Answer:
Sample Response: The math club has 8 members. The youngest member is 9. The oldest member is 13. Therer is a cluster between 11 and 13, with a peak at 13. There is a gap at 10.
What is the volume of this rectangular prism?
3ft by 6 1/4 ft by 14 ft
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 7 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.
A y=1/28x^2
B y=1/42x^2
C y=1/35x^2
D y=1/49x^2
Answer:
[tex]y= \frac{1}{28} x^2[/tex]
Step-by-step explanation:
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
The pipe is located 7 inches from the vertex of the mirror.
The parabola is open upwards . the vertex of the parabola is (0,0)
and pipe is located 7 inches from the vertex (0,0)
7 inches is the focus of the mirror
The distance between the vertex and the focus = 7
Since parabola is upwards and vertex is (0,0) we use formula
[tex]4py = x^2[/tex]
Where p is the distance between the vertex and focus
p = 7 we know
[tex]4*7*y = x^2[/tex]
[tex]28y = x^2[/tex]
Now isolate y by dividing 28 on both sides
[tex]y= \frac{1}{28} x^2[/tex]
A group of hikers buys 8 bags of mixed nuts. Each bag contains 3 1/2 cups of nixed nuts. The mixed nuts are shared evenly among 12 hikers. How many cups of mixed nuts will each hiker receive?
Answer:
Each hiker gets [tex]\frac{7}{3}[/tex] cups of mixed nuts.
Step-by-step explanation:
First, we need to find the total amount of cups by multiplying the number of bags with the amount of cups in each bag:
8 * 3.5 = 28
Now, we divide this by 12 to find the amount of cups per hiker:
28 ÷ 12 = [tex]\frac{7}{3}[/tex] or 2.3333
So each hiker gets [tex]\frac{7}{3}[/tex] cups of mixed nuts.
Using the Law of Detachment, find the conclusion for the following: If two triangles are similar, then their corresponding angles are congruent.
Triangle ABC and Triangle XYZ are similar.
Question 8 options:
AB≅XY
ABC≅XYZ
The statements are not valid.
Answer:
∠ABC ≅ ∠XYZ
Step-by-step explanation:
Given: ΔABC is similar to ΔXYZ.
If two triangles are similar, then
1. the corresponding angles are congruent
2. the corresponding sides are proportional
From the options given,
AB ≅ XY is not applicable for similar triangles. Hence the option is wrong.
∠ABC ≅ ∠XYZ since ΔABC ≅ ΔXYZ
Hence the answer is ∠ABC ≅ ∠XYZ
Given: y varies directly as x. If y = 5 when x = 4, what is the value of y when x = 12? A) 9.6 B) 10 C) 12 D) 15
Answer:
D) 15
Step-by-step explanation:
We know the formula for direct variation is
y=kx
Substituting y=5 and x=4 we can calculate k
5=k4
Divide each side by 4
5/4 =k
Now y= 5/4 x
If x =12
y =5/4*12
y = 15
A scientist is studying bacteria and records the number of bacteria over time. The scientists determines that the function N(t)=300(1.30) models the number of bacteria, N after t hours.
Which statement correctly interprets this model.
A. The number of bacteria is originally 300 and increases by 30%
B. The number of bacteria is originally 300 and decreases by 30 every hour
C. The number of bacteria is originally 30 and increases by 300 every hour
D. The number of bacteria is originally 30 and decreases by 300% every hour
Answer:
(A) The number of bacteria is originally 300 and increases by 30% every hour
Step-by-step explanation:
I am assuming the function should actually read:
[tex]N(t)=300\cdot 1.30^t[/tex]
(i.e., there should be a "t" in the exponent. if this is not the case please disregard my answer).
According to the above exponential function, the initial amount 300 grows as (1+0.3)*300=300+0.3*300. In other words it increases by 30% every hour (t).
Your answer choice (A) is likely a candidate, except I am missing "every hour" at the end (again, am assuming this was omitted by mistake)
Final answer:
The function N(t)=300(1.30)^t represents the bacterial growth model where the initial amount of bacteria is 300 and increases by 30% every hour.
Explanation:
Looking at the function N(t)=300(1.30)^t, this model describes the number of bacteria, N, after t hours. The base number, 300, indicates the initial quantity of bacteria, while the term (1.30)^t suggests that the population changes by a factor of 1.30 each hour, reflecting a 30% increase in the number of bacteria each hour. Therefore, the correct statement that interprets this model is:
A. The number of bacteria is originally 300 and increases by 30% each hour.
15x+8y=56 in slope intercept form
The equation 15x + 8y = 56 can be rewritten in slope-intercept form (y = mx + b) as y = -15/8x + 7, where -15/8 is the slope and 7 is the y-intercept.
Explanation:To convert the equation 15x + 8y = 56 into slope-intercept form (y = mx + b), we want to isolate y. Here are the steps:
Subtract 15x from both sides of the equation, which gives us 8y = -15x + 56.Divide every term by 8 to solve for y. This gives us y = -15/8x + 7.In this equation, -15/8 is the slope, and 7 is the y-intercept. This means the line intersects the y-axis at y = 7, and for every 8 units increase in x, there is a 15 unit decrease in y, as the slope is negative.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Name Score Julia 650 Andrew 550 Jason 380 Cathy 720 Jessica 710 Robert 550 The table gives the scores of 6 students from a class of 25 in a competitive exam. The point estimate of the mean score for the students is . (Round off your answer to the nearest tenth.)
Answer:
Mean score for the students = 593.3
Step-by-step explanation:
Name Score
Julia 650
Andrew 550
Jason 380
Cathy 720
Jessica 710
Robert 550
1) Mean Score = [tex]\frac{Sum of the scores}{Total number of students}[/tex]
= [tex]\frac{650+550+380+720+710+550}{6}[/tex]
= 593.33
2) Upon rounding off to the nearest tenth, we get
Mean Score = 593.3 (since the hundredth digit is lesser than 5, the tenth digit is not increased)
Answer:
593.3
Step-by-step explanation:
Assuming random sample, assuming "point estimate of mean score" means "estimate of mean score in points",
(650+550+380+720+710+550)/6 is 593.3
Sample size 6 population size 25 is irrelevant except to note estimate might not be very good.
I just need help with Number 17 when it comes to writing out the equation
Answer:
132(X) + 64(2X) = $1040.00
Step-by-step explanation:
equations
64a +132s = 1040a = 2ssolution
Adult ticket: $8Student ticket: $4Step-by-step explanation:a. It usually works well to let a variable represent the quantity the problem statement is asking you to find. I like to choose variable names that help me remember what the variable stands for. (x and y rarely do that) So, let's choose "a" for the cost of an adult ticket, and "s" for the cost of a student ticket.
The equations express the relationships described by the problem statement. The first relationship expresses the total revenue in terms of the numbers of tickets sold. You know that multiplying the number of tickets by the cost of the ticket will give the revenue from sales of that ticket. So, the total revenue is ...
... 64a +132s = 1040
The problem statement also tells you the relationship between the costs. An adult ticket is twice the cost of a student ticket, so ...
... a = 2s
These equations are your system of linear equations.
_____
b. The solution can be found using substitution. Since the second equation gives an expression for "a", we can use that in the first equation.
... 64(2s) +132s = 1040
... 260s = 1040 . . . . . . . . simplify
... 1040/260 = s = 4
... a = 2s = 2·4 = 8
An adult ticket costs $8; a student ticket costs $4.
Which of the following represents the equation y = mx + b, where m is a positive integer, written in standard form?
Select one:
A. x+y=mb
B. mx−y=−b
C. −mx+y=0
D. 2y+x=−mb
B. mx−y=−b
Step-by-step explanation:Start with ...
... y = mx +b
Subtract mx.
... -mx +y = b
You want the leading coefficient positive, so multiply by -1.
... mx -y = -b . . . . matches selection B
Answer: B. mx−y=−b
Step-by-step explanation:
The equation of a line in standard form is given by :-
[tex]Ax+By=C[/tex]
, where A is a positive integer , B and C are integers.
The given equation : [tex]y = mx + b[/tex]
, where m is a positive integer.
The convert it into standard form , we subtract y and b from both sides , we get
[tex]y -y-b= mx + b-y-b[/tex]
Simplify,
[tex]-b= mx -y[/tex]
Or we can write it as [tex] mx -y=-b[/tex] → Standard form.
Thus , the equation of line in standard form = [tex] mx -y=-b[/tex] , where m is a positive integer.
Hence, the correct answer is B. mx−y=−b
Factor completely 7x3y +14x2y3 − 7x2y2.
Answer:
7x^2y(x +2xy^2 -y)
Step-by-step explanation:
7, x^2, and y are factors of every term, so we can start by factoring those out.
... = 7x^2y(x +2xy^2 -y)
The trinomial does not factor further, so this is it.
Answer:
7x^2y(x +2xy^2 -y)
Step-by-step explanation:
7x^3y +14x^2y^3 − 7x^2y^2
WE find out GCF
7x^3y= 7*x*x*x*y
14x^2y^3= 7*2*x*x*y*y*y
7x^2y^2 = 7 *x*x*y*y
GCF is 7x^2y
Factor out GCF from the given expression. when we factor out 7x^2y we divide each term by GCF. we put GCF 7x^2y outside
7x^2y(x +2xy^2 -y)
PLZ HELP ASAP WILL MARK BRAINIEST
SEE ATTACHMENT
-3 is a solution of y > -2
Answer:
i think it is true and true
Step-by-step explanation:
Answer:
35. False
36. True
Step-by-step explanation:
35. [tex]-3\:<\:-2[/tex]
On the number line [tex]-3[/tex] is to the left of [tex]-2[/tex].
Therefore [tex]-3[/tex] is not greater than [tex]-2[/tex].
[tex]-3[/tex] is rather less than [tex]-2[/tex].
36. [tex]y\leq 3[/tex] includes three as a possible solution.
The reason is that, the inequality contains an equal sign in it, the boundary is also inclusive, therefore 3 is itself a possible solution.
In order words, the statement
[tex]3\leq3[/tex] is a truth statement.
- 1 (multiplicity 3), 3 (multiplicity 4)
Answer:
-1,81
Step-by-step explanation:
Multiplicity of a number can be written as power
for example
-1(multiplicity 3) can be written as
[tex]-1^{3}[/tex]= -1
similiarly 3(multiplicity 4) can be written as
[tex]3^{4}[/tex]=81
The eleventh-degree polynomial (x + 3)4(x – 2)7 has the same zeroes as did the quadratic, but in this case, the x = –3 solution has multiplicity 4 because the factor (x + 3) occurs four times (that is, the factor is raised to the fourth power) and the x = 2 solution has multiplicity 7 because the factor (x – 2) occurs ... Can you do the rest on your own?
-7=7d-8 solve for the variable d
-7 = 7d - 8
Add 8 to both sides.
1 = 7d
Divide both sides by 7.
d = 1/7Simplify the polynomial by combining like terms.
xy−3x^3y−4xy^2+3x^2+7x^3y
Answer:
it should be 4x^3 y-4xy^2+xy+3x^2
Step-by-step explanation:
A ____________ has no dimension and is represented by a small dot.
Answer:
Point
Step-by-step explanation:
If you are referring to geometry
Find the rational roots of x^4 + 3x^3 + 3x^2 - 3x - 4 = 0
0, 1
1, 2
1, -1
-1, 2
Answer:
C. 1,-1
Step-by-step explanation:
The sum of the coefficient is 0 so x=1 is a root and (x-1) as a factor
so x^4+3x^3+3x^2-3X-4=(x-1)(x^3+4x^2+7x+4)
and the root of that is x=-1 and the factor is (x+1)
SO the answer is: x=1 and x=-1
Answer: -1, 1
Step-by-step explanation:
To solve the polynomial equation x^4 + 3x^3 + 3x^2 - 3x - 4 = 0, do a quick test of polynomials using 1 and -1 in place of x.
This gives the sum of coefficients as zero
Testing with 1: 1 + 3 + 3 - 3 - 4 = 0
Testing with -1: 1 + (-3) + 3 - (-3) - 4
= 1 - 3 + 3 + 3 - 4 = 0
This gives that both (x + 1) and (x - 1) are roots.
(x + 1)(x - 1) = x² - 1 {difference of two squares}
Dividing the polynomial x^4 + 3x^3 + 3x^2 - 3x - 4 by (x² - 1) results in x² - 3x + 4 as quotient. Factorizing this result would give complex roots.
Therefore, x² - 1 = 0
x² = 1
Taking square of both sides of the equation gives
x = ± 1
1 and -1 are the rational roots to the polynomial.
To convert 6 weeks to days, the first ratio is 1 week/7 days . To set up the proportion, the second ratio must be _____
Answer:
6/x weeks
Hope this helps
Answer:
6/x weeks
Step-by-step explanation:
This is the correct answer, credits to the other person who answered.
Frog A eats 8 flies in 4 minutes, while Frog B eats 14 flies in 7 minutes. Which frog eats more flies per minute?
Neither one
Step-by-step explanation:Frog A's "unit rate" is ...
... (8 flies)/(4 minutes) = 2 flies/minute
Frog B's "unit rate" is ...
... (14 flies)/(7 minutes) = 2 flies/minute
Both rates are the same. Each frog eats 2 flies per minute.
Answer:
i dont like frogs
Step-by-step explanation:
Krys bought x boxes of pastries to bring to a party. Each box contains 12 pastries. She decides to keep two boxes for herself. She brings 60 pastries to the party. Which equation can be used to find the number of boxes, x, Krys bought? a. 2x − 12 = 60 b. 12x − 2 = 60 c. 12x − 24 = 60 d. 24 − 12x = 60
Answer:
c. 12x − 24 = 60
Step-by-step explanation:
x is the number of boxes Krys bought.
12x is the number of pastries in those boxes. 2·12 = 24 is the number of pastries in the boxes Krys kept for herself. Then the number of pastries Krys brought to the party is ....
... 12x -24
We are told that number is 60, so we can use this equation to find x:
... 12x -24 = 60
Answer:
Option C : 12x − 24 =60
Step-by-step explanation:
Given :
Krys bought x boxes of pastries to bring to a party.
Each box contains 12 pastries.
She decides to keep two boxes for herself.
She brings 60 pastries to the party.
To Find : Equation can be used to find the number of boxes, x, Krys bought.
Solution :
Krys bought x boxes of pastries .
Each box contains 12 pastries.
So, total pastries she bought = 12 x
She decides to keep two boxes for herself.
Since 1 box contain 12 pastries .
Thus two box contains pastries = 12*2 =24 pastries
Now total pastries she bought is 12 x . Out of which she decides to keep 24 pastries . after keeping 24 pastries from 12 x pastries she bought 60 pastries to the party i.e.
⇒ 12 x - 24 = 60
Thus,Equation can be used to find the number of boxes, x, Krys bought:
12 x - 24 = 60
Hence Option C is correct .
What is the value of x?
Enter your answer in the box.
Since QC and BR are parallel, triangles CDQ and BDR are similar.
This means that corresponding sides are in proportion, so we have
[tex] BD \div QD = RD \div CD [/tex]
Substituting numbers, we have
[tex] 26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x} [/tex]
Multiply both sides by [tex] 39x [/tex]
[tex] 65x = 39(18+x) [/tex]
Expand right hand side:
[tex] 65x = 702 + 39x [/tex]
Subtract 39x from both sides:
[tex] 26x = 702 [/tex]
Divide both sides by 26
[tex] x = \dfrac{702}{26} = 27 [/tex]
Just took the test and got the the correct answer *\(♡°▽°♡)/*
Look at the image down below!!
Jason jumps from a plane at an altitude of 1000 m. His parachute opens after 10 seconds. The graph shows the relationship between the distance traveled and time. How far does he fall in 1 minute and 20 seconds? Continuous graph with the y axis labeled Distance (m) and the x axis labeled Time, min. The function consists of 3 lines, the first is almost vertical with a positive slope connecting the points 0,0, to approximately 1 of 6, 250. From that point the second line connects to the first and passes through the points 1,500, 2,800 and 2 1 over 3, 1000. From that point the function is horizontal.
600 m
Step-by-step explanation:The slope between 1 minute and 2 minutes is ...
... (800 -500)/(2 -1) = 300 . . . . . . m/min
Thus in 20 seconds, 1/3 minute, Jason will fall ...
... (1/3 min)·(300 m/min) = 100 m
This distance is in addition to the 500 m he has already fallen in the first minute.
In 1 min 20 sec, Jason falls 500 m + 100 m = 600 m.
_____
Comment on the graph
We don't expect Jason's rate of fall to change dramatically at the 2-minute mark. We suspect the last point should be (2 2/3, 1000).
A) Between x 2 and x 3, which function has a greater average rate of change than f(x)=1/6^-x
Answer:
4^x+1
Step-by-step explanation:
because i got it wrong
Answer:
[tex]y= 4^{x+1}[/tex]
Step-by-step explanation:
What would be the answer please help
Jack signs up for a credit card that has a APR of 13.99%. Use the periodic (monthly) interest rate to calculate how much interest he owes on his unpaid February balance of $345.67?
Answer:
$3.46
Step-by-step explanation:
Unpaid February balance = $345.67
Annual Percentage Rate(APR) = 13.99 %
= [tex]\frac{13.99}{100}[/tex]
= 0.1399 (converted into decimal)
Periodic (monthly) interest rate = [tex]\frac{0.1399}{12}[/tex] (since there are 12 months in a year)
= 0.01
Interest he owes on his unpaid February balance of $345.67
= Periodic (monthly) interest rate * unpaid February balance
= 0.01 * 345.67
= 3.456
= $3.46 (rounded off to the hundredth place)
what is the equation of the circle with center (0,0) the passes through the point (5,-5). please help
x² + y² = 50
Step-by-step explanation:The circle centered at (h, k) with radius r has equation ...
... (x -h)² + (y -k)² = r²
You have (h, k) = (0, 0), so all we need to do is find r². We can do that by choosing r² so that the equation is true at the given point.
... x² + y² = (5)² + (-5)² = 25 + 25 = 50
Your equation is x² + y² = 50.
how do you prove this?
Answer:
Show ΔBCD ≅ ΔGFE, so ∠C ≅ ∠F. Base angle of an isosceles triangle are congruent, so ΔACF is isosceles.
Step-by-step explanation:
Informally, subtract DE from CE and DF. This will show CD ≅ EF.
Then ΔBCD ≅ ΔGFE by the HL theorem for right triangles.
Corresponding parts of congruent triangles are congruent, namely the angles C and F.
Since base angles of ΔACF are congruent, it is isosceles.
76.8% of what number is 32.64
Answer:
42.5
Step-by-step explanation:
76.8% × ? = 32.64
? =
32.64 ÷ 76.8% =
32.64 ÷ (76.8 ÷ 100) =
(100 × 32.64) ÷ 76.8 =
3,264 ÷ 76.8 =
42.5
To solve for the number that 76.8% of it equals 32.64, you can write an equation and solve for x: 0.768 * x = 32.64. Dividing both sides by 0.768 gives x = 42.5.
Explanation:The question asks about a percentage of a number, which is a math concept. If 76.8% of a number equals 32.64, you can use basic algebra to find that number. Let's call it 'x'. You can write it as an equation: 0.768 * x = 32.64. Solving for x, divide both sides of the equation by 0.768.
x = 32.64 /0.768
When you perform this calculation, you'll find that x is approximately 42.5. So, 76.8% of 42.5 is approximately 32.64.
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Use the information in the diagram to determine the height of the tree to the nearest foot.
the diagram is not to scale.
A. 60
B. 30
C. 28
D. 120
Answer:
The correct option is A. The height of tree is 60 ft.
Step-by-step explanation:
From the given figure it is noticed that the building is creating a right angle triangle from a point and the tree divides the hypotenuse and base in two equal part.
According to midpoint theorem of triangle: In a triangle, if a line segment connecting the midpoints of two sides, then the line is parallel to third side. The length of line segment is half of the length of third side.
Using midpoint theorem of triangle, we can say that the length of tree is half of the building.
[tex]Tree=\frac{1}{2}\times Building[/tex]
[tex]Tree=\frac{1}{2}\times 120[/tex]
[tex]Tree=60[/tex]
Therefore correct option is A. The height of tree is 60 ft.
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm. What are the lengths of the sides of a similar triangle that has a perimeter of 26 cm ?
Answer:
6 cm,12 cm,8 cm
Step-by-step explanation:
add the perimeter of the first triangle to get 65
then divide 65 by 26 to get 2.5
then divide all the side lengths by 2.5
15/2.5=6
20/2.5=8
30/2.5=12
The lengths of the sides of a similar triangle that has a perimeter of 26 cm are 6 cm, 8 cm, and 12 cm and this can be determined by using the given data.
Given :
The lengths of the sides of a triangle are 15 cm, 20 cm, 30 cm.
The following steps can be used in order to determine the lengths of the sides of a similar triangle that has a perimeter of 26 cm:
Step 1 - The formula of the perimeter of the triangle is given below:
[tex]\rm P = a + b + c[/tex]
where a, b, and c are the length of the sides of the triangle.
Step 2 - Now, determine the perimeter of the triangle whose sides are 15 cm, 20 cm, 30 cm.
P' = 15 + 20 + 30
P' = 65 cm
Step 3 - Now, divide both the perimeters of the triangles, that is:
[tex]=\dfrac{65}{26}[/tex]
= 2.5
Step 4 - So, the side length of the sides of a similar triangle is given below:
[tex]\rm \dfrac{15}{2.5} = 6\;cm[/tex]
[tex]\rm \dfrac{20}{2.5}=8 \;cm[/tex]
[tex]\rm \dfrac{30}{2.5}=12\;cm[/tex]
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