Answer:
I think the answer is B Plz tell me if im wrong
Good luck on your test!
Answer:
- 12 divided by 1/6 =n
Step-by-step explanation:
Let the total number of comic books collection be n
Number of comic books=12
Also, according to question number of comic books=1/6 of n
therefore,
1/6 of n=12
n=12×6
n=72
Thus, correct answer is option (a)
Please help with the verifying.
A teacher needs to choose 7 students to hand out papers the total number of ways he may choose the students can be found using a combination
Answer:
Step-by-step explanation:
since the order of choosing out students to hand out papers doesnt matter because the paper handed is just the same and that the purpose or task of each student is just the same, combination should be used. Otherwise, when the order is based on ranking of students for example, permutation is used. answer is true
Find the solution to the system of equations represented by this matrix equation using an inverse matrix.
Answer:
D) [tex]\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right][/tex]
Step-by-step explanation:
For matrix [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
the inverse matrix is the transpose of the cofactor matrix, divided by the determinant: [tex]\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
Your inverse matrix is: [tex]\dfrac{1}{2(-3)-(1)(2)}\left[\begin{array}{cc}-3&-1\\-2&2\end{array}\right][/tex]
so the solution is ...
[tex]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{cc}\frac{3}{8}&\frac{1}{8}\\\frac{1}{4}&-\frac{1}{4}\end{array}\right] \cdot\left[\begin{array}{c}2\\4\end{array}\right] =\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right] \qquad\text{matches selection D}[/tex]
Please please help me
Answer:
12 in²
Step-by-step explanation:
Since the figures are similar
linear ratio = a : b , then
area ratio = a² : b²
linear ratio of sides = 8 : 12 = 2 : 3
ratio of areas = 2² : 3² = 4 : 9
let the area of smaller figure be x then
[tex]\frac{4}{x}[/tex] = [tex]\frac{9}{27}[/tex] ( cross- multiply )
9x = 108 ( divide both sides by 9 )
x = 12
Area of smaller figure is 12 in²
What is the explicit formula for this geometric sequence? 5,10,20,40,80,160,...
Answer:
an = 5·2^(n-1)
Step-by-step explanation:
The explicit formula for a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
Your sequence has a1=5 and r=2, so the explicit formula is ...
an = 5·2^(n-1)
Final answer:
The explicit formula for the geometric sequence 5, 10, 20, 40, 80, 160,... is ,[tex]a_{n}=5(2^{n-1} )[/tex], where 'aₙ' represents the nth term in the sequence.
Explanation:
The student is asking for the explicit formula for a given geometric sequence. In mathematics, a geometric sequence is one where any term after the first is found by multiplying the previous term by a fixed, non-zero number known as the common ratio. Looking at the sequence provided (5, 10, 20, 40, 80, 160,...), we can observe that each term is twice the previous term, thus the common ratio is 2.
To find the explicit formula of a geometric sequence, we use the formula ,[tex]a_{n}=a_{1} (r^{n-1} )[/tex], where an is the nth term, a₁ is the first term in the sequence, r is the common ratio, and n is the term number. For this sequence, a₁ is 5, and r is 2.
The explicit formula for the given geometric sequence is therefore [tex]a_{n}=5(2^{n-1} )[/tex].
Mason gave the waiter a $14.58 tip, which was 15 percent of the dinner bill. What was the amount of the dinner bill before he added the tip?
Answer:
$97.20
Step-by-step explanation:
Divide the tip amount $14.58 by the percentage given 15% or .15.
$14.58 ÷ .15 =$97.20
Check your work by multiplying the answer $97.20 by the percent of tip 15%. $97.20 × .15 =$14.58 (tip amount)
Answer:
C
Step-by-step explanation:
What is the name of the shape graphed by the function r = 2 - costheta
Answer:
limaçon (no inner loop)
Step-by-step explanation:
The equation of a limaçon is written generically as ...
r = b + a·cos(θ)
For b=2 and a=1, this would put the flat side on the left. Rotating it 180° can be accomplished by adding or subtracting π from θ. Then the equation can be ...
r = 2 + cos(θ-π) . . . . or ...
r = 2 - cos(θ)
Find the range of the following data set. 1 1/4, 5/8, 3/4, 1/2, 1 1/2, 1 3/4
A) 1
B) 1 1/8
C) 1 1/4
Answer:
Option C is correct
Step-by-step explanation:
First we will convert the mixed fractions into fraction form.
5/4, 5/8, 3/4, 1/2, 3/2, 7/4
Now, to find the range the formula used is:
Range= Maximum Value - Minimum Value
To find the maximum value and minimum value in fractions, we need to make the denominator of each fraction same. Since the highest value of denominator is 8, so other fractions denominator should be 8.
10/8, 5/8, 6/8,4/8,12/8,14/8
Maximum Value = 14/8 (having highest numerator)
Minimum value = 4/8 (having lowest numerator)
Range of data set = Maximum Value - Minimum value
= 14/8 - 4/8
= 10/8 = 5/4
= 1 1/4
so, option C is correct.
Answer:
The answer is C. 1 1/4
Step-by-step explanation:
To get the range of a set of data, all you need to do is get the difference between the highest value and the lowest value. Since you have different fractions, you first need to determine which is the highest and the lowest.
Since your given are not similar fractions (they do not have the same denominator), you need to make them similar first.
What I did first is make all mixed fractions into improper to make it easier for me to make them similar.
[tex]1\dfrac{1}{4},\dfrac{5}{8},\dfrac{3}{4},\dfrac{1}{2},1\dfrac{1}{2},1\dfrac{3}{4}\\\\\\\dfrac{5}{4},\dfrac{5}{8},\dfrac{3}{4},\dfrac{1}{2},\dfrac{3}{2},\dfrac{7}{4}[/tex]
The LCD of all fractions is 8 so I will need to get the proper proportion that will make all of them have 8 as the denominator.
[tex]\dfrac{5}{4}\times\dfrac{2}{2}[/tex] , [tex]\dfrac{5}{8}\times\dfrac{1}{1}[/tex] , [tex]\dfrac{3}{4}\times\dfrac{2}{2}[/tex] , [tex]\dfrac{1}{2}\times\dfrac{4}{4}[/tex] , [tex]\dfrac{3}{2}\times\dfrac{4}{4}[/tex] , [tex]\dfrac{7}{4}\times\dfrac{2}{2}[/tex]
So now we have the new set of fractions to compare:
[tex]\dfrac{10}{8}, \dfrac{5}{8},\dfrac{6}{8}, \dfrac{4}{8}, \dfrac{12}{8},\dfrac{14}{8}[/tex]
Looking at the set, all you have to do is get the fraction with the highest numerator (which will be our highest value) and get the fraction with the lowest numerator (which is the lowest value), then get the difference.
[tex]\dfrac{14}{8}-\dfrac{4}{8} = \dfrac{10}{8}[/tex] or [tex]1\dfrac{2}{8}[/tex]
Simplify it and you will get:
[tex]1\dfrac{1}{4}[/tex]
Help with this question, please! I don't understand!!
Answer:
A
Step-by-step explanation:
The volume (V) of a pyramid is calculated using the formula
V = [tex]\frac{1}{3}[/tex] × area of base × height
note the height = 48 × 10 = 480 ( 48 storeys at 10 feet )
V = [tex]\frac{1}{3 }[/tex] × 571,536 × 480
= 91,445,760 ft³
[ 1 yd³ = 27 ft³ ], hence
V = [tex]\frac{91445760}{27}[/tex] = 3, 386, 880 yd³ → A
Can y’all help me out ?
Answer:
B
Step-by-step explanation:
It is less than 50% and more tha 10%
It’s B I just took the test or quiz
Place the indicated product in the proper location on the grid.
(2x - 3y )(4x - y )
Answer:
8x^2 - 14xy + 3y^2
Step-by-step explanation:
You need to find the product of (2x - 3y )(4x - y ). To solve this, we're going to be using the distributive distribution as follows:
(2x - 3y )(4x - y ) = 8x^2 - 2xy - 12xy + 3y^2
Combining like-terms:
(2x - 3y )(4x - y ) = 8x^2 - 14xy + 3y^2
Therefore, the result is: 8x^2 - 14xy + 3y^2
Answer:
8x^2 - 14xy - 3y^2
the other explains it, it just forgets to factor in a negitive
A.find X the figure is not drawn to scale
B. Is the triangle equilateral isosceles or scalene? Explain
GIVING BRAINLIEST (image attached)
Answer:
A. 15
B. Scalene
Step-by-step explanation:
8x-10+6x+10x+10=360
24x=360
x=15
8x-10
8(15)-10=110
6x
6(15)=90
10x+10
10(15)+10=160
The triangle is scalene because none of the three sides are equal to each other.
Which container Could logically have a capacity of 1000 L A kitchen sink B bathtub C measuring cup D hot tub
Answer:
D. Hot tub
Explanation:
1000 L is equal to about 246 gallons and even a deep bathtub couldn't hold that much water.
p.s. Loving your username
Please give an explanation.
Answer:
option D
Step-by-step explanation:
So we know that [tex]\sqrt{a} \sqrt{b} = \sqrt{ab}[/tex]
Applying this to our function, we have that:
[tex]\sqrt{(x-5)} \sqrt{(x+2)} = \sqrt{(x+2)(x-5)}[/tex]
We know that the argument of a square root should always BE POSITIVE.
So we need to evaluate in which points the expression (x+2)(x-5) is positive.
So we know that (x+2) is possitive when x>-2 and negative when x<-2.
Also we know that (x-5) is possitive when x>5, if x<5 then x is negative.
Then we have:
if x<-2, then:
(x-5) is negative
(x+2) is negative
Then (x+2)(x-5) is positive.
If x>5 then:
(x-5) is positive
(x+2) is positive.
Then (x+2)(x-5) is positive.
If -2<x<5 then:
(x-5) is negative
(x+2) is positive
Then (x+2)(x-5) is negative, so it's undefined.
So the function is defined for x>5 and x<-2
So the correct option is option D.
Match the function with its graph.
1)y = tanx
2)y= cot x
3)y= -tan x
4)y= -cot x
Answer:
To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.
Please see the attached image below, to find more information about the graph
s
The equations are:
1) y = tan (x)
2) y = cot (x)
3) y = -tan (x)
4) y = -cot (x)
Looking at the graphs, we can see which corresponds to each equation
1) y = tan (x)
Graph C
2) y = cot (x)
Graph A
3) y = -tan (x)
Graph B
4) y = -cot (x)
Graph D
Answer:
A) 1C, 2A, 3B, 4D
Step-by-step explanation:
We can graph each of the functions in your preferred grapher, the we compare each graph with the corresponding example. (attached images)
By doing this we can see that graph C is tanx, graph A is cotx, graph B is -tanx, graph D is -cotx
Consider x=h(y,z)x=h(y,z) as a parametrized surface in the natural way. write the equation of the tangent plane to the surface at the point (3,0,3)(3,0,3) given that ∂h∂y(0,3)=−5∂h∂y(0,3)=−5 and ∂h∂z(0,3)=−3∂h∂z(0,3)=−3.
The equation of the tangent plane to the surface x=h(y,z) at the point (3,0,3) given that ∂h/∂y=−5 and ∂h/∂z=−3 is x = -5y -3z + 12.
Explanation:
In Mathematics, the equation for the tangent plane to a surface x = h(y,z) at a point can be determined by the following formula: x - x0 = ∂h/∂y(y - y0) + ∂h/∂z(z - z0). In your expression ∂h/∂y (derivatives of h with respect to y) is given as -5 and ∂h/∂z (derivatives of h with respect to z) is given as -3. By plugging the value of these derivatives and the point (3,0,3) into the formula, the equation of the tangent plane would be: x - 3 = -5(y - 0) - 3(z - 3).
After simplifying this, we'll get x = -5y -3z + 12. It's worth noting that derivation of the equation for a tangent plane to a parametrized surface relies heavily on partial derivatives and the study of multi-variable calculus.
Learn more about Tangent Plane Equation here:https://brainly.com/question/33705650
#SPJ3
what is the recursive rule for the sequence?
-7.4, -21.2, -35, -48.8, -62.6,...
Final answer:
The recursive rule for the given sequence is [tex]a_n = a_{n-1} - 13.8[/tex],
where a₁ = -7.4 and n > 1.
Explanation:
You are looking for the recursive rule for the sequence -7.4, -21.2, -35, -48.8, -62.6, and so on. To find this, we observe how the sequence progresses from one term to the next. The pattern here is that each term decreases by the same amount when compared to the previous term. By calculating the difference between successive terms, we can identify the common difference.
For instance, the second term (-21.2) minus the first term (-7.4) equals the third term (-35) minus the second term (-21.2), and this difference equals -13.8. Hence, each term is -13.8 less than the term before it.
To express this as a recursive formula, we start by stipulating the first term:
a₁ = -7.4Then, we provide the recursive rule that relates each term to the one before it:
aₙ = aₙ₋₁ - 13.8, for n > 1Using this recursive formula, given any term in the sequence, we can find the next term by subtracting 13.8 from the given term.
A rectangular prism is 4 inches long, 6 inches wide, and has a height of 5 inches. What is its volume?
a. 60 in3
b. 120 in3
c. 148 in3
d. 240 in3
Answer:
b.120in3
Step-by-step explanation:
you just take the high width and length and times together
4*5*6=120
Ally has one coupon for $5.00 off and another coupon for 25% off. The store only allows one coupon per purchase. If Ally's purchase costs $21.89 before the coupon, which coupon should she use to get the bigger discount?
Answer:
25%
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 21.89 × 25/100
Discount = 547.25/100
You save = $5.4725
Final Price = Original Price - Discount
Final Price = 21.89 - 5.4725
Final Price = $16.4175
Answer:
25% off
Step-by-step explanation:
Which set of points contains the solutions to the inequality y ≥ 1⁄4x + 5?
A. {(–3,–17), (4,11), (7,19)}
B. {(4,6), (8,8), (–3,6)}
C. {(3,4), (2,3), (8,27)}
D. {(–2,–1), (4,–7), (5,1)}
First answer get's brainliest
Answer:
B. {(4,6), (8,8), (–3,6)}
Step-by-step explanation:
The given inequality is
[tex]y\ge\frac{1}{4}x+5[/tex]
The set of points that satisfy the inequality are solutions.
We can verify that,all the points in the set {(4,6), (8,8), (–3,6)} satisfy the given inequality.
[tex]6\ge\frac{1}{4}(4)+5[/tex] ;[tex]\implies 6\ge6[/tex]: True
[tex]8\ge\frac{1}{4}(8)+5[/tex] ;[tex]\implies 8\ge7[/tex]: True
[tex]6\ge\frac{1}{4}(-3)+5[/tex] ;[tex]\implies 6\ge4.25[/tex]: True
Therefore, the correct answer is B.
Yet another question.
Answer:
t= 3 years
Step-by-step explanation:
So far we have 2 useful relationships[tex]P_{t}= P_{o} e^{r*t}[/tex] and [tex]P_{t}=2P_{0}[/tex]
Now, clearing t
[tex]P_{t}= P_{o} e^{r*t} \\\frac{ P_{t}}{P_{o}} = e^{r*t}\\\frac{2 P_{0}}{P_{o}} = e^{r*t}\\2 = e^{r*t}[/tex]
I apply logarithm
[tex]log(2)=r*t\\ t=\frac{log(2)}{r}\\t=\frac{0.3}{0.1} \\ t=3[/tex] years
Done
Please help me out please
Answer:
the area of the hexagon is approx. 187.1 in²
Step-by-step explanation:
Picture this regular polygon as being a hexagon made up of six equilateral triangles of side 12 in. We find the area of one such triangle and then multiply that by 6 to obtain the total area of the hexagon.
One such equilateral triangle has three sides all of length 12 in, and all the interior angles are 60°. The height of one such triangle is
h = (12 in)sin 60°, or
√3
h = (12 in) -------- = 6√3 in
2
So, with base 12 in and height 6√3 in, the area of one such equilateral triangle is
A = (1/2)(12 in)(6√3 in) = 36√3 in²
and the total area of the hexagon is 6(36)√3 in², or approx. 187.1 in²
Emergency funds should have a mix of _____.
A. cash, regular savings accounts, insurance policies, and CDs
B. checking accounts, regular savings accounts, and CDs
C. checking accounts, savings accounts, and investment accounts
D. cash, checking accounts, and other investment accounts
Answer:
c
Step-by-step explanation:
Help!! - 2.10 - (4 points)
1. Would you factor out the GCF, use the Perfect Square Trinomial pattern, or the Difference of Squares Pattern?
4x^2 - 25
2. Show how you would use the approach you picked by factoring this binomial.
Answer:
Approach: Difference of Squares Pattern
[tex]4 {x}^{2} - 25 = (2x - 5)(2x + 5)[/tex]
Step-by-step explanation:
The given binomial is:
[tex]4 {x}^{2} - 25[/tex]
We can rewrite to obtain:
[tex] {(2x)}^{2} - {5}^{2} [/tex]
This is a difference of two squares, so we will factor using difference of squares pattern.
Recall that:
[tex] {a}^{2} - {b}^{2} = (a + b)(a - )[/tex]
If we let
[tex]a = 2x[/tex]
and
[tex]b = 5[/tex]
Then we can factor the given binomial to obtain:
[tex] {2x}^2 - {5}^{2} = (2x - 5)(2x + 5)[/tex]
[tex] \therefore4 {x}^{2} - 25 = (2x - 5)(2x + 5)[/tex]
Three boxes are shipped on a truck. Each box has a base of 16 square feet. Two of the boxes have a height of 3 feet and one box has a height of 5 feet. What is the total volume, in cubic feet, of the three boxes?
Answer:
176 cubic feet
Step-by-step explanation:
volume of each box is given by area of base * height.
Volume of Box 1 = 16 * 3 = 48
Volume of Box 2 = 16 * 3 = 48
Volume of Box 3 = 16 * 5 = 80
Total Volume = 48 + 48 + 80 = 176 ft^3
To calculate the total volume of the three boxes, we sum the individual volumes of two boxes at 48 cubic feet each and one box at 80 cubic feet, resulting in a total of 176 cubic feet.
Explanation:To find the total volume of the three boxes shipped on a truck, we need to calculate the volume of each box and then sum the volumes. The volume of a rectangular prism (which is the shape of the boxes) is calculated by the formula Volume = length × width × height. In this case, the boxes have a common base of 16 square feet.
The two boxes with a height of 3 feet each have a volume of 16 square feet × 3 feet = 48 cubic feet per box. For both, this gives us a total of 48 cubic feet × 2 = 96 cubic feet.
The third box with a height of 5 feet has a volume of 16 square feet × 5 feet = 80 cubic feet.
Adding the volumes of all three boxes together, the total volume is 96 cubic feet + 80 cubic feet = 176 cubic feet. This is the total volume of the three boxes combined.
If y = 4x + 3 were changed to y = -4x + 3, how would the graph of the new function compare with the original?
A.It would be steeper.
B.It would be less steep.
C.It would change orientation and slant down.
D.It would change orientation and slant up.
Answer: The answer is C. it would change orientation and slant down.
Step-by-step explanation:
The two lines are just mirror images of each other. In this case, the slope is just the opposite, causing it to be the way it is. The y intercept is the same which also causes the mirror imaging.
Answer:
It would change orientation and slant down.
Step-by-step explanation:
Judy wants to save $175 for a trip to an amusement park. She sets aside $14 of her allowance at the end of each week. How many weeks will it take her to save enough money for the whole trip?
[tex]175 - 14[/tex]
I think that will help you I'm not sure you just have to try to resolve if you get ranked if you get it wrong just send me a message cuz I am a fifth grade teacher
Three tennis balls are packaged in a cylindrical container as shown. The tennis balls touch the top and bottom of the canister and each other. (Use 3.14 for pi.) Round each answer to the nearest tenth.
A) Each tennis ball has a diameter of 2.6 inches.
What is the height of the cylinder? _____
B) Find the volume of one tennis ball.
Volume of one tennis ball= ____________
C) Find the volume of the cylinder.
Volume of cylinder = ______________
D) What is the volume of space in the cylinder not taken by the tennis balls?
Volume of unused space = ___________
Answer:
Part A) The height of the cylinder is [tex]7.8\ in[/tex]
Part B) The volume of one tennis ball is [tex]9.2\ in^{3}[/tex]
Part C) The volume of the cylinder is [tex]41.4\ in^{3}[/tex]
Part D) The volume of space in the cylinder not taken by the tennis balls is [tex]13.8\ in^{3}[/tex]
Step-by-step explanation:
Part A) Each tennis ball has a diameter of 2.6 inches
What is the height of the cylinder?
we know that
The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3
so
[tex]h=2.6*3=7.8\ in[/tex]
Part B) Find the volume of one tennis ball
The volume of the sphere (one tennis ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=2.6/2=1.3\ in[/tex] ----> the radius is half the diameter
[tex]\pi=3.14[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(1.3)^{3}[/tex]
[tex]V=9.2\ in^{3}[/tex]
Part C) Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=2.6/2=1.3\ in[/tex] ----> the radius is half the diameter
[tex]\pi=3.14[/tex]
[tex]h=2.6*3=7.8\ in[/tex]
substitute
[tex]V=(3.14)(1.3)^{2} (7.8)[/tex]
[tex]V=41.4\ in^{3}[/tex]
Part D) What is the volume of space in the cylinder not taken by the tennis balls?
we know that
The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis
[tex]V=41.4-(3)*(9.2)=13.8\ in^{3}[/tex]
Answer:
Part A) The height of the cylinder is
Part B) The volume of one tennis ball is
Part C) The volume of the cylinder is
Part D) The volume of space in the cylinder not taken by the tennis balls is
Step-by-step explanation:
Part A) Each tennis ball has a diameter of 2.6 inches
What is the height of the cylinder?
we know that
The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3
so
Part B) Find the volume of one tennis ball
The volume of the sphere (one tennis ball) is equal to
we have
----> the radius is half the diameter
substitute
Part C) Find the volume of the cylinder
The volume of the cylinder is equal to
we have
----> the radius is half the diameter
substitute
Part D) What is the volume of space in the cylinder not taken by the tennis balls?
we know that
The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis
Step-by-step explanation:
The owner of a catering company wants to select a random sample of clients to find out about their food preferences. Select Yes or No to tell whether each method results in a random sample of the population. Yes or No The owner uses a database to print the names of all clients on slips of paper. The owner chooses 20 of the slips of paper without looking. The owner sends a survey to every client who spent more than $500 with the catering company in the past year. The owner sends a survey to all clients whose phone number ends in 5. The owner sends a survey to the last 20 clients who used the catering company's services.
Answer:
Select Yes or No to tell whether each method results in a random sample of the population.
1. The owner uses a database to print the names of all clients on slips of paper. The owner chooses 20 of the slips of paper without looking.- yes
3. The owner sends a survey to every client who spent more than $500 with the catering company in the past year. - no
4. The owner sends a survey to all clients whose phone number ends in 5.- yes
5. The owner sends a survey to the last 20 clients who used the catering company's services.- yes
Help me with this please!!
[tex]\displaystyle\\\frac{22}{10}=\frac{x}{12}=\frac{33}{y}\\\\\frac{22}{10}=\frac{x}{12}\implies~x=\frac{22\times12}{10}=\frac{264}{10}=\boxed{\bf26.4}\\\\\frac{22}{10}=\frac{33}{y}\implies~y=\frac{10\times33}{22}=\frac{10\times3}{2}=5\times3=\boxed{\bf15}[/tex]