Adriana made 30 pet collars to bring to the pet fair. She wants to display 3 pet collars on each hook. How many hooks will Adriana need to display all 30 pet collars
Answer:
10 hooks!
Step-by-step explanation:
if Adriana has 30 and wants to display 3 on each hook you would have to divide 30 by 3.
Item 9 A group of tourists spends $156 to rent snorkels and fins. A total of 15 snorkels and 18 pairs of fins are rented. Renting a snorkel costs four times as much as renting a pair of fins. How much does it cost to rent a snorkel?
Answer:
$8
Step-by-step explanation:
A group of tourists spends $156 to rent snorkels and fins.
They rented 15 snorkels and 18 pairs of fins.
Renting a snorkel costs four times as much as renting a pair of fins.
Let us assume that the rental cost of a pair of fins is x, so the rental cost of snorkel will be 4x.
Then total cost of 15 snorkels and 18 pairs of fins will be,
[tex]=15(4x)+18x[/tex]
[tex]=60x+18x[/tex]
[tex]=78x[/tex]
But it is given as $156, so
[tex]\Rightarrow 78x=156[/tex]
[tex]\Rightarrow x=2[/tex]
Therefore, the rental cost of a pair of fins is $2 and cost of snorkel is [tex]2\times 4=\$8[/tex]
2. Use a graph to find the solution.
You want to set up an aquarium and need to determine what size tank to buy...
Answer:
The correct option is 3. Capacity of smallest tank is 15-gallons.
Step-by-step explanation:
The graph shows the relationship between capacity of tank and combined length of fish it can hold.
The line passing through (0,1) and (1,2).
Slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{1-0}=1[/tex]
Slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of the line is 1 and the y-intercept is 1, therefore the equation of line is
[tex]y=x+1[/tex] ..... (1)
If we want four 2-inch platys, three 1-inch guppies and a 3-inch loach, then the combined length of fish is
[tex]4\times 2+3\times 1+1\times 3=8+3+3=14[/tex]
Therefore the combined length of fish is 14.
Put x=14 in equation 1.
[tex]y=14+1=15[/tex]
Therefore, the capacity of smallest tank is 15-gallons and option 3 is correct.
Answer: got answer from someone, 12 and 14 were wrong.
Step-by-step explanation:
connexus unit 8 lesson 1 PRACTICE!
1) B
2) C
3) A
4) C
5) B
6) A
7) D
8) A
9) D
10) A
11) A
12) not C
13) D
14) not C
15) B
What is the midpoint of a segment whose endpoints are (9, −9) and (−3, 7)?
Answer:
The midpoint is (3,-1)
Step-by-step explanation:
The midpoint of a segment is found by adding the ends together and dividing by 2
midpoint = (x1+x2)/2 , (y1+y2)/2
=(9+-3)/2 , (-9+7)/2
= 6/2, -2/2
=3,-1
if f(x)=x^2-1 what is the equation for f^-1(x)
Answer:
see below
Step-by-step explanation:
Swap y and x, then solve for y.
Original:
... y = f(x) = x² -1
Swap y and x:
... x = y² -1
Add 1:
... x + 1 = y²
Take the square root:
... ±√(x+1) = y . . . . . matches the 3rd selection
Rewrite as the inverse relation: (not a function)
... f^-1(x) = ±√(x+1)
_____
Comment on the graph
The attached graph shows the function f(x) in red, and the inverse relation g(x) in blue. You will note that g(x) is double-valued for most values of x, so is not a function. The function and its inverse relation are mirror images of each other in the line y=x. (That is, swapping y and x changes the function to its inverse, and vice versa.)
The inverse function of f(x)=x^2-1, denoted as f^-1(x), is calculated as f^-1(x) = sqrt(x+1), if x>=0 and f^-1(x) = - sqrt(x+1), if x<0.
Explanation:To find the inverse of the function f(x)=x^2-1, denoted as f^-1(x), first replace f(x) with y, so the equation becomes y = x^2 - 1. The next step is to swap x and y, giving you x = y^2 - 1. Now, you should solve this new equation for y, resulting in y = sqrt(x+1). However, considering the domain, we have to separate into positive and negative square roots. Therefore, the complete inverse function is f^-1(x) = sqrt(x+1), if x>=0 and f^-1(x) = - sqrt(x+1), if x<0.
Learn more about Inverse Function here:https://brainly.com/question/35509335
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Which angles are corresponding angles
Answer:
Step-by-step explanation:
corresponding angles are congruent to eachother for example 1&3, 5&7, 2&4, 8&6
Answer:
Option B, C, D are the correct options
Step-by-step explanation:
When two parallel lines are intersected by a transverse then two angle which are relatively at the the same position are called as corresponding angles.
As given in the picture attached, ∠1 and ∠2 are corresponding angles.
Similarly, ∠3 and ∠4 re corresponding angles.
Now we come to our question. In this question corresponding angles are
1) 2 and 4
2) 6 and 8
3) 1 and 3
4) 5 and 7
Therefore, Options. B, C and D are the correct options.
A student multiplied –8 × 334 as shown. One step is missing. Which is the missing step? –8 × 334 = ? = –8 × 3 + (–8) × 34 = –24 + −8 × 324 = –24 + −244 = –24 + (–6) = –30
Answer:
–24 + −8 × 324
Step-by-step explanation:
Well, if you go through the answer choices, there is only one that gives you the correct answer. The product is -2672, and the only answer choice that this satisfies is the second one.
Answer:
It's C
Step-by-step explanation:
A horseback riding trail is 1 mi 40.8 ft long. How long is the trail in yards, feet, and inches?
Answer: 1773.6 yards 5320.8 feet 64324.8 inches
Step-by-step explanation:
1 mile in yards = 1760 40.8 feet in yards = 13.6 1760 + 13.6 = 1773.6 yards
1 mile in feet = 5280 + 40.8 = 5320.8 feet
1 mile in inches = 63360
40.8 feet in inches = 964.8
63360 + 964.8 = 64324.8 inches
hope this helps :)
Simplify the expression
Answer:
729
Step-by-step explanation:
[(-1)^3]^2 /[(-3)^-3]^2
= 1 * [(-3)^3]^2
= 1 * 729
= 729
Answer:
729
To solve this, we need to start on the inside and work out; solving one part at a time.
[{(-1)^3 / (-3)^-3}]^2
1. (-1)^3 = -1
2. (-3)^-3 = - 1/27
3. (-1) / (- 1/27) = 27
4. 27^2 = 729
Find the square root of these numbers to the nearest tenth.
72 =
32 =
481 =
Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangle. What are the possible measures of the angle opposite side AB? Please explain the process.
Answer:
C = 45.8 or C = 117.69
Step-by-step explanation:
Remark
Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.
Given
AB = 15
<A = 35
point C opposite line AB such that CB = 12 These givens give a unique answer.
Solution
Sin(35) / 12 = Sin(C) / 15 Multiply both sides by 15
15*Sin(35) / 12 = Sin(C) Find 15/12
1.25*sin(35) = Sin(C) Write Sin(35)
1.25*0.5736 = Sin(C) Multiply the left
0.71697 = Sin(C) Take the inverse Sin
C = 45.805 degrees This is the angle opposite AB
Angle B = 180 - 35 - 45.805 = 99.2
Ambiguous Case
If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.
I will set up the Sin law for you, and let you solve it
Sin(B) / 12 = Sin(35)/15
When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees
C = 180 - 35 - 27.31 = 117.69
So that's two values that C could have. I think that's all given these conditions.
Two Cases or None
<A = 35 degrees
AC = 15
CB = 12
This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.
Camp Oakes gets 32 juice boxes of orange juice and 56 boxes of apple juice each shelf in the cup board can hold eight boxes of juice what is the least number of cells needed for all the juice box
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answer:
Width of rectangular storage room= 5 feet.
Step-by-step explanation:
Let x be the width of storage room.
We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.
We are also given that the area of the room is 40 square feet.
Since the area of a rectangle is length times width.
[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]
Let us substitute our given values in area formula.
[tex]40=x*(x+3)[/tex]
Upon distributing x we will get,
[tex]40=x^2+3x[/tex]
[tex]x^2+3x-40=0[/tex]
Now let us factor out our quadratic equation using splitting the middle term.
[tex]x^2+8x-5x-40=0[/tex]
[tex]x(x+8)-5(x+8)=0[/tex]
[tex](x+8)(x-5)=0[/tex]
[tex]x+8=0[/tex] or [tex]x-5=0[/tex]
[tex]x=-8[/tex] or [tex]x=5[/tex]
Since width can not be negative, therefore, the width of rectangle will be 5 feet.
Let us verify our answer.
Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.
Given: Area=40 square feet.
5*8=40.
Hence, width of rectangular storage room is 5 feet.
Carmen sells electronics. She made a 10% commission on every dollar sale that she makes. One month Carmen got a commission check for $2500. What were her sales in dollars that month.
Answer: 25000
Step-by-step explanation:
.1=10%
So, 2500/.1=25000
25000*.1=2500
Help me with these math questions.. WITH SCREENIES
Answer: 3
Step-by-step explanation:
log₇343 = x
343 = 7ˣ
7³ = 7ˣ
3 = x
******************************************
Answer: 1950
Step-by-step explanation:
s = r θ
325π = r * 30 * [tex]\frac{\pi}{180}[/tex]
325 = r * [tex]\frac{\pi}{6}[/tex]
6(325) = r
1950 = r
******************************************
domain: x is All Real Numbers --> (-∞, ∞)
range: y > 0 --> (0, ∞)
y-intercept: when x = 0, y = e² --> e²
horizontal asymptote: since y ≠ 0, then H.A. is --> y = 0
Real estate values in a town are increasing at a rate of 9% per year.
Mr. Townsend purchased a building for $375,000 in 2010.
How much can he expect to sell the building for in 2020, assuming this trend continues?
Enter your answer in the box.
Round to the nearest whole dollar.
$
Answer:
In 2020 building price is $ 887761
Step-by-step explanation:
Time = 2020 - 2010 = 10 years
In 2011 building price = 375000 × [tex]\frac{9}{100}[/tex] + 375000 =$408750
In 2012 building price = 408750 × [tex]\frac{9}{100}[/tex] + 408750 =$445537.5
In 2013 building price = 445537.5 × [tex]\frac{9}{100}[/tex] + 445537.5 =$485635.88
In 2014 building price = 485635.88 × [tex]\frac{9}{100}[/tex] + 485635.88 = $529343.11
In 2015 building price = 529343.11 × [tex]\frac{9}{100}[/tex] + 529343.11 = $576983.99
In 2016 building price = 576983.99 × [tex]\frac{9}{100}[/tex] + 576983.99 =$628912.55
In 2017 building price = 628912.55 × [tex]\frac{9}{100}[/tex] + 628912.55 =$685514.68
In 2018 building price = 685514.68 × [tex]\frac{9}{100}[/tex] + 685514.68 = $747211
In 2019 building price = 747211 × [tex]\frac{9}{100}[/tex] + 747211 =$814459.99
in 2020 building price = 814459.99 × [tex]\frac{9}{100}[/tex] + 814459.99 =$887761.38 ≈ $887761
Second method
Total time(t) = 10 years
Rate(r) = 9%
Principal value = $375000
Now,
selling price (in 2020) = principal value [tex](1+\frac{r}{100}) ^{t}[/tex]
= 375000 [tex](1+\frac{9}{100} )^{10}[/tex] = $887761.38 ≈$887761
Mrs. Johnson is 3 times as old as her son. Ten years ago she was 5 times as old as her son was then. Find each of their ages
Answer:
her son is 20, Mrs. Johnson is 60
Step-by-step explanation:
if her son is x, Mrs. Johnson is 3x,
Ten years ago,
her son is x-10, Mrs. Johnson is 3x-10,
so:
3x-10=5(x-10)
x=20
The price of a cantaloupe at a fruit stand goes up 4 cents each month. The first month the stand was open, a cantaloupe cost $1.25.
What will the cost of a cantaloupe be in the 40th month?
A. $157.25
B. $16.85
C. $3.35
D. $2.81
Answer:
D. $2.81
Step-by-step explanation:
The statement says that the price of a cantaloupe goes up 4 cents each month and that the cost of the cantaloupe was $1.25 on the first month. Tto determine the cost in the 40th month, you have to multiply 4 cents for 39 months as the price for the first month was given and then you have to add this with the price for the first month:
0,04*39= 1.56
1.56+1.25= $2.81
The price in the 40th month is $2.81.
Use the graph of f(x) = |x(x2 − 1)| to find how many numbers in the interval [0.5, 0.75] satisfy the conclusion of the Mean Value Theorem.
Answer:
1 time
Step-by-step explanation:
f(x) = |x(x^2 − 1)|
The mean value theorem states
f'(c) = f(b) -f(a)
-------------
b-a
b = .75
a = .5
f(b) = abs(.75 * (.75^2 -1)) = abs (.75*(-.4375))=abs(-.328125)
= .328125
f(a) = abs(.5 * (.5^2 -1)) = abs(.5*(-.75))=abs(-.375) = .375
.328125- .375
f'(c) = -------------------------------------------------
.75-.5
f'(c) = -.1875
Please help Mrs.Johnson spend $611 buying lunch for 78 students. If all lunches cost the same, about how much did she spend on each lunch
Answer:
She spend 7.33 on each lunch.
Step-by-step explanation:
We have been given that Mrs. Johnson spend $611 buying for 78 students
If each lunch cots the same we have to find how much did she spend on each lunch:
We can calculate the price of each lunch by dividing the total cost she spend upon the lunch she bought.
let the cost of each lunch be x
Hence, [tex]x=\frac{611}{78}=7.33[/tex]
The sum of two numbers is 37
and the difference is 13
. What are the numbers?
Answer:
25, 12
Step-by-step explanation:
let x represent one number and y represent the other number
x+y=37 (sum is addition)
x-y=13 (difference is subtraction)
Im solving using the substitution method
x-y=13 add y to both sides to get x by itself
x=13+y
13+y+y=37 substitute x for the solution above in the other equation and simplify
2y=24
y=12
plug in y into one of the equations
x+12=37 subtract 12 from both sides
x=25
Find the domain of the following graph:
−7 < x ≤9
−7 < y ≤ 9
−7 < x ≤5
−7 < y ≤ 5
Answer:
[tex]-7<x\leq 9[/tex]
Step-by-step explanation:
The domain is the set of all x-values. We can find the domain by finding the left boundary of the graph (the furthest left x-value) and then the right boundary (the furthest right x value).
The furthest left x-value is -7. Notice it has a large open circle here that is not filled in. This means the function does not include -7 but includes numbers very close to it like-6.999999..... We sue use an inequality sign without an equal to to write -7. x >-7.
The furthest right x value is 9. It has a closed circle or "filled in" circle so we write with an equal to sign. [tex]x\leq 9[/tex].
We combine the two into [tex]-7<x\leq 9[/tex].
A 25-foot ladder is leaning against the side of a house. The top of the ladder is 20 feet above the ground. To the nearest degree, find the angle of elevation between the ground and the ladder.
To find the angle of elevation between the ground and the ladder, we can use the tangent function and the given measurements. The angle is approximately 39.8 degrees.
Explanation:To find the angle of elevation between the ground and the ladder, we can use trigonometry. Since the top of the ladder is 20 feet above the ground and the ladder is 25 feet long, we can use the opposite and adjacent sides of a right triangle. The trigonometric function that relates these sides is the tangent function:
tan(angle) = opposite/adjacent
Plugging in the known values, we get: tan(angle) = 20/25
Using a calculator to find the inverse tangent (arctan) of both sides, we get the angle to be approximately 39.8 degrees to the nearest degree.
Shiloh opens a savings account in which interest is compounded annually. The balance in the account is given by the following exponential expression, where t represents the time in years. Which statement correctly interprets the given expression? 125(1.025)t
A. Shiloh initially invested $125, which grows annually at a rate of 2.5%.
B. Shiloh initially invested $125, which grows annually at a rate of 1.025%.
C. Shiloh initially invested $1,025, which grows annually at a rate of 12.5%.
D. Shiloh initially invested $1,025, which grows annually at a rate of 1.25%.
Help asp
Answer:
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
Step-by-step explanation:
The balance in the account is given by the following exponential expression,
[tex]125(1.025)^t[/tex]
Exponential growth formula is
[tex]A= P(1+r)^t[/tex]
Where P is the initial amount invested
r is the rate of interest
When we compare the formula with given expression , we can see that we have 125 in the place of P
So initial amount invested is $125
Now we find out 'r'
1+ r = 1.025
Subtract 1 on both sides
r= 0.025
To get percentage we multiply by 100
0.025 * 100 = 2.5%
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
In the pully system shown in this figure, MQ = 10 in, NP = 3in and QP=24in. Find MN
a. 25
b. 26
c. 27
d. 28
Answer:
The correct option is a. The length of MN is 25.
Step-by-step explanation:
Given information: MQ = 10 in, NP = 3 in and QP=24 in.
If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is
[tex]l=\sqrt{d^2-(r_1-r_2)^2}[/tex]
[tex]24=\sqrt{d^2-(10-3)^2}[/tex]
Square both sides.
[tex]576=d^2-49[/tex]
[tex]625=d^2[/tex]
Take square root both sides.
[tex]25=d[/tex]
Therefore length of MN is 25 and option a is correct.
To find MN in the given pulley system, we can use the concept of similar triangles.
Explanation:In the pulley system shown in the figure, we can use the concept of similar triangles to find MN. The triangle MQP is similar to the triangle MNP. This means that the ratios of their corresponding sides are equal.
So we have:
MQ/MP = NP/MN
Substituting the given values:
10/24 = 3/MN
Cross multiplying:
10 * MN = 24 * 3
MN = (24 * 3) / 10
MN = 72/10
MN = 7.2 inches
Therefore, the length MN is approximately 7.2 inches.
How many 3 over 8 pound bags of trail mix can be made from 6 and 3 over 8 pounds of trail mix ? Write a division expression
Answer:
[tex]\frac{\frac{51}{8}} {\frac{3}{8}}[/tex]
17 bags.
Step-by-step explanation:
We are asked to find the number of bags with weight 3/8 pound can be made from [tex]6\frac{3}{8}[/tex].
To find the number of
[tex]\text{Number of bags that can be made from available mix trail}=6\frac{3}{8}\div \frac{3}{8}[/tex]
Convert mixed fraction into improper fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\div \frac{3}{8}[/tex]
Since we know that dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of 2nd fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\times \frac{8}{3}[/tex]
After cancelling out 8 from numerator and denominator we will get,
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{3}[/tex]
[tex]\text{Number of bags that can be made from available mix trail}=17[/tex]
Therefore, 17 bags each of weight 3/8 pounds can be made from [tex]6\frac{3}{8}[/tex] pounds of mix trail.
A flagpole casts a 16-foot shadow at the same time a 4-foot pole casts a 5-foot shadow. How tall is the flagpole?
Set up a proportion:
The 4 foot pole casts a 5 foot shadow is written as 4/5
Let the height of the flagpole = x.
The flag pole casts a 16 foot shadow so it is written as X/16
Now set the two proportions equal to each other:
4/5 = X/16
Solve for X by cross multiplying:
5X = 64
Divide both sides by 5:
X = 64/5
X = 12.8
The flag pole is 12.8 feet tall.
Based on the information the tall of the flagpole is 12.8 feet tall .
Tall of the flagpoleSet up a proportion and let x = Height of the flagpole
4/5 =16/x
Solve x by cross multiplying
5x = 64
Divide both sides by 5x
x= 64/5
x=12.8 feet tall
Inconclusion the tall of the flagpole is 12.8 feet tall .
Learn more about tall of the flagpole here:https://brainly.com/question/317739
The cost of 5 cans of dog food is $4.35.At the price,how much do 11 cans of dog foo cost.
Answer:
11 cans cost $9.57
Step-by-step explanation:
There are two ways of doing this, one being the longer and the other being the shorter.
The shorter one is simply multiplying the number by the new number over 5:
[tex]4.35 * \frac{11}{5}[/tex]
This works because this finds the amount the 5 has increased from 5 to 11 and muliplies the number by this.
[tex]4.35 * \frac{11}{5}[/tex] = 9.57
So 11 cans cost $9.57
HELP ASAP 98 points and brainliest
Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Answer:
The correct option is 1.
Step-by-step explanation:
Statement 1: AB is parallel to DC and AD is parallel to BC.
Reason: Definition of parallelogram
Statement 2: ∠1 = ∠2, ∠3 = ∠ 4.
Reason: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.
Statement 3: BD = BD.
Reason: Reflexive Property.
Statement 4: ΔADB≅ΔCBD.
Reason: If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.
Statement 5: AB = DC, AD = BC.
Reason: Corresponding parts of congruent triangles are congruent.
The missing information for reason 2 in the chart is alternate interior angles .
Therefore the correct option is 1.
Brandon buys a radio for 43.99 in a state where sales tax is 7%.What is the total brandon pays for the radio