How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table
Answers
We can form an equation for this linear relationship.
The relationship is in the form [tex]y=ax+b[/tex] where
y = number of cookies of 'x' batches
x = number of batches
a = changing rate = 16
b = the number of cookies when the batch is 0
We need to find the value of 'b' and we can achieve this by keep subtracting 16 from 165, which is batch 5 until we get to batch 0.
Batch 5 = 165
Batch 4 = 165 - 16 = 149
Batch 3 = 149 - 16 = 133
Batch 2 = 133 - 16 = 117
Batch 1 = 117 - 16 = 101
Batch 0 = 101 - 16 = 85 ⇒ this is the value of 'b'
So the equation is [tex]y=16x+85[/tex]
We will use this equation to work out the number of cookies if we cook another 6 batches.
6 batches more than batch 9 will give us batch number 15
We have: x=15, a=16, b=85
y = 16(15) + 85 = 325 cookies
Answer:
325 cookies
Step-by-step explanation: I just took the test and got it right.
Related Questions
Jessica attains a height of 4.7 feet above the launch and landing ramps after 1 second. Her initial velocity is 25 feet per second. Find the angle of her launch. a. Which equation can you use with the given information to solve for ?
Answers
Height = 4.7 ft x (1 m/ 3.28 ft) = 1.43 m
Velocity = 25 ft / s x (1 m / 3.28 ft) = 7.62 m/s
The maximum height that can be attained by an object following a projectile path is calculated through the equation,
H = (v₀²)(sin²θ) / 2g
where v₀ is the initial velocity, H is the maximum height and g is the acceleration due to gravity.
Transforming the equation to calculate for θ,
sinθ = sqrt ((H)(2g) /(v₀²))
sinθ = sqrt ((1.43)(2)(9.8)) / (7.62²))
sinθ = 0.76
We calculate for the angle by getting the arcsin.
sin⁻¹ (0.76) = 49.46°
ANSWER: 49.46°
A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 find the radius of the beach ball. use the formula , where a is the surface area and r is the radius of the sphere. 576 in. 48 in. 75 in. 24 in.
Answers
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
help me plox 20 points
Answers
if they were rounded to the tens place
18 would round to 20
16 would round to 20
17 would round to 20
14 would round to 10
so April would be different.
Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry. f(x), g(x), h(x) f(x), h(x), g(x) g(x), h(x), f(x) g(x), f(x), h(x)
Answers
Answer:
f(x), h(x), g(x)
The length of a rectangle is 22 meters longer than the width. if the area is 2626 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
Answers
l*w=2626
Substitute 22w for l, getting 22w^2=2626. Divide by 22 to get 119.36 (and more decimals!), and square root that to get 10.9 (rounded) for the width and 240.4 (rounded) for the length
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
Answers
[tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{x}\implies tan\left( -\frac{3\pi }{4} \right)=\cfrac{y}{-1} \\\\\\ -1\cdot tan\left( -\frac{3\pi }{4} \right)=y\implies -1\cdot \cfrac{sin\left( -\frac{3\pi }{4} \right)}{cos\left( -\frac{3\pi }{4} \right)}=y \\\\\\ -1\cdot \cfrac{-1}{-1}=y\implies -1[/tex]
The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.
Given :
The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.
The following steps can be used in order to determine the point on the terminal side:
Step 1 - Write the given expression.
[tex]\theta = -\dfrac{3\pi}{4}[/tex]
Step 2 - The value of the trigonometric function is given by:
[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]
Step 3 - The trigonometric function can also be written as:
[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]
Step 4 - Substitute the value of 'x' in the above expression.
y = -1
So, the point on the terminal side is (1,-1).
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A tree grows 1 3/4 feet per year. How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?
Answers
[tex]\bf 37-21\frac{1}{4}\implies 37-\cfrac{21\cdot 4+1}{4}\implies 37-\cfrac{85}{4}\impliedby LCD~is~4 \\\\\\ \cfrac{148-85}{4}\implies \cfrac{63}{4}[/tex]
so hmmm now, its growth rate is [tex]\bf 1\frac{3}{4}\implies \cfrac{1\cdot 4+3}{4}\implies \cfrac{7}{4}[/tex]
so.... the tree grows 7/4 in 365 days( a year ), how many days does it take it to get to 63/4 feet?
[tex]\bf \begin{array}{ccll} \stackrel{growth}{feet}&\stackrel{time}{days}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{7}{4}&365\\\\ \frac{63}{4}&d \end{array}\implies \cfrac{\frac{7}{4}}{\frac{63}{4}}=\cfrac{365}{d}\implies \cfrac{7}{4}\cdot \cfrac{4}{63}=\cfrac{365}{d} \\\\\\ \cfrac{28}{252}=\cfrac{365}{d}\implies d=\cfrac{252\cdot 365}{28}\implies d=\cfrac{91980}{28}\implies \boxed{d=3285}[/tex]
Can someone simplify 2y-3x^2+6x^2-3y ?
Answers
Bring like terms together:-
6x^2 - 3x^2 + 2y - 3y
= 3x^2 - y <----- Answer
3x^2-y
Find the selling price of an item listed at $400 subject to a discounted series of $25%, 10%, and 5%
A. $256.50
B. $270.00
C. $225.00
D. $300.00
Answers
$300 - ($300 x 0.10) = $270
$270 - ($270 x 0.05) = $256.50
answer
A. $256.50
Answer:
Selling price of an item is $256.50 (A).
Step-by-step explanation:
Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .
To find : Find the selling price of an item.
Formula used : Selling price = marked price - discount.
Solution : We have an item listed at = $400.
Discount percentage = $25% , $10% , $5.
Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.
Selling price = $400-100 = $300.
Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.
Selling price = $300-30 = $270.
Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.
Final selling price = $270-13.50 = $256.50.
Therefore, Selling price of an item is $256.50 (A).
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.
Answers
2) Call x the length of the sides of the squares cut off.
3) The base of the box will have dimensions: (13 - 2x) and (8 - 2x)
4) The height of the box will be x
5) The volume of the box will be the area of the base times the height:
Volume = (13 - 2x)(8 -2x)x = (4x^2 - 42x + 104)x = 4x^3 - 42x^2 + 104x
6) The maximum volume is calculated by finding the point where the derivative of the volume is zero =>
d (volume) / dx = 12x^2 - 84x + 104 = 0
7) Solve the quadratic equation 12x^2 - 84x + 104 = 0
=> 4(3x^2 - 21x + 26) = 0
=> 3x^2 - 21x + 26 = 0
=> 3 (x^2 - 7x) + 26 = 0
=> 3 [(x - 7/2)^2 - (7/2)^2] + 26 = 0
=> 3 (x - 7/2)^2 - 3* 49/4 + 26 = 0
=> 3 (x - 7/2)^2 = 3*49/4 - 26
=> (x -7/2)^2 = (49/4 - 26/3)
=> x = 7/2 +/- √(49/4 - 26/3)
x = 7/2 + √3.583 and x = 7/2 - √3.583
x = 5.393 and x = 1.607
=> Volume =
1) 4(5.393)^3 - 42(5.393)^2 + 104(5.393) = -33.26 ---> it does not have physical meaning
2) 4(1.607)^3 - 42(1.607)^2 + 104(1.607) = 75.27 ---> this is the answer
Answer: 75.27 in^3
An ice cream store sells 2 2 drinks, in 3 3 sizes, and 8 8 flavors. in how many ways can a customer order a drink?
Answers
If an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It given that, An ice cream store sells 2 drinks, in 3 sizes, and 8 flavors.
We have to find the number of ways can a customer order a drink,
It is obtained by multiplying all the possible cases for that event, Multiplication is one type of arithmetic operation. There are basically four types of arithmetic operations.
=2×3×8
=48
Thus, if an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
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Use basic identities to simplify the expression. sin^2θ + tan^2θ + cos^2θ
Answers
so it simplifies to 1 + tan^2 theta
and this = sec^2 theta
True or false an inscribed angle is formed by two radii that share an endpoint
Answers
True or false an inscribed angle is formed by two radii that share an endpoint
the correct answer is : FALSE
Answer:
The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
Step-by-step explanation:
Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.
The inscribed angle is explained with the help of a diagram below :
In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.
Thus, the inscribed angle is not formed with the help of radii that share a common end point.
Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
please help me idk how to do this at all I've been stuck on it for awhile.
Answers
(x,y)
we are given x=2
find what y is when x=2
subsitute 2 for x
y=2x+5
y=2(2)+5
y=4+5
y=9
so the blank is 9
when numbers are in parenthesis the first number is x the second is y
(x,y)
sine they give you (2, blank)
2 = x so replace x in the equation with 2
so y=2x+5 becomes y=2(2)+5
so y = 2*2+5 = 9
y=9
so it should be (2,9)
Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12
Answers
x + y ≥ 4
2x + 3y < 12
For the first step, let's disregard the inequality symbols and take it like any conventional algebraic equation. This is to be able to graph the lines on a Cartesian planes first.
For the first equation, x+y=4. To find the x- and y-intercepts, let the other variable be 0. For example,
x-intercept:
x+0=4
x=4
y-intercept:
0+y=4
y=4
Therefore, you can graph the equation line by plotting the intercepts (4,0) and (0,4) and connecting them together. The same thing is done to the second equation:
x-intercept:
2x + 0 = 12
x=12/2=6
y-intercept:
0 + 3y =12
y= 12/3 = 4
Therefore, you can graph the equation line by plotting the intercepts (6,0) and (0,4) and connecting them together. The graph is shown in the left side of the picture.
The next step would be testing the inequalities. Let's choose a point that does not coincide with the lines. That point could be (-5,-1).
x + y ≥ 4
-5 + -1 ≥4
-6 ≥ 4 --> this is not true. Thus, the solution of the graph must not include the area of this point. It includes everything to the right of the line denoted by the blue-shaded region.
2x + 3y < 12
2(-5) + 3(-1) <12
-13 < 12 ---> this is true. Thus, the solution would include this point. That includes all points to the left of the orange line denoted by the orange-shaded the region.
The region where blue and orange overlap is the solution of the system of equations, denoted by the green-shaded region.
Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If the soccer player taking four penalty shots is simulated 2500 times, in about how many of the simulations would you expect at least one missed shot?
Answers
100 -22.4 = 77.6%
So the number of simulations that he/she will miss at least one shot in 2500 simulations would be...
2500 x 77.6% =
2500 x .776 = 1940
1940 ~~~~~~~~~~~~ APEX
Find the slope in line perpendicular x-y=16
Answers
X - y = 16
-y = -x + 16
So slope = - 1 / 1
You and six friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly distributed back to each person. Find the probability that everyone gets back his or her own name.
Answers
Answer with explanation:
Total number of different candidates who are playing the game=7
Suppose, Seven candidates are represented by ={A,B,C,D,E,F,G}
Total Possible Outcome =7
→Probability that , "A" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{7}[/tex]
→Now, 6 candidates are left.
Probability that , "B" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{6}[/tex]
→Now, 5, candidates are left.
Probability that , "C" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{5}[/tex]
→Now, 4 candidates are left.
Probability that , "D" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{4}[/tex]
→Now, 3 candidates are left.
Probability that , "E" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{3}[/tex]
→Now, 2 candidates are left.
Probability that , "F" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{2}[/tex]
→Now, a single candidates is left.
Probability that , "G" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{1}=1[/tex]
Required Probability
[tex]=\frac{1}{7} \times\frac{1}{6} \times\frac{1}{5} \times\frac{1}{4} \times\frac{1}{3} \times\frac{1}{2} \times 1\\\\=\frac{1}{5040}[/tex]
A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=140-8t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answers
The time would be 2.71 seconds after the ball is thrown does it hit the ground.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s.
The ball's height h (in feet) after t seconds is given by the following.
⇒ h = 140-8t - 16t²
h = 0 at the ground.
We divide both sides of the equation by (-8) to yield:
⇒ 0 = 2t² + t - 17.5
where a = 2, b= 1, c = -17
[tex]t = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t = \dfrac{-1\pm\sqrt{2^2-4\times2\times-17.5}}{2\times2}[/tex]
t = [-1 ± √141] / (4)
t = 2.71 and -3.21
For this problem, time can only be positive, so ignore the negative solution.
Therefore, the time would be 2.71 seconds after the ball is thrown does it hit the ground.
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(02.01 LC)
Figure ABCD is transformed to figure A′B′C′D′:
Which angle in Figure A′B′C′D′ is equal to Angle CDA.?
Angle D prime A prime B prime.
Angle A prime B prime C prime.
Angle B prime C prime D prime.
Angle C prime D prime A prime.
Answers
Answer:
I think it is Angle B prime C prime D prime
Step-by-step explanation:
A'B'C'D' is a translation so they are congruent.So the figure B'C'D' is congruent or equal to BCD. Please let me know if i'm right
slope of -8 and Y intercept of (0, 12) in slope intercept form.
Answers
Kenji buys 3 yards of fabric for 7.47$. Then he realizes that he needs 2 more yards. How much will the extra fabric cost?
Answers
7.47 / 3 = 2.49
Now that we know that each yard costs $2.49, we can multiply it by the number of yards you need to buy (two).
2 • 2.49 = 4.98
Your total for two yards of fabric is $4.98
In the game of roulette, a player can place a $99 bet on the number 3333 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3333, the player gets to keep the $99 paid to play the game and the player is awarded an additional $315315. otherwise, the player is awarded nothing and the casino takes the player's $99. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose? note that the expected value is the amount, on average, one would expect to gain or lose each game.
Answers
Find an exact value. sin(17pi/12)
a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4
Answers
feel free to ask if you have any doubts.
The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric function is given in the question, as follows:
sin(17π/12)
To find the value of sin(17π/12), we can use the following trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
In this case, we can write:
sin(17π/12) = sin(π/3 + π/4)
We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.
Therefore, we can use the above identity to get:
sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6/4) + (√2/4)
= (√6 + √2)/4
So the answer is option (c): √6 + √2 / 4.
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Hey there! I would like some help please :) Thanks!
Answers
Congruent triangles have exactly the same three angles, so ∠D = ∠B.
You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation. in standard form that represents your distance from home y after x hours.
b. find the y-intercept of the graph. what does this represent?
c. find the x-intercept of the graph. what does this represent?
Answers
6x+y=9
b) from the first, we had it in slope intercept form, mx+b where b is the y-intercept. y=-6x+9
So the y-intercept is the point (0,9) which represents the starting distance before you start biking. You start being 9 miles from your house.
c) The x intercept occurs when y=0 so:
y=9-6x, so if y=0
0=9-6x
6x=9
x=9/6
x=1.5
This represent the time when you will arrive home and the total time that has elapsed to get there.
The distance and speed are illustrations of linear equations
The standard form is [tex]\mathbf{6x + y = 9}[/tex]The y-intercept is 9The x-intercept is 1.5The given parameters are:
[tex]\mathbf{Rate = 6}[/tex]
[tex]\mathbf{Initial = 9}[/tex]
(a) The standard equation
Because the distance reduces with time, the equation is:
[tex]\mathbf{y = Initial-Rate \times x}[/tex]
This gives
[tex]\mathbf{y = 9 - 6\times x}[/tex]
[tex]\mathbf{y = 9 - 6x}[/tex]
Add 6x to both sides
[tex]\mathbf{6x + y = 9}[/tex]
(b) The y-intercept
This is the initial distance away from home.
So, the y-intercept is 9
(c) The x-intercept
Set y to 0, to calculate the x-intercept
[tex]\mathbf{6x + y = 9}[/tex]
[tex]\mathbf{6x + 0 = 9}[/tex]
[tex]\mathbf{6x = 9}[/tex]
Divide both sides by 6
[tex]\mathbf{x = 1.5}[/tex]
This is the initial time away from home.
So, the x-intercept is 1.5
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Larry travels 60 miles per hour going to a friend’s house and 50 miles per hour coming back, using the same road. he drove a total of 5 hours. what is the distance from larry’s house to his friend’s house, rounded to the nearest mile?
Answers
V2=50
T=t1+t2=5. 5-t2=t1
60×(5-t2)=50×t2
300-60×t2=50×t2
300=50×t2+60×t2
300=t2×(50+60)
300=t2×110
300/110=t2
S=50×300/110
Final answer:
To find the distance from Larry's house to his friend's house, we use the relationship between distance, speed, and time for his trip to and from his friend's house, taking into account the different speeds and total travel time of 5 hours.
Explanation:
The student's question asks to find the distance from Larry's house to his friend's house given his speed and total travel time in both directions. To solve this problem, we use the formula distance = speed × time. Let's call the distance one way d, the time to travel to the friend's house t1, and the time to travel back t2. Larry's speed going to the friend's house is 60 miles per hour and coming back is 50 miles per hour. The total travel time is 5 hours.
So for the trip to the friend's house we have:
d = 60 × t1
And for the trip back:
d = 50 × t2
Since the total travel time is 5 hours:
t1 + t2 = 5
Substituting the expressions for d from the first two equations into the third, we get:
60t1 + 50t2 = 60(5)
Using the fact that t1 + t2 = 5, we solve for either variable, say t1, which gives us t2 as well. After finding t1 and t2, we plug either of those back into the original distance equations to find d, which will be the distance from Larry's house to his friend's house. The answer should be rounded to the nearest mile.
A 31-in. television has a 31 in. diagonal and a 18 in. width. what is the height of the 31-in. television?
Answers
[tex]height = \sqrt{31^2-18^2}= \sqrt{961-324}= \sqrt{637}\approx25.24 \ in[/tex]
Use the table to determine the appropriate model of the function, x 1 2 3 4 5 f(x) 15 12 9 6 3 linear quadratic cubic exponential
Answers
The actual line is just f(x)= -3x+18
The appropriate model of the function is:
Linear model
Step-by-step explanation:We are given a table of values as:
x f(x)
1 15
2 12
3 9
4 6
5 3
Clearly we could observe that with each increasing value of x the value of function decreases by 3.
This means that the range of change is constant.
Hence, the relation is linear ( as the rate of change is constant )
Also, the equation that models this data set is given by:
[tex]y=f(x)=18-3x[/tex]
A quick-loan company charges an 18% fee on any loan that is paid up to one week late. A woman borrowed $400 and paid the loan back 3 days late. What is the total she has to pay, including any fee?
Answers
fee percent: 18 %
fee = 18% * $400 = 0.18 * $400 = $72
Total payment = amount borrowed + fee = $400 + $72 = $472.
Answer: $472.