x will be:
= 198 - 5n
= 198 - 5(14)
= 198 - 70
= 128
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AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC
Answer:
60°
Step-by-step explanation:
Arc BC and Angle BWC are the same number of degrees.
When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.
Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.
180° - 120° is 60°
Angle BWC is 60° so Arc BC is 60°
A bowl contains 28 black, 21 red, 23 blue, and 10 green balls
A ball is drawn at random. P (blue).
Answer:
P (blue) = 23 / 82
Step-by-step explanation:
There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls
or,
23 / 82
So, the probability of a blue ball being chosen is 23/82
(or a 28% chance [rounded])
At her sisters birthday party Cheyenne thought it would be funny to drink lemonade from a party hat if the radius is 4.8 cm and the height of a hat is 12 cm how many cubic centimeters of lemonade can Cheyenne pour into the hat
92.16 pi cm^3.
Step-by-step explanation:
Shape of a party hat : conical
Volume of a cone = (1/3)(pi)(r^2)(h)
(pi(1/3)(23.04)(12))cm^3
Therefore, approximately
92.16 pi cm^3.
Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.
What’s the result of adding these two equations? Please help
Answer:
u should subract those not add
Write an expression to describe the
situation.
A car travels 50 miles per hour, h. What expression
represents the total distance you've traveled?
Answer:
m = 50h, where m is the distance traveled in miles
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $3,128 was collected on the sale of 1,336 tickets. How many of each type of ticket were sold?
Answer:
Adults = 448
Students = 888
Step-by-step explanation:
Write equations with info given
A = Adult tickets
S = Student tickets
5A+1S=3,128
A+S=1336
Subtract equations from each other
4A=1792
Solve for A
A=448
Plug A into second equitation
448+S=1336
Solve for S
S=888
jackson bought 3 pounds of candy for $9.60.
What was the price of this candy in cents per pound ?
PLS HELP ITS DU IN 5 MIN !!!!!!!!!!!!!!!!!!!!!!
Answer:
320 cents per pound
Step-by-step explanation:
so we do 9.60 divided by 3, which is 3.20. So, 3.20 for each pound. Now we need in cents. 3 dollars is 300 cents, plus another 20, so 320 cents. I hope this helped.
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
The solution to the given system of equation is (4, 4)
Factorizing quadratic functionsFrom the solved steps, the final quadratic functions is given as;
x^2 - 8x + 16 = 0
Factorize to have;
x^2 - 4x - 4x + 16 = 0
x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0
x = 4 and 4
Hence the solution to the given system of equation is (4, 4)
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