Pablo is buying chips and salsa for a party and has a budget of no more than $36.Chips cost $3 per bag and a container of salsa costs $4
Which of the following sets of four numbers has the largest possible standard deviation? (1, 2, 5, 6) (4, 5, 5, 6) (1, 3, 5, 7) (6, 7, 8, 9)
what is the value of h in the figure below?
the answer on APEX is 6
Which of these problem types can not be solved using the Law of Sines?
A. SSS
B. ASA
C. AAS
D. SAS
Answer: The correct option are A, B and D.
Explanation:
The law of sine states that,
[tex]\frac{\sin A}{a} =\frac{\sin B}{b}=\frac{\sin C}{c} [/tex]
Where A, B, C are interior angles of the triangle and a, b, c are sides opposite these angles respectively as shown in below figure.
Since we need the combination of two angles and one side or two sides and one angle.
The Law of sine is useful for AAS and SSA type problems.
Reason for correct option:
In option A three sides are known but no angle is not given, therefore the SSS problem can not be solved by Law of sine and the option A is correct.
In option B a side is known and two inclined angle on that line are known. But to use Law of sine we want the line and angle which in not inclined on that line, therefore the ASA problem can not be solved by Law of sine and the option B is correct.
In option D two sides and their inclined angle is known. But to use Law of sine we want the side and angle which in not inclined on that line, therefore the SAS problem can not be solved by Law of sine and the option D is correct.
Reason for incorrect option:
In option C, the two consecutive angles are given and a side which makes the second angle with base side, therefore the first angle is opposite to the given side, so the law of sine can be used for AAS problems.
Therefore, option C is incorrect.
Find the exact value of sin(11pi/8).
Choices are in the attachment.
Which of the following quadratic functions has a graph that opens downward?
Check all that apply.
A. y=2x-x^2
B. y= 1/3x^2-8x-13
C. y=2/3x^2-13x+5
D. y= -(3+x^2)
...?
D. Y=-(3+x^2)
A. Y=2x-x^2
Answer:
The answers are a) y=2x-x^2 and d) y=-(3+x^2) and in the attached file are the graphs.
Step-by-step explanation:
Quadratic equations are those where the exponent of the unknown term is squared, that is, the unknown is elevated to exponent 2. They have the general form of a trinomial:
ax2 + bx + c = 0
where a, b and c are real numbers and are called coefficients. Thus, a is the coefficient of x2, b is the term or coefficient of x and c is the independent term.
use the table below to find (FoG)(1)
x 0 1 2 3 4 5 6 7
f(x) 5 7 9 11 13 15 17 19
g(x) 3 6 9 12 15 18 21 24
Answer:
value of [tex](f o g)(1)[/tex] is, 17
Step-by-step explanation:
We have to find the [tex](f o g)(1)[/tex]
Using the given tables;
[tex](f o g)(1) = f(g(1))[/tex] ......[1]
At x = 1
g(1) = 6
Substitute this in [1] we have;
[tex](f o g)(1) = f(6)[/tex]
At x = 6
f(6) = 17
then;
[tex](f o g)(1) = 17[/tex]
Therefore, the value of [tex](f o g)(1)[/tex] is, 17
What is the ratio 4:6 in simplest form?
Write an equation of a line that is parallel to x=8 and that passes through the point (-3,-2)
Answer:
The answer is x=-3.
Step-by-step explanation:
I'm not sure how to word it, but I did this question on khan, and got this answer and it was right.
Ryan's gas tank is 1/10 full. After he buys 11 gallons of gas, it is 3/5 full. How many gallons can Ryan's tank hold?
Which is NOT a way to state the meaning of the expression h + 7?
A-7 more than a number
B-A number added 7 times
C-A number increased by 7
D-7 is added to a number
How to get my mother to celebrate her birthday, she thinks that it is not important and that she should not celebrate her birthday, how do i convince her to celebrate her birthday? Please help me...!
What is the quotient and remainer for 32÷6?
What is the length of chord in O below?
A. 5 units
B. 5.70 units
C. 2.5 units
D. 10 units
The length of chord CD is 5 unit.
What is Chord?The line segment connecting any two locations on a circle's circumference is referred to as the chord of the circle. It should be emphasised that the diameter is the circle's longest chord, which runs through its centre.
We have,
As, the distance to both chords are 5.70 unit.
and, both chords are 90 degrees from the line then the chords are identical.
As, the length of Chord AB = 5 unit then the length of chord CD =5.
Thus, the length of chord CD is 5 unit.
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Four less than the quotient of a number and 3 is - 10
To solve the equation, let’s translate the given information into an algebraic equation. The solution to the equation is x = -18.
Explanation:To solve the equation, let’s translate the given information into an algebraic equation. Let the number be represented by 'x'. The quotient of the number and 3 is x/3. The problem states that four less than the quotient of a number and 3 is -10, so we can write the equation as:
x/3 - 4 = -10
To solve for x, we can start by adding 4 to both sides:
x/3 = -6
Next, we can multiply both sides of the equation by 3 to isolate x:
x = -18
Therefore, the solution to the equation is x = -18.
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m∠6 is (2x – 5)° and m∠8 is (x + 5)°. What is m∠3?
Answer:
m∠3=115°.
Step-by-step explanation:
It is given from the figure that line q is parallel to s and r is the transversal.
Since, m∠6 and m∠8 forms a linear pair as they are on the straight line r, therefore using the linear pair property, we have
m∠6+m∠8=180°
⇒[tex]2x-5+x+5=180^{\circ}[/tex]
⇒[tex]3x=180^{\circ}[/tex]
⇒[tex]x=60^{\circ}[/tex]
Thus, the measure of ∠6 is [tex]2x-5=2(60)-5=120-5=115^{\circ}[/tex]
Now, m∠3=m∠6=115° as both m∠3 and m∠6 forms the alternate interior angle pair.
Therefore, the measure of m∠3=115°.
A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. The rancher wants the enclosed area to be 350 square meters. What dimensions should the rancher use to obtain this area?
Final answer:
The dimensions of each corral should be 40 meters by 10 meters.
Explanation:
To find the dimensions of the rectangular corrals, we can set up an equation using the perimeter and area of the enclosed space. Let's call the length of one corral x and the width y. The perimeter of the two corrals is 2x + 2y, which equals 100 meters. The area of the enclosed space is xy, which equals 350 square meters.
Using these equations, we can solve for x and y. Rearranging the perimeter equation, we get x = 50 - y. Substituting this into the area equation, we have (50 - y)y = 350.
Simplifying the equation, we get y^2 - 50y + 350 = 0. This is a quadratic equation that can be factored as (y - 35)(y - 10) = 0. Therefore, the possible values for y are 35 and 10.
Since we are looking for positive values for the dimensions, we choose the values y = 10 and x = 50 - y = 50 - 10 = 40. Therefore, the dimensions of each corral should be 40 meters by 10 meters.
To find the dimensions of the rectangular corrals, we can set up a system of equations. By solving the system of equations, we find that the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.
Explanation:To find the dimensions of the rectangular corrals, we can set up a system of equations. Let x represent the width of one corral and y represent the length. Since the rancher wants to enclose a total of 350 square meters, we have the equation xy = 350. The perimeter of each corral is 2x + y, so the total amount of fencing used would be 4x + 2y.
Given that the total fencing available is 100 meters, we can set up the equation 4x + 2y = 100. Now we can solve the system of equations:
xy = 3504x + 2y = 100By substituting the value of y from the first equation into the second equation, we can solve for x. After finding the value of x, we can substitute it back into the first equation to find the corresponding value of y. The solutions will give us the dimensions of the rectangular corrals.
Let's solve the system of equations:
350 = x(100 - 2x)350 = 100x - 2x^22x^2 - 100x + 350 = 0x^2 - 50x + 175 = 0(x - 25)(x - 7) = 0The solutions for x are x = 25 and x = 7. Plugging these values back into the equation xy = 350, we find that the corresponding values for y are y = 14 and y = 50, respectively. Therefore, the dimensions of the rectangular corrals can be either 25 meters by 14 meters or 7 meters by 50 meters to obtain a total area of 350 square meters.
The temperature, t, in Burrtown starts at 21°F at midnight, when h = 0. For the next few hours, the temperature drops 4 degrees every hour. Which equation represents the temperature, t, at hour h?
A. t = 21h + 4
B. t = 4h + 21
C. t = –4h + 21
D. t = –21h + 4
Answer:
C. t = –4h + 21
Step-by-step explanation:
We know that when h = 0, t = 21°F. Replacing h = 0 in equation A and D we get:
A.
t = 21h + 4
t = 21(0) + 4
t = 4
D.
t = –21h + 4
t = –21(0) + 4
t = 4
So, none of them are correct.
The temperature drops 4 degrees every hour, this means that for h = 1 then t = 21 - 4 = 17. Replacing h = 1 in equation B and C we get:
B.
t = 4h + 21
t = 4(1) + 21
t = 25
C.
t = –4h + 21
t = –4(1) + 21
t = 17
In consequence, C is the correct option.
in one week there are 10,080 minutes. what is this number in scientific notation?
Which equation can be simplified to find the inverse of y = x2 – 7?
To find the inverse of the function y = x² - 7, interchange x and y to get x = y² - 7, then solve for y to get the inverse function y = (x + 7), taking into account both the positive and negative square roots.
To find the inverse of the function y = x² − 7, we need to swap the x and y variables and then solve for y. Here's a step-by-step process:
Replace y with x and x with y to get the equation x = y² − 7.Add 7 to both sides to isolate the y² term: x + 7 = y².Take the square root of both sides, remembering to consider both the positive and negative roots: y = ±√(x + 7).This results in the inverse function y = ±√(x + 7), but typically, we only take the principal square root for the inverse function, which would be y = √(x + 7) assuming x ≥ -7.
Find the equation of the line tangent to the graph of y = cos(2x) at x = pi/4 ...?
Blake has more than five friends.
Let f represent the number of Blake's friends.
Which inequality describes the number of Blake's friends?
f < 5
f > 5
f ≤ 5
f ≥ 5
Answer: The correct option is (B) [tex]f>5.[/tex]
Step-by-step explanation: Given that Blake has more than five friends.
We are to select the inequality that describes the number of Blake's friends.
The number of Blake's friends is represented by f.
According to the given information, we have
the inequality that describes the number of Blake's friends is given by
[tex]f>5.[/tex]
Thus, (B) is the correct option.
How to solve this please help
Which of the following points are solutions to the system of inequalities shown below? Check all that apply. x + y 5 + 2 y > 2 A. (1, 1) B. (5, 2) C. (2, 5) D. (3, 6) E. (1, -1) F. (2, -5)
The points that are solutions to the system of inequalities x + y 5 + 2 y > 2 below are (5, 2), (3, 6), (1, 1). Options B, C, A, and D. For is mathematically given as
What are inequalities?Generally, inequalities are simply defined as the relationship between two non-equal expressions using a symbol like "not equal to," "greater than," or "less than."
In conclusion, The points (5, 2), and (2, 5), (1, 1) are the ones that are the solutions to the system of inequalities x + y 5 + 2 y > 2 below (3, 6).
For (5, 2),
5 + 2* 5 + 2 *2 > 2
19>2
For (2, 5)
2 + 5* 5 + 2*5 > 2
37>2
For (3, 6).
3 + 6*5 + 2*6 > 2
45>2
For (1, 1)
1 + 1* 5 + 2*1 > 2
8>2
For (1, -1)
1 + -1* 5 + 2 *-1 > 2
-6<2
For (2, -5)
2 + -5* 5 + 2*-5 > 2
−33<2
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Which equation can be used to solve the problem?
How many 12-packs of juice boxes contain a total of 84 juice boxes?
A.
12 + b = 84
B.
12 ÷ b = 84
C.
12b = 84
D.
b ÷ 12 = 84
You have a 32-foot fence around a square garden. You paint 1/3 of one side of the fence. What fraction of the fence did you paint?
is .485 lower than .5
Given a polynomial f(x), if (x + 3) is a factor, what else must be true?
What applies here is one of the laws of the factorization of polynomials, called the factor theorem and it states that:
For a polynomial f(x) , if for any value a, f(a) =0 then (x-a) is factor of f(x)
Example:
Consider the polynomial
[tex]f(x) = x^{3} - 3x^{2} - 8x+4[/tex]
For a =3,
[tex]f(a) = (3)^{3} - 3(3)^{2} - 8(3)+24[/tex]
= 27-27-24+24 = 0
f (3)= 0
which means (x-3) is a factor of f(x)
Applying the above rule to the question:
if (x + 3) is a factor of a polynomial f(x), then f(-3) = 0
note that (x+3) can also be written as (x- (-3)).
A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100?
f(n) = f(n - 1) • 0.3 + 25, n > 0
f(n) = 100 - f(n - 1) • 0.3 + 25, n > 0
f(n) = f(n - 1) • 0.7 + 25, n > 0
f(n) = 100 - f(n - 1) • 0.7 + 25, n > 0
How many grains of sand fit in a 5 gallon bucket?
To estimate the number of grains of sand that fit in a 5-gallon bucket, we can calculate the volume of the bucket and the volume of a grain of sand. By assuming the grains are approximately the same size and shape, we can use the formula for the volume of a sphere to estimate the number of grains.
Explanation:To answer this question, we need to make some assumptions. Let's assume that the grains of sand are roughly the same size and shape. We can estimate the number of grains of sand that fit in a 5-gallon bucket by considering the volume of the bucket and the volume of a grain of sand. The volume of a grain of sand can be approximated as a sphere.
Using the formula for the volume of a sphere (V = (4/3)πr³), we can find the volume of a grain of sand. If the grain of sand has sides that are 1.0 mm long, the radius of the sphere would be 0.5 mm (half of the side length).
Now, we can calculate the volume of the 5-gallon bucket, convert it to cubic millimeters, and divide it by the volume of a grain of sand to estimate the number of grains that fit in the bucket.
A 5-gallon bucket can hold approximately 36 million grains of sand.
To estimate the number of grains of sand that can fit into a 5-gallon bucket, we need to start with the volume of the bucket and an average sand grain.
A standard 5-gallon bucket is approximately 18.927 liters (since 1 gallon = 3.78541 liters).
An average grain of sand has a diameter ranging from 0.063 mm to 2 mm. We'll use an average grain size of 1 mm for our calculations. The volume V of a sphere (which we can use to approximate a sand grain) is given by the formula:
V = 4/3 π r³
For a grain of sand with a 1mm diameter, the radius r is 0.5 mm or 0.0005 meters. Therefore:
V = 4/3 π (0.0005)³ ≈ 5.24 x 10-10 m³
The volume of the 5-gallon bucket in cubic meters is:
18.927 liters = 0.018927 m³
Dividing the volume of the bucket by the volume of a single grain of sand gives us:
Number of grains = 0.018927 / 5.24 x 10-10 ≈ 3.613 x 107 grains
Therefore, approximately 36 million grains of sand can fit into a 5-gallon bucket.