at maximum. dt/dh=0
if you differentiate you will get
-32t=-100
t=3.125
The Castel del Monte in Apulia, Italy, was built more than 750 years ago. The fortress has one central building with eight surrounding towers. Which polygon do you see repeated in the structure? How many sides, angles, and verticles does this polygon have?
Answer:
Polygon: Octagon
Sides: 8
Angles: 8
Vertices: 8
Total interior angle: 1080
Step-by-step explanation:
8 sides so it's an octagonal figure,
8 sides, 8 vertices and 8 angles
Total angle:
(8 - 2)×180
1080
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function
f(g) =
.
Answer:
The correct result would be f(g) = g * $1 - $50.
Step-by-step explanation:
If you would like to find the function that gives the profit Betty makes by selling a number of glasses of lemonade, you can find this using the following steps:
p ... profit
g ... glasses of lemonade
f(g) = p = g * $1 - $50
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Jessica gets her favorite shade of purple by mixing 1/3 cup of blue with 1/2 of red. How many of blue and red paint does Jessica need to make 20 cups of her favorite purple paint?
Answer:
8 cup of blue
12 cup of red
Step-by-step explanation:
The first thing is to calculate how much black paint is produced, assuming that the volumes add up, we have to:
1/2 + 1/3 = 5/6
5/6 cup of paint is produced, I want to know how much I need to produce 20 cups, I divide the value I want by the ideal value, that is, 5/6 and thus I obtain the factor that I require:
20 / (5/6) = 24
Now I multiply by 24 each quantity of blue and red paint
1/2 * 24 = 12
1/3 * 24 = 8
Which means you need 12 cups of red paint and 8 cups of blue paint
can somebody explain how to do this ?
Answer:
-6
Step-by-step explanation:
12(5+2y) = 4y - (6-9y)
60+24y = 4y-6+9y
24y + 60 = 13y - 6
24y-13y = -6-60
11y = -66
y = -6
Answer:
[tex]y=-6[/tex] is the correct answer.
Step-by-step explanation:
The steps involved in solving an algebraic equation in one variable are as stated as:
Step 1: If necessary, simplify the expressions on each side of the equation. This would involve things like removing parentheses, adding like terms, removing fractions.
To remove fractions: Since fractions are another way to write division, and the inverse of divide is to multiply, you remove the fractions by multiplying both sides by the "Least Common Divisor" of all your fractions.
Step 2: Use Addition / Subtraction properties to move the variable term to one side and all other terms to the other side.
Step 3: Use Multiplication / Division properties to remove any values that in front of the variable.
Step 4: Check your answer.
Step-by-Step Solution:
[tex]12\left(5+2y\right)=4y-\left(6-9y\right)\\\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\\\\mathrm{Expand\:}12\left(5+2y\right)\:\:=\:\: 60+24y\\\\\mathrm{Expand\:}4y-\left(6-9y\right)\:\:=\:\: 13y-6\\\\60+24y=13y-6\\\\\mathrm{Subtract\:}60\mathrm{\:from\:both\:sides}\\\\60+24y-60=13y-6-60\\\\24y=13y-66\\\\\mathrm{Subtract\:}13y\mathrm{\:from\:both\:sides}\\\\24y-13y=13y-66-13y\\\\11y=-66\\\\\mathrm{Divide\:both\:sides\:by\:}11\\\\\frac{11y}{11}=\frac{-66}{11}\\\\y=-6[/tex]
Andrea was chosen to participate in a game show. At the end of the
first round, she had a score of -250. At the end of the second round,
she had a score of 600. How many points did Andrea score during the
second round?
its 350 because you -250 + 650 = 350
-4x - 2 = -22
WILL MARK THE BRAINIEST
Answer:
x = 5
Step-by-step explanation:
-4x - 2 = -22
-4x = -22 + 2
-4x = -20
x = -20 / -4
x = 20 / 4
x = 5
Answer:
x = 5
Step-by-step explanation:
-4x - 2 = -22
add 2 to both of the sides
-4x -2 + 2 = -22 + 2
solve it
-4x = -20
then divide
-4x/4
-20/-4 = 5
x = 5
Sorry if my explanation was bad
A scale factor of 2 is used to enlarge a figure as shown below. A rectangle with an area of 18 inches squared. How many square inches is the area of the enlarged figure? 27 36 54 72
Answer:
36
Step-by-step explanation: All you have to do is multipy the area of the original figure by the scale factor. (18 times 2) which is 36.
You're welcome <3
Answer:
Its D.72
Step-by-step explanation:
A truck can be rented from company A for $80 a day plus $0.60 per mile. Company B charges 30$ a day plus $0.80 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Company A a better deal than Comoany B's?
For company A to have a better deal, the truck must be driven more than __ miles per day.
Answer:
More than 250 miles
Step-by-step explanation:
Rental cost of company A is $80 + $0.6 per mile driven and company B also has a rental cost of $30 + $0.8 per mile driven.
To find the moment when company A rental cost matches that of company B,we have to create an equation that is ideal for both parties.
80 +0.6x = 30 + 0.8x
Where x is the number of miles traveled by both trucks.
Simplifying the above equation, we have
0.2x = 50 divide both sides by 0.2
= 250 miles is when both rental cost matches .
Therefore, the number of miles needed to be driven so as the rental cost of company A to better company B should be more than 250 miles
To determine when renting a truck from Company A becomes cheaper than Company B, we set the cost equations for both companies equal and solve for the number of miles. In this case, Company A becomes the better deal when the truck is driven more than 250 miles in a day.
Explanation:The cost of renting a truck from each company can be defined using linear equations: Company A's cost as $80+0.60x = y$ and Company B's cost as $30+0.80x = y$, where 'x' is the number of miles driven and 'y' is the total cost. To find out when Company A's cost is less than Company B's, we set the equations equal to each other and solve for 'x': $80+0.60x = $30+0.80x$. Simplifying this equation gives, $x = ((80-30)/(0.80-0.60))$, thus 'x' = 250. Therefore, for company A to be a better deal, the truck must be driven more than 250 miles in a day.
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The students in Brenna's grade voted to select a guest speaker. 15 students voted for a
famous athlete. The other 45 students in Brenna's grade voted for a famous actor. What
percentage of the students voted for the athlete?
Write your answer using a percent sign (%)
Final answer:
To find the percent of students who voted for the athlete, divide the number of students who voted for the athlete by the total number of students, and then multiply by 100. This results in 25% of the students voting for the athlete.
Explanation:
To calculate the percentage of students who voted for the athlete, you would use the formula: part over total, times one hundred, equals percent. In this case, the part is the number of students who voted for the athlete (15), and the total is the combined number of students who voted for the athlete and actor (15 + 45).
So, the calculation would be as follows: (15 / (15 + 45)) x 100 = (15 / 60) x 100 = 0.25 x 100 = 25%. Therefore, 25% of the students voted for the athlete.
9x - 13 = 23
what does x =
Answer:
4
Step-by-step explanation:
Im not quite sure how to explain this without a picture. But its the thing where you do the opposite to each side to find the value of X.
Hope this helps!
Answer:
x = 4
Step-by-step explanation:
9x - 13 = 23
+13 +13
9x 36
_ = _
9 9
x=4
Write an equation in standard form of the line that is
graphed. Then find the x- and y-intercepts.
The equation of the line in standard form is
1.) 4x - 5y = -1
2.) 4x - 5y = 9
3.) 5x - 4y = 9
4.) 5x - 4y = -1
The x-intercept is
1.) -9/5
2.) -5/4
3.) 1/5
4.) 9/4
The y-intercept is
1.) -9/5
2.) -5/4
3.) 1/5
4.) 9/4
Answer: equation= 4x-5y= 9
x intercept= 9/4
y intercept= -9/5
Step-by-step explanation: It was right on E2020
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take points (1, -1) and (-4, -5)
so, slope of line
= -5 + 1 / (-4 -1)
= -4 /(-5)
= 4/5
So, the equation of line is
y+ 1= 4/5 ( x- 1)
y + 1 = 4/5x -4/5
y= 4/5x - 4/5 - 1
y= 4/5x - 9/5
4x - 5y = 9
So, the x- intercept is 9/4 and y- intercept is -9/5.
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Four equivalent forms of a quadratic function are given. Which form displays the zeros of function h?
A.) h(x) = -4(x2 − 4)
B.) h(x) = -4x2 + 16
C.) h(x) = -4(x − 2)(x + 2)
D.) h(x) = -2(2x2 − 8)
The Answer is : C.) h(x) = -4(x − 2)(x + 2)
Final answer:
The quadratic function in form C displays the zeros of the function directly by being in factored form, showing x = 2 and x = -2 as the zeros.
Explanation:
Form C. h(x) = -4(x - 2)(x + 2) displays the zeros of function h because it is in factored form, making it easy to identify the zeros directly as x = 2 and x = -2.
By setting h(x) = 0 in form C, the solution can be seen as:
-4(x - 2)(x + 2) = 0
x = 2, x = -2
Therefore, form C, h(x) = -4(x - 2)(x + 2), directly shows the zeros of the function h to be x = 2 and x = -2.
I need help, how many chirps per minute?? and why?
A metal cube has sides of length 4.5 cm, correct to the nearest 0.5 cm.
The cube is melted down and the metal is used to make small spheres.
Each sphere has a radius of 3 mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal.
828 small spheres can be made from the metal.
Step-by-step explanation:
Side of the cube = 4.5cm
Volume = (a x a x a)
= (4.5 x 4.5 x 4.5)
= 91.125 cubic cm
Radius of the sphere = 3mm = 0.3 cm
Volume of 1 sphere = (4/3) π(r x r x r)
= (4/3) (3.14) (0.3 x 0.3 x 0.3)
= (4/3) (3.14) (0.027)
= 0.34/3
= 0.11 cubic cm
No. of spheres = 91.125/0.11
= 828.4
So, 828 small spheres can be made from the metal.
whats 7/12 of a full rotation?
Pls mark Brainliest.
Answer:
210°
Step-by-step explanation:
360° is a full rotation. 'Of' also represents a multiplication sign in some places. It basically means that 7/12 of a full rotation is the same as 7/12 * 360° which is equal to 210°.
The equivalent of 7/12 of a full rotation (360°) is; 210°.
According to the question;
The equivalent of 7/12 of a full rotation is to be the determined.We must however remember that a full rotation is given as the angle at a point;
In essence, a full rotation in degrees is 360°.
Consequently;
7/12 of a full rotation = (7/12) × 360°= 7 × 30= 210°Read more:
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10
20
30
40
50
60
Which of the following statements is not true?
The range of the two sets is the same.
The difference between the median of each set is 40.
Set B has a higher mean than set A
The mode of set A is 50 less than the mode of set B.
What is the Awnser
Answer:
The range of the two sets are the same
Step-by-step explanation:
1200$ invested at a rate of 3.5% compounded quarterly; 4 years
Step-by-step explanation:
1st year:
(1200 x 3.5 x 1) ÷ 100 = $42
2nd year:
(1242 x 3.5 x 1) ÷ 100= $43.47
3rd year:
(1285.47 x 3.5 x 1) ÷ 100= $44.99≈ $45
4th year:
(1330.47 x 3.5 x 1) ÷ 100= $46.56
Compound interest:
$(42 + 43.47 + 45 + 46.56)
=$ 177.03
Valerie mixes 5 parts liquid fertilizer for every 9 parts water to make fertilizer for her garden. How many quarts of water and fertilizer does she need to make 20 quarts solution?
Answer:
7.14 Quarts of Liquid Fertilizer and
12.86 Quarts of Water
Step-by-step explanation:
Parts of Liquid Fertilizer Needed=5
Parts of Water Needed=9
Total=9+5=14
Therefore:
Proportion of Liquid Fertilizer Needed=5/14
Proportion of Water Needed=9/14
If she wants to make 20 Quarts of solution
Quarts of Liquid Fertilizer Needed=(5/14)*20=7.14 Quarts
Quarts of Water Needed=(9/14)*20=12.86 Quarts
In the survey of 891 US adults who follow baseball in a recent year, 184 said that the Boston red sox would win the world series. Construct a 90% confidence interval for the population proportion of US adults who follow baseball who in a recent year said the Boston red sox would win the world series
Answer:
90% confidence interval for the population proportion of US adults who follow baseball
( 0.1842 , 0.22880)
Step-by-step explanation:
Explanation:-
Given data the survey of 891 US adults who follow baseball in a recent year, 184 said that the Boston red sox would win the world series.
The sample proportion [tex]'p' = \frac{184}{891} = 0.20650[/tex]
q = 1-p = 1- 0.20650 =0.79350
Confidence intervals
90% confidence interval for the population proportion of US adults who follow baseball
[tex](p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p + Z_{\alpha } \sqrt{\frac{pq}{n} } )[/tex]
The tabulated value Z₀.₉₀ = 1.645
[tex](0.20650-1.645\sqrt{\frac{0.20650X0.7935}{891} } , 0.20650 + 1.645\sqrt{\frac{0.20650X0.7935}{891} } )[/tex]
(0.20650 - 0.02230 , 0.20650+0.02230)
( 0.1842 , 0.22880)
Conclusion:-
90% confidence interval for the population proportion of US adults who follow baseball
( 0.1842 , 0.22880)
if angle y measures 65 degrees how much does x measure?
Answer:
supplementary angles add up to 180°
given y=65° thus...
x+y=180°
x + 65°=180°
x=180°- 65°
x=115°
Answer:
x = 115°
Step-by-step explanation:
x ; y = suplementary =>
=> x + y = 180° } => x = 180° - 65° = 115°
y = 65°
4.
Find the domain of the following function:
y = x3 − 8
_________
x2 + 9
Select the appropriate response:
A) 483xy
B) domain: all values of y
C) all values of x
D) Not possible to solve
Answer:
C) all values of x
Step-by-step explanation:
The denominator has no real roots which means it's not 0 for any x. Hence x can take any real value
Answer:
C
Step-by-step explanation:
All values of x
I hope this is what you need
Robin and Evelyn are playing a target game. The object
of the game is to get an object as close to the center as
possible. Each player's score is the number of
centimeters away from the center. Robin's mean is 107,
and Evelyn's mean is 138. Compare the means. Explain
what this comparison indicates in the context of the data.
Who is winning the game? Why?
S
Answer:
Robin's mean score is lower than Evelyn's mean score. This means Robin is winning as you need to minimise your score in order to be as close to the target as possible.
Evelyn because she has a better mean then robins
Evelyn has the greater mean. It indicates that, on average, her objects landed farther away from the center than Robin’s. This difference means that Robin is winning the game.
i hope it helps :)
The composite figure is made up of a rectangle and two pentagons. Find the
area
O
A. 332 sq. units
B. 290 sq. units
O
C. 200 sq units
D. 552 sq units
Given:
A composite figure made up of a rectangle and two pentagons.
To find:
The area of the composite shape.
Solution:
If a pentagon has a side length of s and an apothem of a, the area of the pentagon is given by
[tex]A=\frac{5}{2} (a)(s).[/tex]
In the given diagram, the pentagons have side lengths of 8 units and an apothem of 5.5 units.
The area of a pentagon [tex]= \frac{5}{2} (5.5)(8) = 110[/tex] sq units.
The area of 2 such pentagons [tex]= 2(110)= 220[/tex] square units.
The rectangle has a length of 14 units and a width of 8 units.
The area of a rectangle [tex]= (l)(w).[/tex]
The area of the rectangle [tex]= (14)(8)=112[/tex] square units.
The area of the composite shape is the sum of the individual areas of the different shapes.
The area of the composite shape [tex]=220+112=332[/tex] sq units.
The area of the composite shape is option A. 332 sq units.
Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter .fn. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional?
Answer:
0.3678
Step-by-step explanation:
Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it?
Given that the total number of thousands of miles(X) that an auto can be driven
before it would need to be junked is an exponential random variable with parameter 1/20.
=> X ≅ Exponential(λ= 1/20)
=> f(x) = 1/20 * e^(-x/20) , 0 < x < ∞
=> F(X) = P{X < x} = 1 - e^(-x/20)
The probability that she would get at least 20,000 additional miles out of it.
P{X > 20} = 1-P{X < 20}
P{X > 20} = 1-(1 - e^(-20/20))
= e^(-1)
= 0.3678
Simplify the ratio.
25: 40 : 15 =
Answer:
1
— = 0.04167
24
Step-by-step explanation:
Step 1 :
5
Simplify —
8
Equation at the end of step 1 :
5
— ÷ 15
8
Step 2 :
5
Divide — by 15
8
Final Answer:
1
__ = 0.04167
24
Ana ha comprado libros, todos del mismo precio, por valor de 120 euros. El librero le regala 3 libros por lo que cada libro le cuesta 2 euros menos. ¿Cuántos libros ha comprado?
Answer:
El primer paso será darle un nombre a nuestras variables:
x= Numero de libros comprados inicialmente
y=Precio inicial de los libros
Ahora analizamos el enunciado,
Lorena ha comprado libros todos del mismo precio por valor de 120 €
x*y=120 € (1)
El librero le regala 3 libros por lo que en realidad cada libro que cuesta 2 € menos
(x+3)(y-2)=120€ (2)
Tenemos entonces dos ecuaciones con dos incógnitas, así que podemos resolver,
Despejamos en (1)
x=120/y
Sustituimos en (2)
(120/y +3)(y-2)=120
120 - 240/y + 3y -6 =120
3y-240/y =120-120+6
3y -240/y =6
y- 80/y=6
y²-80=6y
y²-6y-80=0
Resolvemos la ecuación de segundo grado
a=1
b=-6
c=-80
Aplicando la resolvente,
(6+- √36+320)/2
6+-√356/2
(6+-18,86)/2
Como el valor de y no puede ser negativo la unica respuesta válida será:
y=12,43
Cada libro le costo 12,43€
Sustituyendo en (1)
x=120/12,43
x=9,65 como no puede ser un número racional
x=9
Lorena ha comprado 9 libros
Ana originally bought 12 books.
Explanation:Let's say Ana originally bought x books, each costing p euros.
The total cost of all the books is 120 euros, so we can write the equation:
x * p = 120
After the bookseller gives Ana 3 free books, the new total number of books she has is x + 3 and each book costs p - 2 euros.
The new total cost of all the books is still 120 euros, so we can write the equation:
(x + 3) * (p - 2) = 120
Simplifying this equation, we get:
px + 3p - 2x - 6 = 120
Combining like terms:
px - 2x + 3p - 6 = 120
Substituting the equation px = 120, we get:
120 - 2x + 3p - 6 = 120
Simplifying further:
3p - 2x - 6 = 0
Let's rewrite this equation:
3p - 2x = 6
When we substitute the equation px = 120 into this equation:
3p - 2(120/p) = 6
Simplifying:
3p - 240/p = 6
Multiplying through by p:
3p^2 - 240 = 6p
Rearranging:
3p^2 - 6p - 240 = 0
Using the quadratic formula to solve for p:
p = (-(-6) ± sqrt((-6)^2 - 4*3*(-240)))/2*3
p = (6 ± sqrt(36 + 2880))/6
p = (6 ± sqrt(2916))/6
p = (6 ± 54)/6
For the positive value of p:
p = (6 + 54)/6 = 60/6 = 10
Now, substituting p = 10 back into the equation px = 120:
10x = 120
x = 120/10 = 12
So, Ana originally bought 12 books.
An _____
to a circle is a line, ray or segment in the plane of the circle that intersects
the circle in exactly one point.
Answer:
Tangent
Step-by-step explanation:
A TANGENT to a circle is a line, ray or segment in the plane of the circle that intersect the circle in exactly one point.
An tangent to a circle is a line, ray or segment in the plane of the circle that intersects the circle in exactly one point.
A circle is defined as a plane figure bounded by a single curved line, with every point on that line being equally distant from the center point. Tangents have a unique property where they touch the circle at precisely one point and are perpendicular to the radius drawn to the point of contact. This concept is fundamental to understanding circles and their geometric properties.
Find the input of the relation when the output is y= -1.
6x-3y = -15
X= ?
Answer:
2
Step-by-step explanation:
Jon ate too many holiday cookies and gained 2.2, point, 2 kilograms in December. Then he went on a diet and lost 1.5, point, 5 kilograms in January. Then he lost another 3.7, point, 7 kilograms in February. Jon wants to know what the total change in his weight was over these three months.
Which of the following equations matches the situation above?
Choose 1 answer:
(Choice A)
2.2+(-1.5)+(-3.7) =
(Choice B)
2.2+1.5-3.7 =
(Choice C)
None of the above
Answer:
-2.9 kg. (loss)
Step-by-step explanation:
Total change in weight = 2.3 - 1.5 - 3.7
Total change in weight = -2.9 kg.
Step-by-step explanation:
The correct equation that represents the total change in Jon's weight over the three months is (Choice A) 2.2 + (-1.55) + (-3.77), which equals a total weight loss of 3.12 kilograms.
The total change in Jon's weight over the three months can be determined by adding his weight gain and subtracting his weight loss for each month. In December, Jon gained 2.2 kilograms, represented as "+2.2". Then he went on a diet and lost 1.55 kilograms in January, represented as "-1.55" and lost another 3.77 kilograms in February, represented as "-3.77".
The correct equation that matches this situation is (Choice A) 2.2 + (-1.55) + (-3.77). This equation takes into account the weight gain and losses, with losses represented by negative numbers. When we perform the calculation, we get:
2.2 - 1.55 - 3.77 = -3.12 kilograms
This means that Jon's total change in weight over the three months is a loss of 3.12 kilograms.
Consider a school with two classes, A and B. In class A there are 15 girls and 17 boys. In class B, there are 19 girls and 10 boys. Both classes plan extracurricular activities for which each class forms a committee consisting of three students. How many possible committees are there such that the total of committee members of both classes combined consists of 4 girls
Answer: 7700 committee
Step-by-step explanation:
Given that In class A there are 15 girls and 17 boys. And In class B, there are 19 girls and 10 boys
To find possible committees of 3 such that the total of committee members of both classes combined consists of 4 girls, we will use combination technique
(15C2 × 17C1) + (19C2 × 10C1)
Or
(15C1× 17C2) + (19C3 ×10C0)
Or
(15C3 × 17C0) + (19C1 × 10C2)
Note that "or" means addition
(1785 + 1710) + (2040 + 855) + (455 + 855)
= 3495 + 2895 + 1310
= 7700 committee