Cole is saving money at a constant rateSuppose he initially has $190 saved, and after 3 months, he has $265 saved. Which of these expresses the rate at which Cole is saving?
Answers
Answer:
His unit rate per month is 25 dollars
Step-by-step explanation:
Cole has saved 25 dollars per month. by subtracting 190 from 265 you are left with 75. when left with 75 you can divide by 3 for the the 3 months hes been saving his money. 75 divided by 3 is 25.
Related Questions
2.5 kg rice at $1.90 per kg and 1.5 kg cornmeal at $2.92 per kg
Answers
Answer: 2.5kg rice costs $4.75 and 1.5kg cornmeal costs $4.38
Rice:
1kg costs $1.90
2.5kg will cost 1.90 * 2.5
--> $4.75
Cornmeal:
1kg costs $2.92
1.5kg costs 2.92*1.5
--> $4.38
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
Answers
Answer:
Hope this helps ^^
Step-by-step explanation:
Part A: To determine the values where the pogo stick's spring will be equal to its non-compressed length, we set the function equal to zero:
f(θ) = 2cos(θ) + √3
To find the values of θ that satisfy this equation, we solve:
2cos(θ) + √3 = 0
Subtracting √3 from both sides:
2cos(θ) = -√3
Dividing by 2:
cos(θ) = -√3/2
Using the unit circle, we can find the angles where cosine is equal to -√3/2. These angles are π/6 and 11π/6.
Therefore, the values where the pogo stick's spring will be equal to its non-compressed length are θ = π/6 and 11π/6.
Part B: If the angle θ is doubled, that is, θ becomes 2θ, we substitute 2θ into the original function:
f(2θ) = 2cos(2θ) + √3
Using the double angle formula for cosine:
f(2θ) = 2(2cos²(θ) - 1) + √3
Expanding and simplifying:
f(2θ) = 4cos²(θ) - 2 + √3
Comparing this to the original function f(θ), we see that the new function has the same form but with different coefficients. The solutions for f(2θ) in the interval [0, 2π) will be the same as the solutions for f(θ), but they will occur at double the angles. In other words, if θ is a solution for f(θ), then 2θ will be a solution for f(2θ).
Part C: To find the times when the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal, we set the two functions equal to each other:
f(θ) = g(θ)
2cos(θ) + √3 = 1 - sin²(θ) + √3
Rearranging the equation:
sin²(θ) + 2cos(θ) = 0
Using the Pythagorean identity sin²(θ) = 1 - cos²(θ), we substitute:
1 - cos²(θ) + 2cos(θ) = 0
Rearranging and simplifying:
cos²(θ) - 2cos(θ) + 1 = 0
Factoring:
(cos(θ) - 1)² = 0
Taking the square root:
cos(θ) - 1 = 0
cos(θ) = 1
This occurs when θ is a multiple of 2π.
Therefore, the lengths of the springs from the original pogo stick and the toddler's pogo stick are equal at θ = 2πn, where n is an integer.
Help pls! I will give 50 points!
Answers
Answer:
1&2 are -2x^(3)+3x^(2)+x or Factored is −-x(2x^(2)-3x-1)
3&4 are 2x^(4)-3x^(3)-x^(2) or Factored is x^(2)(2x^(2)-3x-1)
5 is Yes
Step-by-step explanation:
1. (x+1*2x^(2)-x)(-1)
2x^(3)-x^(2)+2x^(2)-x(-1)
2x^(3)-3x^(2)-x(-1)
-2x^(3)+3x^(2)+x
−-x(2x^(2)-3x-1)
2. (2x^(2)-x*x+1*2x)(-1)
2x^(3)-x^(2)+2x^(2)-x(-1)
2x^(3)-3x^(2)-x(-1)
-2x^(3)+3x^(2)+x
−-x(2x^(2)-3x-1)
3. (x+1*2x^(2)-x)(x)
2x^(3)-x^(2)+2x^(2)-x(x)
2x^(3)-3x^(2)-x(x)
2x^(4)-3x^(3)-x^(2)
x^(2)(2x^(2)-3x-1)
4. (2x^(2)-x*x+1*2x)(x)
2x^(3)-x^(2)+2x^(2)-x(x)
2x^(3)-3x^(2)-x(x)
2x^(4)-3x^(3)-x^(2)
x^(2)(2x^(2)-3x-1)
5. (2x^(2)-x*x+1*2x)(x)=(x+1*2x^(2)-x)(x)
(2x^(2)-x*x+1*2x)(x)-2x^(2)-x=(x+1*2x^(2)-x)(x)-2x^(2)-x
(x+1)(x)=(x+1)(x)
(x+1)(x)-(x+1)=(x+1)(x)-(x+1)
X=X
An ice cream parlor makes 1/3 of it's income from cones and 40% from sundaes. What fraction of it's income comes from other items
Answers
Answer:
4/15
Step-by-step explanation:
40% = 2/5 = 6/15
1/3 = 5/15
15/15 - 6/15 - 5/15 = 4/15
4/15 of its income comes from other items.
Find m∠2
Any help on this would be great!
Answers
Finding m∠2 is c. 44°.
Measure of angleFirst step is to find the Measure of angle 1 which is m∠1
Measure of angle 1 = (68° + 68°) or (68°×2)
Measure of angle 1 = 136°
Second step is to find m∠2
Since we have find the measure of angle 1 in order for us to find or determine m∠2 we would have to deduct or subtract m∠1 from 180°
Now let find m∠2
m∠1 = 136°
m∠1 + m∠2 = 180°
136° + m∠2 = 180°
m∠2 = 180° - 136°
m∠2 = 44°
Therefore finding m∠2 is c. 44°.
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Suppose an investigator takes a random sample of n = 50 birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean is y¯ = 3.15 kg and the standard deviation is 250 grams. (a) Calculate a 95% confidence interval for the population mean birth weight in these hospitals. (b) The typical weight of a baby at birth for the US population is 3.25 kg. The investigator suspects that the birth weights of babies in these teaching hospitals is different than 3.25 grams, but she is not sure if it is smaller (from malnutrition) or larger (because of obesity prevalence in mothers giving birth at these hospitals). Carry out the hypothesis test that she would conduct.
Answers
a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).
(b)The P-value is 0.0068.
What is hypothesis testing?To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.
Why is hypothesis testing used?A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.
C.I=x-t(alpha/2)xs/sqrt{n}
=3150+_2.01*250/sqrt{50}
=(3078.9358,3221.0642)
b) P value =P(t<-2.83)+P(t>2.83)
use calculator
=0.0034+0.0034
=0.0068
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what is 70.5 and 79.5 on a number line 60-100?
Answers
Answer:
s
Step-by-step explanation:
What is the area of this figure?
15 mm
4 mm
Submit
3 mm
3 mm
5 mm
5 mm
7 mm
8 mm
Write your answer using decimals, if necessary.
square millimeters
Answers
Graph the line that represents this equation: y +2 = 1/2 (x+2) Undo Drawing Tools Click on a tool to begin drawing Select Point 10 Line 8 6 2 4 2. 6 8 2. 4 -10 -6 -8 orved
Answers
The given equation of line is:
\(y+2=\frac{1}{2}(x+2)\)Graph for this line is:
Raquel informed her stockbroker that she wanted to buy a certain amount of stock. The broker informed her that because of the margin requirement of 55% she would need at least $825 in cash what is the dollar value of the stock that Raquel wants to purchase?
Answers
The dollar value of the stock that Raquel wants to purchase is $1,833.33.
If the margin requirement is 55%, then the amount of cash wanted is 45% of the total value of the inventory.
Consequently, we will set up the following equation like this:
0.45x = 825
Wherein:
x is the dollar value of the stock Raquel wants to purchase.
To solve for x, we are able to divide both aspects of the equation by way of 0.45:
x = 825 ÷ 0.45
x = $1,833.33
Therefore, the dollar value of the stock that Raquel wants to purchase is $1,833.33.
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Estimate!
16 3/4 divided by 2 1/2
Answers
Answer:7
Step-by-step explanation:
6.7 to the 10 is 7
maximum value of P+4x+5y+21 given the following: y-x<1, 21x+7y<25, x>-2, y>-4
Answers
The maximum value of the objective function is 31.787
How to maximize the function?The given parameters are:
Objective function:
Max P = 4x + 5y + 21
Subject to:
y- x < 1
21x + 7y < 25
x>-2, y>-4
Rewrite the inequalities as equation
y - x = 1
21x + 7y = 25
Add x to both sides in y - x = 1
y = x + 1
Substitute y = x + 1 in 21x + 7y = 25
21x + 7x + 7 = 25
Evaluate the like terms
28x = 18
Divide both sides by 28
x = 0.643
Substitute x = 0.643 in y = x + 1
y = 0.643 + 1
y = 1.643
So, we have:
Max P = 4x + 5y + 21
This gives
P = 4 * 0.643 + 5* 1.643 + 21
Evaluate
P = 31.787
Hence, the maximum value of the objective function is 31.787
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The family is having grilled steak for dinner. Ian gets a 7-ounce steak. He eats 1/2 of it. How many ounces of steak does he eat?
Answers
Answer:
3.5 ounces
Step-by-step explanation:
A rectangle has a perimeter of 42 ft its length, L, is 3 feet more than twice its width, W.
(c) Solve the system of equations that you just created by substitution to find the values of the length and width.
Answers
Answer:
Length of rectangle = 15 feet
Width of rectangle = 6 feet
Step-by-step explanation:
Given:
Perimeter of rectangle = 42 ft
Length of rectangle = 2[Width of rectangle] + 3
Find:
Value of length and width
Assume:
Width of rectangle = w
SO,
Length of rectangle = 2[w] + 3
Perimeter of rectangle = 2[l + b]
42 = 2[2w + 3 + w]
2[3w + 3] = 42
6w + 6 = 42
6w = 42 - 6
6w = 36
w = 36 / 6
w = 6
So,
Width of rectangle = 6 feet
Length of rectangle = 2[w] + 3
Length of rectangle = 2[6] + 3
Length of rectangle = 12 + 3
Length of rectangle = 15 feet
An article is sold for Rs.150 at a gain. Had it been sold for Rs.135 there would have been a loss equal to 50% of the original gain. Find the cost price of the article.
Answers
The cost price of the article, which is sold for Rs. 150 at a gain but if sold for Rs. 135 would have resulted in a loss equal to 50% of the original gain, is Rs. 127.50.
How the cost of the article is determined:The cost price is the difference between the selling price and the profit or gain.
The difference is determined by subtraction.
Selling price of the article = Rs. 150
Loss if sold at Rs. 135 = 50% of the original gain
Original gain = Rs. 15 (Rs. 150 - Rs. 135)
50% of the original gain = Rs. 7.50 (Rs. 15 x 50%)
Cost price of the article = Rs. 127.50 (Rs. 135 - Rs. 7.50)
Thus, the cost price is Rs. 127.50.
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I have finished half of this problem but i am still unsure on how to finish.
Answers
Answer:
Triangle PQR maps onto triangle KLM. This is possible because △PQR ≅ △KLM by ASA, and one congruent figure can be mapped onto another using rigid motions.
Step-by-step explanation:
For the first blank, we are given congruence statements for 1 side on each triangle and their two adjacent angles. This means we can use the Angle-Side-Angle theorem to declare △PQR and △KLM congruent.
For the second blank, we know that rigid transformations do not change the figure, they simply move its position on a plane, so this is the correct answer; had the △PQR and △KLM not been congruent, a non-rigid transformation would have to have occured, but this is not the case here.
Answer:
ASArigidStep-by-step explanation:
Given triangles PQR and KLM with QR ≅ LM, ∠Q ≅ ∠L, and ∠R ≅ ∠M, you want to know the applicable congruence postulate and whether the triangles are mapped to each other by rigid or non-rigid motion.
Sides and anglesThe segment QR has angle Q at one end and angle R at the other end. That means the side lies between the two angles. Likewise, segment LM lies between angles L and M.
When claiming congruence of these triangles, the appropriate postulate is the one that refers to the geometry with the congruent side between the congruent angles: ASA.
Motion"Rigid" motion is motion that preserves angle and length measures. By contrast, "non-rigid" motion may involve stretching or compression in one or more directions. It may or may not preserve angles or lengths.
Congruence is about showing that angles and lengths are the same from one figure to another. If you want to map congruent figures to each other, you must do so using rigid motion.
__
Additional comment
The rigid motions include ...
translationrotationreflection.<95141404393>
2(x + 4) + 5( 6 - x)
Answers
Answer:
3x+32
Step-by-step explanation:
2(x+4) +5(6-x)
Use the distributive property
2x+8+24-5xSimplify
3x+32What is the simplified expression for -3(2x-7)+2y+ 2(x+y)?
Answers
Answer:
-4x+42+4yStep-by-step explanation:
-3(2x-7) + 2y + 2 (x+y)
-6x+42 + 2y + 2x + 2y
Take the same coefficents and subtract or add
-6x + 2x= -4x
2y + 2y= 4y
For the function, f(x)=1/4x-2, find x if f(x)=-1
Answers
f(x) = 1/4x-3
When f(x) = -1,
= 1/4(-1)-3
= -13/4
Answer
-2.25
Step-by-step explanation:
(1/-4) -2= (1/-4)- 2^4= -9/4= -2.25
I need the answers for the table below.
Answers
The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively
Given the function :
tan(πx)/7xSubstitute the given value of x to obtain the corresponding f(x) values :
x = -0.6
f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358
x = -0.51
f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350
x = -0.501
f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967
x = -0.5
f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959
x = -0.4999
f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958
x = 0.499
f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951
x = -0.49
f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188
x = -0.4
f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125
Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013
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Whats the answer to this?
Answers
The stem and leaf plot shown above indicates that the range is 33.
How is the range determined?The difference between the greatest number in a data set and the lowest number in the same set is referred to as the data set's range.
The stem and leaf plot shown above shows that the maximum number is 50 and the lowest number is 17.
As a result, the range is:
= 50 - 17
= 33
Therefore, we may say that the data set's range is 33.
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. A real estate company charges a base amount of $ 400 plus 3 % of the selling price to sell a house. If a house sells for $ 250, 000. How much will the agent charge? *
Answers
Answer:
400 + .03(250,000) = $7900
Step-by-step explanation:
An equation of a circle is given as (x + 6)2 + (y − 7)2 = 81. Find the center and radius of the circle.
Answers
The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2
h and k are the center point and r is the radius.
In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.
Center (-6,7)
Radius = 9
The required center is \((-6,7)\) and the radius is 9 units.
Given equation is,
\((x + 6)^2 + (y-7)^2 = 81\)....(1)
Equation of the circle: The general equation of the circle with the center (a,b) and the radius r is represented by,
\((x-a)^2+(y-b)^2=r^2\)...(2)
We can write the given equation as,
\((x + 6)^2 + (y-7)^2 = (9)^2\)
Comparing equations (1) and (2) we get,
The Centre of the given circle is \((-6,7)\)
The radius of the given circle is 9 units.
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******Please help me please help me help please help*****
A.
B.
Answers
Answer:
The answer would be A
Step-by-step explanation:
If you were to divide 36 by 5 you would be finding how many calories are in 1/5 of a bar.
Kate multiplied two binomials using the distributive property. she made a mistake in one of the steps. where did she first make a mistake?
(x – 2)(3x + 4)
1. (x – 2)(3x) + (x – 2)(4)
2. (x)(3x) + (2)(3x) + (x)(4) + (2)(4)
3. 3x2 + 6x + 4x + 8
4. 3x2 + 10x + 8
A. Step 2
B. Step 3
C. Step 4
Answers
step 3 is the answer because i just did it.
She first made a mistake in A. Step 2
What is Distributive property?It means to divide something. when a same number a multiplied with sum or subtraction of any numbers than we can divide that or distribute that.
For example: (a+b)*(c+d) = (a+b)*c+(a+b)*d
What is the mistake?While distributing (X-2)(3X) + (X-2)(4) sign remains the same Whereas she changed the sign form - to + which is incorrect.
How to solve?(X-2)(3x) + (X-2)(4)
(x)(3x) + (-2)(3x) + (x)(4) + (-2)(4)
3\(x^{2}\) - 6x + 4x - 8
3\(x^{2}\) - 2x -8
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need help real baddddddddddddd
Answers
Answer:
x≥2 and x<2 : ∅
x≥2 or x<2 : All real numbers
x≤2 and x≥2 : 2
Step-by-step explanation:
the first one must follow both conditions, so no number would work.
the second one works with any number, so all real numbers.
the third one has only one condition that works, 2
Solve for x round to the nearest tenth of a degree if necessary. HURRYYYY TY
Answers
The value of x is 58.51 degree.
We have,
Perpendicular= 8
Base = 4.9
Using trigonometry
tan x = Perpendicular/ Base
tan x = 8/4.9
tan x= 1.63265306122449
x = 58.51253064
Thus, the value of x is 58.51 degree.
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Compund Inequalities. Solve for x. 11x+4 −25 A. -3/2 -3/2 C. x<1 D. There are no solutions. E. All values of x are solutions.
Answers
Answer:
A
Step-by-step explanation:
11x + 4 < 15 OR 12x - 7 > -25
11x < 11 OR 12x > -18
x < 1 or x > -1.5
The answer is -3/2 < x < 1.
f(x)=x+2 g(x)=3x^2-5 find (f•g)(x)
Answers
9514 1404 393
Answer:
(f•g)(x) = 3x^3 +6x^2 -5x -10
Step-by-step explanation:
(f•g)(x) = f(x)•g(x) = (x +2)(3x^2 -5)
= x(3x^2 -5) +2(3x^2 -5) . . . . . . . . use the distributive property
= 3x^3 -5x +6x^2 -10 . . . . . . . and again
(f•g)(x) = 3x^3 +6x^2 -5x -10 . . . . put in standard form
Referring to the figure, find the missing length x. Round the answer to the nearest hundredths.
Answers
Using cosine function:
\(\begin{gathered} \cos (\theta)=\frac{adjacent}{_{\text{ }}hypotenuse} \\ \cos (45)=\frac{8}{x} \\ solve_{\text{ }}for_{\text{ }}x\colon\text{ } \\ x=\frac{8}{\cos (45)} \\ x=8\sqrt[]{2} \\ x\approx11.31 \end{gathered}\)Answer:
x = 11.31
