a 12oz box of cereal costs $3.50. An 18oz box of cereal costs $5.40. Set up equations to determine which is the better buy.
Answer:
12oz box of cereal for $3.50 is the better buy
Step-by-step explanation:
12oz=$3.50
36oz = $10.50
----------------------------
18oz=$5.40
36oz=$10.80
Find both unit rates.
: An object traveled 691.12 feet in 21.2 seconds.
Question 1 options:
A: 32.6 s/ft and approximately 0.03 s/ft
B: 32.6 ft/s and approximately 0.03 s/ft
C: 32.6 ft/s and approximately 0.03 ft/s
D: 32.6 s/ft and approximately 0.03 ft/s Warning: Whoever Answers this wrong will be reported. :l
The unit rate is 32.6 ft/s and approximately 0.03 s/ft.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
An object traveled 691.12 feet in 21.2 seconds.
So, the unit rate as feet per second.
= 691.12/ 21.2
= 32.6 ft/s
and, the unit rate as second per feet
= 21.2/ 691.12
= 0.03 s/ ft
Hence, the unit rate is 32.6 ft/s and approximately 0.03 s/ft
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Slope = -1/5, y-Intercept = -1/4
Answer:
[tex]\sf y =\dfrac{-1}{5}x-\dfrac{1}{4}[/tex]
Step-by-step explanation:
Slope y-intercept form of equation: y =mx +bHere, m is the slope and b is the y-intercept.
Substitute the values of m and b in the above equation.
[tex]\sf m = \dfrac{-1}{5} \\\\b = \dfrac{-1}{4}[/tex]
Slope y-intercept form:
[tex]\sf \boxed{y=\dfrac{-1}{5}x - \dfrac{1}{4}}[/tex]
Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 3, [0, 2], 4 rectangles
Two approximations of the area of the region between the graph are
(9, 11)
Given;
To calculate two approximations of the area of the region between the graph of the function and the x-axis across the given interval, use the left and right endpoints and the specified number of rectangles. rectangles f(x) = 2x + 3, [0, 2], 4
The graph is positive and the width of each subinterval will be,
a = 0, b = 2, n = 4
Δx = b-a/n = 2-0/4
= 0.5
Now for different values;
x → f(x) = 2x+3
x₀ = 0 → f(x₀ ) = 2x+3 = 2(0)+3 = 3
x₁ = 0.5 → f(x₁) = 2x+3 = 2(0.5)+3 = 4
x₂ = 1.0 → f(x₂) = 2x2+3 = 2(1) +3 = 5
x₃ =1.5 → f(x₃) = 2x+3 = 2(1.5)+3 = 6
x₄ = 2 → f(x₄) = 2x+3 = 2(2)+3 = 7
The area by using the approximation using 4 approximating rectangles and right endpoints is given by,
A ≈ R₄ = ∑f(x) Δx = ( ƒ(x1)Δx + ƒ (x2)Δx+ ƒ (x3)Δx + ƒ (x4)Δx)
= 0.5 (4 + 5 + 6 + 7)
= 0.5 × 22
= 11
The area by using the approximation using 8 approximating rectangles and left endpoints is given by.
A ≈ L₄ = ∑f(x) Δx = ( ƒ(x0)Δx + ƒ (x1)Δx+ ƒ (x2)Δx + ƒ (x3)Δx)
= 0.5 (3 + 4 + 5 + 6)
= 0.5 × 18
=9
Thus, 9 < Area < 11.
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an article in a medical journal suggested that approximately 18% of such operations result in complications. using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.06?
The needed Sample size is 32.2 so that the confidence interval will have a margin of error of 0.06.
We have provided that , An article in a medical journal approx. 18% of operation results complications.
Using the estimate formula, for standard margin of error
Margin of error (E) = Z x √p(1-p)/n
where , E---> margin of error
Z---> estimate value
p----> sample proportion
n -----> Sample size
we have the value of E = 0.06 , p = 18% = 0.18
put all the values in above formula we get,
0.06 = Z × √0.18× 0.82/n
critical value or Z-value for sample proportion 0.18 is 0.91
Now, 0.06 = 0.91 × √0.18×0.82/n
=> √0.14/n= 0.065 => 0.14/n = 0.0043
=> n= 32.2
So, sample size is 32.2
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What’s the unit rate for three dollars for 2 1/2 hours of work
The unit rate for three dollars for 2 1/2 hours of work will be $1.2 using the concept of unitary method.
What is unitary method?The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. The unitary technique is a method for determining the value of any necessary quantity by first obtaining the value of the unit (one) quantity.
Here,
$3 for 2.5 hours of work,
1 hour will cost $x,
3/2.5=x/1
2.5x=3
x=$1.2
Using the unitary technique, the unit rate for three dollars for two and a half hours of labour will be $1.2.
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What value of a makes lines m and n parallel?
Answer:
20
Step-by-step explanation:
3x + 5 should be equal to 65
3x + 5 = 65
3x = 65 - 5
3x = 60
x = 60/3
x = 20
A certain insect can beat its wings 10 times per second. Write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times the insect beats its wings.
The equation in slope-intercept form that shows the relationship is y = 10x
How to determine the equation?From the question, we have the following parameters that can be used in our computation:
Rate of beating wings = 10 times per second
The equation in slope-intercept form of the relationship is then represented as
y = Rate of beating wings * x
Where
y is the number of times
x is the wings
So, we have
y = 10 * x
Evaluate
y = 10x
Hence, the equation is y = 10x
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the anser answer are A(250 feet)-(b)150 feet)-c)100 feet)-d(200 feet)
Answer:
(b) 150 feet
Step-by-step explanation:
You want to know the height of a kite at the end of 225 feet of string, flying at an angle of elevation of 45°.
Right triangleThe 45° angle in the given right triangle tells you this is one of the "special" right triangles. Its side lengths have the ratios ...
1 : 1 : √2
where √2 is the hypotenuse.
That means the other two legs of this right triangle are ...
(225 ft)/√2 ≈ 159.099 ft
Rounded to the nearest 50 feet, this is about 150 feet.
__
Additional comment
The sine function relates the angle value to the opposite side:
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse · Sin
height = (225 ft)·sin(45°) = 225 ft/√2 ≈ 159.099 ft
50 POINTS TO WHOEVER ANSWER THIS QUESTION!! THANKS SO MUCH!!!
The value of side x is given by (C) 14.7 units approximately.
Given the triangle is a right angled triangle.
Now given also that, Height of triangle is = x units
Base of triangle is = 15 units
Hypotenuse of triangle is = 21 units
So by Pythagoras theorem, we get the sum of squares of base and height is equal to the square of hypotenuse. So,
[tex]x^2+15^2=21^2\\\Rightarrow x^2+225=441\\\Rightarrow x^2=441-225\\\Rightarrow x^2=216\\\Rightarrow x\approx14.7[/tex]
So the value of x is 14.7 units approximately.
Hence the correct option is (C).
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Eric owns shares of a certain stock. If he sells off 8 shares each month for a year, find the change in the number of shares of stock he owns.
After solving the word problem, the change in the number of shares of stock he owns, is x-96.
In the given question we have to find the change in the number of shares of stock he owns.
As given that Eric owns shares of a certain stock. If he sells off 8 shares each month for a year.
Let Eric owns x shares of a certain stock.
If he sells off 8 shares each months for a year.
So as we know that in a year have 12 months.
In 1 month = 8 shares sells
12 months = 12×8 shares sells
12 months = 96 shares sells
So in a year Eric sells 96 shares and he have total x shares.
So the remaining shares are x-96.
Hence, the change in the number of shares of stock he owns, is x-96.
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The function h(x)=x² +5 maps the domain given by the set {-2, -1, 0, 1, 2}. Which of the following sets
represents the range of h(x)?
(1) {0, 6, 10, 12)
(2) {5,6,7}
(3) {5, 6,9}
(4) {1, 4, 5, 6,9}
For the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 } .
As given in the question,
Given function is equal to :
h(x) = x² +5
Domain of the function h(x) = x² +5 maps by the set { -2, -1, 0, 1, 2 }
Range of the function h(x) = x² +5 is represented by the set as follow :
Substitute the value x = -2, -1, 0, 1, 2 in the function h(x) = x² +5 we get,
h(-2) = (-2)² + 5
= 9
h(-1) = (-1)² + 5
= 6
h(0) = (0)² + 5
= 5
h(1) = (1)² + 5
= 6
h(2) = (2)² + 5
= 9
Range of the function is represented by the set : { 5, 6, 9 }
Therefore, for the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 }.
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question is at the bottom !! anyone know the answer ??
PLS DONT ANSWER IF YOU DONT KNOW IT, i will report u if you do this.
ONLY ANSWER IF U KNOW!
12 is the marginal cost at the production level of 1000 units.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The marginal cost represents the additional cost if 1 more unit is produced. So, we can find the marginal cost by computing C(1,001) and subtracting (1,000)
First, let's evaluate the cost at both x= 1,001 and x=1,000
C(1000)=0.002(1000)^2+8(1000)+6000
=0.002(1000000)+8000+6000
=2000+8000+6000
=16000
C(1001)=0.002(1001)^2+8(1001)+6000
=2004.002+8008+6000
=16012
The difference between these costs is $12.002. Rounding to the nearest cent, we find a marginal cost of $12 per unit. Let's see if we get a similar result from the derivative.
Hence 12 is the marginal cost at the production level of 1000 units.
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A z-test with a z observed of 2.56 (two-tailed) would have a p-value of ______, which would lead a research to _______ the null hypothesis if alpha is .05.
A z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.
Given:
z - score = 2.56
p value at z = 2.56 is:
p = 0.010467
The result is statistically significant: you can reject the null hypothesis and accept the alternative.
This decision is made at significance level α = 0.05.
Therefore a z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.
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a rectangle has a area of 50
the length is x+10
the width is x
solve for x.
The value of x in the rectangle is -5 + 5√3.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides are parallel to each other.
Therefore, the area of a rectangle can be found as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
length = x + 10
width = x
Hence,
50 = x(x + 10)
50 = x² + 10x
x² + 10x - 50 = 0
using quadratic formula,
[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 1
b = 10
c = -50
Therefore,
x = [tex]\frac{-10+\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex] and x = [tex]\frac{-10-\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]
Hence,
x = -5 + 5√3 and x = -5 - 5√3
Therefore, we can't use negative values
The value of x = -5 + 5√3
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what 27 over 54 in lowest terms
Answer: 1/2
Step-by-step explanation: Divide both the numerator and denominator by the GCD (Greatest Common Denominator)
27 ÷ 27
54 ÷ 27 (its 27/54 divided by 27/27
Reduced fraction:
1/2
Therefore, 27/54 simplified to lowest terms is 1/2.
23. A group of friends is collecting aluminum for a recycling drive. Each person
who donates at least 4.25 pounds of aluminum receives a free movie coupon.
The weight of each person's donation is shown in the table.
Brenda
4.3
Claire
5.5
Jim
61/10
Micah
15
4
Weight
(lb)
a. Order the weights of the donations from greatest to least.
Peter
43
b. Which of the friends will receive a free movie coupon? Which will not?
c. What If? Would the person with the smallest donation win a movie
coupon if he or she had collected pound more of aluminum? Explain. Which of the friends will receive a free movie coupon?which will not
Answer:
Step-by-step explanation:
a. 6.17 , 5.5 , 4.375 , 4.3 , 3.75
b. Everyone except Micah.
C. Micah got 3.75 pounds and if he got 0.5 pounds more, then he would have; 3.75+0.5=3.75 pounds. Then he would have got the coupon as a minimum of 4.25 pounds is required.
write and solve a system of linear equations to find the values of $x$ and $y$ . a quadrilateral. the angles of the quadrilateral are 5x degrees, (4y minus 2 )degrees, (13x plus 10 )degrees, and 10y degrees.
As per the angle sum property of quadrilateral, then values of x is 245 and the value of y is 341
Angle sum property of quadrilateral:
The angle sum property states that the sum of all the angles of the quadrilateral is 360 degree.
Given,
The angles of the quadrilateral are 5x degrees, (4y minus 2 )degrees, (13x plus 10 )degrees, and 10y degrees.
Now we have to write and solve a system of linear equations to find the values of x and y.
While we looking into the given angles, then we get the values
=> 5x°
=> (4y - 2)°
=> (13x + 10)°
=> 10y°
We know that, the sum of all the angles of the quadrilateral is 360°.
So, it ca be written as,
=> 5x° + (4y - 2)° + (13x+ 10)° + 10y° = 360°
=> 18x° + 14y° - 8° = 360°
=> 18x° + 14y° = 354°
When we divide all of them by 2, then we get the equation as,
=> 9x° + 7y° = 177°
Now we have to rewrite the given equation as,
=> 9x° = 177° - 7y°
=> x° = (177° - 7y°)/9
Apply these value on the angles, then we get,
=> 13(177 - 7y)/9 = -10
=> 13(177 - 7y) = 90
=> -7y = -90 - 2301
=> 7y = 2391
=> 341
Then the value of x is
=> 245
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Write the equation of the line that goes through point (-4, 1) and is perpendicular to the line 2y - 4x = -10. Write the equation in slope intercept form.
Answer:
y = 1/2x + 3
Step-by-step explanation:
first we change the first equation to slope-intercept form to find the reciprocal slope
2y - 4x = -10
add 4x to both sides
2y = 4x - 10
divide both sides by 2
y = 2x - 5
since perpendicular lines have reciprocal slopes the slope of our new line is 1/2
y = 1/2x + b
to find b we plug in the point
1 = 1/2(-4) + b
1 = -2 + b
add 2 to both sides
3 = b
___
our new line is
y = 1/2x + 3
Answer:
-83+8=19
Step-by-step explanation: how i figured this out is by guessing so i can get more points sorry guys.
Are these 4 problems SSS SAS ASA AAS HL
1. The first figure posses the SSS property.
2. The second figure posses the ASA property.
3. The third figure posses the hypotenuse length property.
4. The fourth figure posses the SAS property.
Given:
1. The first figure shows the SSS property.
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
hence the two triangles are congruent.
2. The second figure posses the ASA property.
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
hence the two triangles are congruent.
3. The third figure posses the hypotenuse length properety.
RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.
hence the two triangles are congruent.
4. The fourth figure posses the SAS property.
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
hence the two triangles are congruent.
Hence we get the required answer.
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please help me
what ∞ times x = what
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Infinity is denoted by ∞.
∞ = 1/0
∞ times x is ∞
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Infinity is denoted by ∞.
∞ = 1/0
Now,
∞ times x = ∞
Whatever we multiply with infinity will always give us infinity.
Thus,
∞ times x is ∞
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There is a line whose y-intercept is -2 and whose slope is 1. What is its equation in
slope-intercept form?
please help me fast!!
Answer:
4(y+3)(y+5)
Step-by-step explanation:
4y^2+32y+60 = 4(y^2+8y+15) = 4(y+3)(y+5)
y^2+8y+15 = (y+3)(y+5)
LCD = 4(y+3)(y+5)
i need to know how to find the slope!!
Answer:
Step-by-step explanation:
Slope of a straight line is the gradient of that line.
Formula for gradient is rise over run. Meaning: m = (y2 - y1) / (x2 - x1)
To use this formula, you need 2 points of the straight line. They have already given you one: (8, -3). For the second one, we consider the equation of the line. The y-intercept is given too: -4.
Now, keep in mind, the y intercept is the point of the line that passes from x = 0. Meaning, the point where the line touches the y axis, and at y axis, x = 0. So our second point is (0, -4).
Now as we have 2 points, (8, -3) and (0, -4), we put the values in the formula: m = (y2 - y1) / (x2 - x1) = (-4 - (-3)) / (0 - 8) = -1 / -8 = 1 / 8
what is the value of the expression below ?
Answer: -10.
Step-by-step explanation:
30/3 = 10.
However, there is a negative number in the expression.
A rule you need to remember is when you divide 2 numbers with different signs, the answer is negative. If you divide 2 numbers with the same sign, the answer is positive.
30/-3 = -10.
Based on the following calculator output, determine the mean of the dataset, rounding to nearest 100th if necesssrt.
The mean is 63.12 using the data given.
Given that,
Calculate the dataset's mean using the output from the following calculator, rounding to the nearest 100th if necessary.
1-Var-Stats
[tex]\bar x[/tex] = 63.1428571429
∑x = 442
∑x² = 28266
Sₓ = 7.71208081364
σₓ = 7.13999942834
n = 7
minX = 48
Q₁ = 58
Med = 66
Q₃ = 69
maxX = 69
Mean value is defined as sum of all data values divided by the total number of data values
Using the given data output
We get,
Mean = 63.14 (rounded to 2 decimals)
Therefore, The mean is 63.12 using the data given.
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fill in the blank, somebody help please. will mark brainliest + 20pt
Answer:
c) divide both sides by 8
hope this helps!
Answer:
Its the 3 option
determine lf (t) for the functions f (t), with t > 0, defined below. make sure to specify the frequency domain for s as well, namely, the domain of convergence of the laplace transform.
An Integral transform that converts a function of a real variable to a function of a complex variable is a Laplace Transformation.
F =L (f)
We are interested in signal defined for t≥ 0.
The Laplace transformation of a signal function (f) if the function
F = L(f)
F(s) = ∫∞ ₀ f(t) e⁻ᵃᵇ dt
for those a ∈ C for which the integral makes sense.
F is a complex valued function is a complex numbers.s is called the complex frequency variable with units sec⁻¹, t is called the time variable in sec.Lets find Laplace transformation of f(t) =eᵃ
F(s) = ∫₀∞ eᵃ e⁻ᵃᵇ da
= [ 1/1-a e⁽¹ ⁻ ᵃ⁾ ] = 1 / a-1
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Prove: <1= <3
Complete the proof (reasons A and B).
A. Definition of supplementary angles
And Substitution property
B. Angle addition postulate
And Subtraction property of equality
C. Subtraction property of equality
And Definition of linear pair
D. Addition property of equality
And Angle addition postulate
The reason that proves the above conditions is option A. Definition of supplementary angles And Substitution property.
Supplementary angles:
The pair of angles that gives 180° on adding is known as Supplementary angles. In other words, the sum of two supplementary angles is 180°. Two pairs of Supplementary angles will always form a linear pair.
Here we have
∠1, ∠2, ∠3, and ∠4 are formed by 2 intersecting lines
As we know
∠1, ∠2 is a linear pair and form supplementary angles
=> Sum of the ∠1, ∠2 will equal 180°
∠2, ∠3 is a linear pair and form supplementary angles
=> Sum of the ∠2, ∠3 will equal 180°
Therefore,
By the Definition of supplementary angles ∠1+∠2= 180° and ∠2+∠3= 180°
From the above observations,
=> ∠1+∠2= 180° and ∠2+∠3= 180°
=> ∠1 + ∠2 = ∠2 + ∠3
Therefore,
By the Substitution property ∠1 + ∠2 = ∠2 + ∠3
Hence,
The reason that proves the above conditions is option A. Definition of supplementary angles And Substitution property
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Determine the equation of the axis of symmetry for the parabola that passes through
points (-4,0) and (6,0).
(A) x = -2
(B) x=2 (C) x=-1
10
D
с
a
b
n
d
(D) x = 1
Answer:
D
Step-by-step explanation:
the axis of symmetry is a vertical line with equation x = c
where c is the value of the x- coordinates the line passes through.
the line crosses the x- axis at the midpoint of the zeros
given (- 4, 0 ) and (6, 0 ) , that is
zeros are x = - 4 and x = 6
then equation of axis of symmetry is
x = (- 4 + 6) ÷ 2 = 2 ÷ 2 = 1 , that is
x = 1 ← axis of symmetry