Answer:
x > -2
Step-by-step explanation:
-4x < 8
-8 < 4x
-2 < x
x > -2
Original price: $35
Percent of discount:
Sale price: $31.50
Answer:
ok i agree
Step-by-step explanation:
A rectangular aquarium is 1.5 ft wide, 6ft long, and 2 ft tall. If 1 ft^3 = 7.5 gallons, how much water can the aquarium hold?
Answer:
The aquarium is 1.5 * 6 * 2 = 18 cubic feet
Water measures 7.5 gallons per cubic foot, then the aquarium can hold
(7.5 * 18) = 135 gallons
**************************
By the way, there are 7.48052 gallons per cubic foot to be EXTREMELY accurate.
Step-by-step explanation:
work out the circumference of this circle take pie to be 3.142and give your number to 1 decimal place and the radius is 11.2cm
The required circumference of circle up to 1 decimal place is 70.4.
Radius = 11.2 cm
π = 3.142
The circumference of the circle is to be determined.
The circumference of object is its boundary measure.
Here, Circumference of circle = [tex]2\pi r[/tex]
= 2 x 3.142 x 11.2
= 70.4
Thus, the required circumference up to 1 decimal place is 70.4.
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Identify the conic that is formed by the intersection of the plane described and the double-napped cone.
The plane intersects one nappe and is parallel to n.
What is the conic section formed?
A. ellipse
B. hyperbola
C. parabola
Answer:
B
Step-by-step explanation:
because a hyperbola is a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. and if you view the picture its the same thing
Answer:
c
Step-by-step explanation:
The plane only intersects one cone and is parallel to n.
So it has to be a parabola.
A diameter of a circle has endpoints.
A) center: (-3, 2)
B) radius: √65
C) equation: (x +3)² +(y -2)² = 65
Betsy has $468 in a personal bank account, and then withdraws $9 per week. Carlos has $18 in a personal bank account, and then deposits $66 earned from yard work each week. After how many weeks will they have the same amount of money in the bank?
Answer: 9 weeks
Step-by-step explanation:
First, we would have to set up an equation.
468 - 9w = 18 + 66w
The variable w stands for weeks.
We need to figure out when their bank account will become equal.
So, we need to solve for w.
First, let’s combine like terms. I will move 9w to the other side.
468 = 18 + 66w + 9w
Then simplify:
464 = 18 + 55w
Then, do the same as you did before, just move the 18 to the other side. Keep in mind that when a number switches sides, it’s switches signs (from negative to positive or positive to negative)
464 + 18 = 55w
482 = 55w
To isolate the variable, you would have to divided 55w by 55. Keep in mind, what you do to one side of an equation you must do to the other.
482/55 = 55w/55
8.76 = w
When you round to the nearest whole number, it will be 9 weeks.
Therefore, it will take 9 weeks for them to have the same amount of money in the bank.
The unknown length can be found using the Pythagorean theorem.
The theorem states that the of the squares of the legs is the square of the hypotenuse.
The missing length is feet.
Answer:
he theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.
The missing length is 35 feet.
Step-by-step explanation:
i just did it
Answer: 1:sum 2:equal to 3:35
Step-by-step explanation:
I did the assignment on edge and got it right.
Evaluate the function f(x) = 4^x for x = 3.
A. 12
B. 24
C. 32
D. 64
Answer:
D 64
Step-by-step explanation:
f(x) = 4^x
Let x = 3.
f(3) = 4^3
= 4*4*4
= 64
George’s parents are saving for his college fund. They put $5,000 into an interest bearing account with a compound interest rate of 5.5%. George’s parents want to determine what the balance of his college fund account will be after 15 years. Using the formula A = P (1 + r) Superscript t, which is the correct substitution for the formula?
Answer:
see below
Step-by-step explanation:
A = P (1 + r) ^t
A is the amount in the account
P is the principle or the amount invested
r is the interest rate
t is the time
A = 5000 (1 + .055)^15
5000(2.23247)
Rounding to 2 decimals since we round to the nearest penny
11162.38
Answer: A
Step-by-step explanation:
XD
If you are good at figuring out sequences in math please help! Rewarding more points
Answer:
-1,048,572
Step-by-step explanation:
Please mark brainliest :)
A large rectangular area is to be fenced off ( a large rectangle divided into 2 smaller rectangles). The fence used to divide the space cost $10 per foot and the fence used for the perimeter costs$15 per foot. If the total budget for the project is $60000 what are the dimensions that yield the largest area
Answer:
Length of area is 857.14 ft
Width of area is 857.14 ft
Length of dividing fence is 857.14 ft
Step-by-step explanation:
Here we have
Area of rectangle = Length × Width
The dimension, of the rectangle with the largest area is the dimension of a square, hence we have;
Length of rectangle = Width of rectangle = x
Hence, the perimeter of the area = 4·x, while the width of the dividing fence = x
Therefore, since the we have;
Cost of the perimeter fence = $15/foot
Cost of the dividing fence = $10/foot
Then;
4·x × 15 + x × 10 = 60000
60·x + 10·x = 60000
x = 60000/70 = 857.14 ft
Which gives the following dimensions;
Length of area = 857.14 ft
Width of area = 857.14 ft
Length of dividing fence = 857.14 ft.
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
-5
-3
-2
-1
1
2
3
O
4
5
+
+
4
-3
-2
-1
0
1
2
4
5
+
w+ W0
+
at at at
+
fr
-3
-2
-1
o
1
2
3
4
5
+
-3
-2
-1
ó
1
2 3
4
5
Answer:
3 < x
Step-by-step explanation:
3(8 - 4x) < 6(x - 5)?
Distribute
24 -12x< 6x -30
Add 12x to each side
24-12x+12x < 6x+12x-30
24 < 18x-30
Add 30 to each side
24+30 < 18x-30+30
54 < 18x
Divide each side by 18
54/18 < 18x/18
3 < x
Seven students worked together on a project. How many ways can their teacher choose four to present the project?
The teacher can choose four students to present the project out of seven in 35 different ways. This is calculated using the combination formula in combinatorics, a concept in mathematics.
Explanation:The question involves the concept of combinatorics in mathematics, specifically the combination formula. The combination formula is used when the order of selection does not matter. In this case, the teacher is selecting 4 students out of 7 to present the project, and the order in which the students are chosen is irrelevant.
To calculate the number of ways the teacher can choose four students out of seven, we use the combination formula which is C(n, r) = n! / [(n-r)!r!], where:
n = total number of items r = number of items to choose C(n, r) = combinations of n items taken r at a time n! = n factorial = n*(n-1)*(n-2)*...*3*2*1 (n-r)!r! = (n-r) factorial times r factorial
Applying this to our scenario, n = 7 (total number of students), and r = 4 (students to be chosen to present). Plugging the values into the formula gives us C(7, 4) = 7! / [(7-4)!4!] = 35. So, there are 35 ways the teacher can choose four students to present the project.
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The teacher can choose 4 students to present the project in 35 ways.
Explanation:The teacher needs to choose 4 students out of a group of 7 to present the project.
To find the number of ways to choose 4 students from a group of 7, we use the combination formula.
The formula for combinations is C(n, r) = n! / (r! * (n-r)!), where
n is the total number of students and
r is the number of students to be chosen.
Substituting n = 7 and r = 4 into the formula, we get
C(7, 4) = 7! / (4! * (7-4)!) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1 * 3 * 2 * 1) = 35.
Therefore, there are 35 ways for the teacher to choose 4 students to present the project.
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A bag contains 2 red marbles, 3green marbles, and 4 blue marbles. If we choose a marble, then another marble without putting the first one back in the bag, what is the probability that the first marble will be green and the second will be red?
Answer:
6/81
there are 9 marbles and 3 are green so 3/9 and 2 are red so2/9 then times to get 6/81
Alice makes a batch of cookies for her mom’s
birthday. She adds 2 3/4
cups of fl our and
1 1/2
cups of sugar to a bowl. How many cups of
dry ingredients does Alice add to the bowl?
identify the x and y for y=5x
y = 5x
and x = y/5
you can then put any value for x and y and it will make sense
I need help bad only with the first 2
Answer:
C =75.36 m
A =452.16 m^2
Step-by-step explanation:
The circumference is found by where r is the radius and pi = 3.14
C = 2 * pi *r
C = 2 * 3.14 * 12
C =75.36 m
The area is found by
A = pi r^2
A = 3.14 * 12^2
A =452.16 m^2
Answer:
Circumference: 12.56 m
Area: 452.16 m²
Step-by-step explanation:
Circumference:
2 × 3.14 × 12
12.56 m
Area:
3.14 × 12²
452.16 m²
The bases of a right prism are parallelograms with length of one of its sides a=8.5 cm and the length of the altitude to that side is ha = 4 cm. Find the volume of the prism, if its height is h=14 cm.
Answer:
The volume of the prism is 476 cm^3
Step-by-step explanation:
Mathematically, the volume of a right prism can be calculated using the formula area of the base * height of the prism
Here, the base is a parallelogram and thus, the area of the base can be calculated using the formula A = bh where b is the parallelogram base and h is the height
in the question the parallelogram has a base of 8.5cm with the height at that point as 4cm
The area of that parallelogram is thus 4 * 8.5 = 34 cm^2
the volume of the right pyramid is thus 34 * 14 = 476 cm^3
What two numbers multiply to 60, but add to -16?
Answer:
-6 and -10.
Step-by-step explanation:
Added together you get -16, multiplied together results in 60.
The value of two numbers gives multiplied by 60, but added to -16 are - 10 and - 6.
Given that,
The multiplication of two numbers is 60
And, the addition of two numbers is - 16.
Let us assume that the two numbers are x and y.
Hence we get;
[tex]x y = 60[/tex] ... (i)
And, [tex]x + y = - 16[/tex] .. (ii)
From equation (ii);
[tex]y = - 16 - x[/tex]
Substitute the above values in (i);
[tex]x (- 16 - x) = 60[/tex]
[tex]- 16x - x^2 = 60[/tex]
[tex]x^2 + 16x + 60 = 0[/tex]
[tex]x^2 + (10 + 6)x + 60 = 0[/tex]
[tex]x^2 + 10x + 6x + 60 = 0[/tex]
[tex]x(x + 10) + 6 (x + 10) = 0[/tex]
[tex](x + 10) (x + 6) =0[/tex]
This gives two solutions,
[tex]x = - 10[/tex]
[tex]x = - 6[/tex]
Substitute x = - 10 in (ii);
[tex]x + y = - 16[/tex]
[tex]- 10 + y = - 16\\y = - 16 + 10\\y = - 6[/tex]
Substitute x = - 6 in (ii);
[tex]x + y = - 16[/tex]
[tex]-6 + y = - 16\\y = - 16 + 6\\y = - 10[/tex]
Therefore, both the numbers are - 10 and - 6.
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Greg borrows $1975 at a simple interest rate of 5% for 3 years. Linda borrows $1975 at a simple interest rate of 4.5% for years. Who pays more interest at the end of their loan? How much more
Answer:
Greg pays more interest than Linda
He pays $17.45 more
Step-by-step explanation:
Greg
P=$1975
R=5%=0.05
T=3 years
Simple interest=P×R×T
=$1975×0.05×3
=$296.25
Linda
P=$1975
r=4.5%=0.045
n=1
t=3
Linda's Interest is compounded once per period, so we this formula
Compound Interest =P(1+r)^t
=$1975(1+0.045)^3
=$1975(1.045)^3
=$1975(1.141166125)
=$2,253.80
Interest paid=$2,253.80-$1975
=$278.8
find the perimeter of the figure to the nearest hundredth.
Answer:
49.13 in
Step-by-step explanation:
circle circumference: 25.13
rectangle perimeter: 24
total: 49.13
The perimeter of the figure to the nearest hundredth. is 28.56 in.
To find the find the perimeter of the figure we'll add the sides of square and the circumference.
Perimeter of figure = 2 × Perimeter of semicircle + 2 × side of square + 2 × side length after excluding semicircle
Radius of semicircle = 4/2 = 2 in.
Perimeter of semicircle
= π r
= 3.14 × 2
= 6.28 in.
Side of square = 6 in.
Side length after excluding semicircle = 6 - 4 = 2 in.
Perimeter of figure
= 2 × Perimeter of semicircle + 2 × side of square + 2 × side length after excluding semicircle
= 2 × 6.28 + 2 × 6 + 2 × 2
= 12.56 + 12 + 4
= 28.56 in.
The area of a square is 100 cm². what is the perimeter?
Answer:
40 cm
Step-by-step explanation:
a square has 4 equal length sides, to get area you multiply two of those sides, 10 x 10 = 100, so each side is 10cm long, adding all of the sides together gets you 40cm.
Answer:
40cm
Step-by-step explanation:
We know that the formula for area of a square is side length squared or [tex]s^2[/tex]
In this case, [tex]s^2=100[/tex]. So we can go through the following steps in order to solve for s
[tex]s^2=100\\\sqrt{s^2} =\sqrt{100} \\\\s=10[/tex]
If one side equals 10, and we know all squares have 4 equal sides, then we can multiple 10 * 4 or add 10+ 10 + 10 + 10.
Our outcome is 40!
Please Help!
The point (4, π/6) can also be represented by which of the following polar coordinates?
a. (-4, 7π/6)
b.(4, 5π/6)
c. (4, -π/6)
d. (-4, 13π/6)
The point (4, π/6) can also be represented by the polar coordinates (-4, 7π/6).
We have given that,
a. (-4, 7π/6)
b.(4, 5π/6)
c. (4, -π/6)
d. (-4, 13π/6)
We have to determine the point (4, π/6) that can also be represented by which of the following polar coordinates.
What is the polar coordinate?
The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point is called the pole, and the ray from the pole in the reference direction is the polar axis.
The point (4, π/6) can also be represented by the polar coordinates (-4, 7π/6).
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Final answer:
The point (4, π/6) can also be represented by (-4, 7π/6), utilizing the polar coordinate system's symmetry by extending the radius to the negative side and adding π to the angle.
Explanation:
The point (4, π/6) in Cartesian coordinates corresponds to a point in the first quadrant since the radius is positive and the angle is positive, which is less than π/2. When we want to find an equivalent set of polar coordinates, we can utilize the symmetry of the polar coordinate system.
The point can also be represented by the coordinates (-4, 7π/6) because if you extend the radius to the negative side (so it becomes -4) and add π radians (180 degrees) to the angle, the point ends up in the same location, albeit in the third quadrant. Therefore, the correct answer is a. (-4, 7π/6).
What is 16.4 divide by .72
Answer:
22.7777777778
Step-by-step explanation:
Answer:
22.7777777778
Step-by-step explanation:
Easy Question Easy points
Topic: Volume
Answer:
100; 14400
Step-by-step explanation:
Volume = base * height
a) Base = 4 * 2.5/2 = 5
Height = 20
That makes volume = 5 * 20 = 100
b) Base = 36 * 16/2 = 288
Height = 50
That makes the volume = 288 * 50 = 14400
Answer:
100, 14400
Step-by-step explanation:
A cylinder was enlarged by a scale factor of 4. The new volume is 2,240 cubic units. What was the volume of the original cylinder
We have been given that a cylinder was enlarged by a scale factor of 4. The new volume is 2,240 cubic units. We are asked to find the volume of original cylinder.
We know that a cylinder is a three dimensional object. Since scale factor is 4, so each side of new cylinder will be 4 times the side of original side of cylinder.
Due to 3 dimensions, the volume of new cylinder is [tex]4^3[/tex] times the volume of original cylinder.
[tex]\text{Volume of original cylinder}\times 4^3=\text{Volume of new cylinder}[/tex]
[tex]\text{Volume of original cylinder}\times 64=2240[/tex]
[tex]\frac{\text{Volume of original cylinder}\times 64}{64}=\frac{2240}{64}[/tex]
[tex]\text{Volume of original cylinder}=35[/tex]
Therefore, the volume of the original cylinder is 35 cubic units.
What type of slope is produced from the equation y=6?
Answer:
Slope = 0
Step-by-step explanation:
The slope is zero because it is a straight horizontal line. If it is a straight vertical line, the slope is undefined.
hope this helps :)
What is 6x(-496)=19x12
Answer:
-19/248
Step-by-step explanation:
A bed is on sale for 25% off of its original price. It originally cost $879.00. How much is the sale price of the bed?
Answer:
$659.25
Step-by-step explanation:
Since its 25 percent off we need to see what it would look as a decimal
1-.25=.75
879times.75= 659.25
Answer:
224.25
Step-by-step explanation:
think of quarters, one is 25 cents, and it takes four to make a dollar. Then if you have a dollar and you want a quarter of it, you divide the dollar by 4, divide $879.00 by four to get 224.25!
7 students are running for student counsel. They sit at a circular table in order to
debate the issues. How many different ways can they sit at the table?
There are 720 different ways for 7 students to sit at a circular table for a debate, calculated using permutation principles by fixing one seat and arranging the remaining six students (6!).
The question asks about the number of different ways 7 students can sit at a circular table for a debate, which involves a mathematical concept called permutations. Since a circular arrangement means that the starting point is not fixed, we have to consider one position as fixed to avoid repeating identical seating arrangements caused by rotation. Therefore, with one student fixed, we have 6 seats left to arrange the remaining 6 students. This scenario is a permutation problem without repetition and can be calculated using the factorial operation (6!).
So, the calculation would be:
Fix one student in one seat.Arrange the remaining 6 students in the remaining seats, which is 6! (factorial of 6).Calculate 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720.Therefore, there are 720 different ways the 7 students can sit at the table for the debate.