A candle is 7 in. tall after burning for 1 h. The same candle is 5 1/2 in. tall after burning for 4 h. How tall will the candle be after burning for 6 h?
Answer: 4 1/2 in
Step-by-step explanation: correct on gradpoint
A supplier sells 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel. The supplier sells 173 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell?
Answer:
[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.
Step-by-step explanation:
Mass of mulch sold = x pounds
Mass of gravel sold = y pounds
Total mass of mulch and gravel sold = 173 pounds
x + y = 173 ...[1]
Supplier sells [tex]2\frac{1}{4}[/tex] pounds of mulch for every [tex]1\frac{1}{3}[/tex] pounds of gravel.
That is for [tex]\frac{9}{8}[/tex] pounds of mulch for every [tex]\frac{4}{3}[/tex] pounds of gravel.
Then gravel sold for 1 pound mulch = [tex]\frac{4}{3}\times \frac{8}{9}=\frac{32}{27} pounds[/tex]
Then for x pounds of mulch the gravel sold will be:
[tex]\frac{32}{27} pounds\times x[/tex]
Mass of gravel sold = [tex]y = \frac{32}{27} pounds\times x[/tex]
Putting value of y in [1] :
[tex]x + \frac{32}{27} pounds\times x = 173[/tex]
x =[tex]\frac{4,671}{59} pounds[/tex]
y = [tex]173 pounds -\frac{4,671}{59} pounds=\frac{5,536}{59}pounds[/tex]
[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.
Find the parabola of the form y=ax2+b which best fits the points (−1,0), (5,5), (6,10) by minimizing the sum of squares, s, given by
The optimal least squares fit for the given data is y = 0.2732x² - 0.6452. This curve minimizes the sum of squared errors, providing an accurate representation of the data.
The provided data points are (-1, 0), (5, 5), and (6, 10), denoted as {x} = [-1, 5, 6] and {y} = [0, 5, 10]. The goal is to find the least squares fit for the curve y = ax² + b. To minimize the sum of squared errors between the data and the curve, the normal equations are derived.
The normal equations are given by:
(x₁⁴ + x₂⁴ + x₃⁴)a + (x₁² + x₂² + x₃²)b = x₁²y₁ + x₂²y₂ + x₃²y₃ (Equation 1)
(x₁² + x₂² + x₃²)a + 3b = y₁ + y₂ + y₃ (Equation 2)
By substituting the given data, the equations become:
1922a + 62b = 485
62a + 3b = 15
Solving these equations yields the values: a = 0.2732 and b = -0.6452. Therefore, the curve of the best least squares fit is y = 0.2732x² - 0.6452.
In conclusion, the curve that minimizes the sum of squared errors for the provided data points is y = 0.2732x² - 0.6452. The graph of this curve, along with the given data, visually represents the accuracy of the least squares fit.
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Trey runs 4 miles in 30 minutes. at the same rate, how many miles would he run in 48 minutes?
When x is divided by 3 the quotient is more than 7
Find the exact value of cot60°.
Answer:
The exact value is [tex]\cfrac{\sqrt{3}}3[/tex]
Step-by-step explanation:
Since 60 degrees is an angle we can find on the unit circle, the goal to get an exact value is to use the elements of the unit circle, which are exact values of sine and cosine.
Writing cotangent in terms of sine and cosine
We can use the trigonometric identity
[tex]\cot \theta = \cfrac{\cos \theta }{\sin \theta }[/tex]
Thus for the exercise we will have
[tex]\cot 60^\circ = \cfrac{\cos 60^\circ }{\sin 60^\circ }[/tex]
Identifying the known exact values.
From the unit circle that you can see on the attached image below, we have to identify the exact values of cosine and sine of 60 degrees.
So first try to look for the angle 60 degrees, there you will see a point that has a pair of values, those represent (cosine, sine), thus we get:
[tex]\cos 60^\circ=\cfrac 12 \\\\\sin 60^\circ = \cfrac{\sqrt3}2[/tex]
Finding the exact value of cot 60 degrees.
We can replace the exact values of sine and cosine on the trigonometric identity for cotangent.
[tex]\cot 60^\circ = \cfrac{\cfrac 12 }{\cfrac{\sqrt 3}2 }[/tex]
Working with the reciprocal we get
[tex]\cot 60^\circ = \cfrac 12\times \cfrac2{\sqrt 3}[/tex]
Simplifying we get
[tex]\cot 60^\circ = \cfrac 1{\sqrt 3}[/tex]
Rationalizing since we usually do not want square roots on the denominator we get
[tex]\cot 60^\circ = \cfrac 1{\sqrt 3} \times \cfrac{\sqrt 3}{\sqrt 3}\\\boxed{\cot 60^\circ = \cfrac {\sqrt 3}3}[/tex]
And that is the exact value of cotangent of 60 degrees.
The exact value of cot(60°) is √3 / 3.
How did we get the value?To find the exact value of cot(60°), we can use the identity:
cot(θ) = 1 / tan(θ)
Since tan(θ) = sin(θ) / cos(θ), we need to find the values of sin(60°) and cos(60°).
In a 30-60-90 degree triangle, the sides are in the ratio 1 : √3 : 2. Since the angle is 60°, the opposite side (opposite the 60° angle) has length √3 and the adjacent side (adjacent to the 60° angle) has length 1.
Using these values, we can calculate the sine and cosine of 60°:
sin(60°) = opposite/hypotenuse = √3/2
cos(60°) = adjacent/hypotenuse = 1/2
Now, we can find cot(60°):
cot(60°) = 1 / tan(60°)
= 1 / (sin(60°) / cos(60°))
= 1 / (√3/2 / 1/2)
= 1 / (√3/1)
= 1 / √3
= √3 / 3
Therefore, the exact value of cot(60°) is √3 / 3.
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can someone tell me what the answer for this problem is? (and how you are able to get that answer)
What is 26.895 rounded to (2dp decimal points)
Given the statements, "A square root of 16 is 4," and "A square root of 9 is -3," complete the following blanks with the correct truth-values.
P is (true or false) and q is (true or false) , so the statement, "A square root of 16 is 4 or a square root of 9 is -3" is (true or false) .
Answer:
P is True and q true is , so the statement, "A square root of 16 is 4 or a square root of 9 is -3" is false .
Explanation:
The table of conjunctions show:
If p is true and q is true, then p & q are trueIf p is true and q is false, then p & q are falseIf p is false and q is true, then p & q are falseIf p is false and q is false, then p & q are falseThe first statement, "A square root of 16 is 4," (p), is true.
The second statement, "a square root of 9 is -3," (q), is true.
Therefore, p & q is true.what is the inverse of the function h(x) = 3x^2 - 1?
Which of the following is NOT a typical method of payment for a job?
A. paycheck
B. money order
C. direct deposit
D. cash
A line that passes through the points (2,1) and (k,5) is perpendicular to the line y=3x-9. Find the value of k
The value of k, which forms a line perpendicular to y=3x-9 passing through the points (2,1) and (k,5), is -2. This is determined by using the slope formula and the property that the slope of a line perpendicular to a given line is the negative reciprocal of the given line's slope.
Explanation:The subject of this question is linear equations in mathematics, specifically about finding the slope and working with perpendicular lines. The given equation, y=3x-9, represents a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this given equation, the slope (m) is 3 and the y-intercept (b) is -9.
If another line is perpendicular to this line, its slope is the negative reciprocal of the given line's slope. Therefore, the slope of the line that passes through the points (2,1) and (k,5) would be -1/3.
The slope formula, (m = (y2 - y1) / (x2 - x1)), can be used to find the value of k. So, we have -1/3 = (5 - 1) / (k - 2). From this, you can solve for k to find that k = -2.
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If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
A. (0, –2)
B. (1, –1)
C. (2, 0)
D. (3, 3)
Answer:
(3,3)
Step-by-step explanation:
Greg and Josh want to go whitewater rafting in 3 weeks. Josh is able to save the $480 he needs to go on the trip by saving the pay he received for 5 hours of work each week. Greg must save 8 hours worth of pay each week in order to have enough money. How much more money does Josh make than Greg? a. $10 b. $12 c. $14 d. $20
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
Amount Josh is able to save = $480
Number of hours of work each week = 5
Number of weeks = 3
So, Amount Josh makes is given by
[tex]\dfrac{480}{5\times 3}\\\\=\dfrac{480}{15}\\\\=\$32[/tex]
Similarly,
Number of hours of work each week by Greg = 8
Number of weeks = 3
So, Amount Greg makes is given by
[tex]\dfrac{480}{3\times 8}\\\\=\dfrac{480}{24}\\\\=\$20[/tex]
More amount of money that Josh make than Greg is given by
[tex]32-20\\\\=\$12[/tex]
Hence, Option 'b' is correct.
potatoes are selling for $0.48 per pound. how much is 12 lbs. of potatoes?
A $57.60
B $60.06
C $5.76
D $6.06
Express the given terminating decimal as a quotient of integers. if possible, reduce to lowest terms. 0.66
The number 0.66 can be written as a terminating decimal as a quotient of integers is 33/50.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The decimal number is 0.66 which is non-terminating.
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We can write the number 0.66 as:
= 66/100
= On simplification:
= 33/50
Thus, the number 0.66 can be written as a terminating decimal as a quotient of integers is 33/50.
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Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 855 people, 47 people had hearing aids.
A car is traveling at a rate of 120 kilometers per hour. what is the car's rate in miles per hour? how many miles will the car travel in 5 hours? in your computations, assume that 1 mile is equal to 1.6 kilometers.
The length of a train car is 50.6 feet. this is 5.8 feet less than six time the width. what is the width?
which of the following pairs of functions are inverses of each other?
Answer:
The pair which are inverse of each other are:
Option: C
[tex]f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}[/tex]
Step-by-step explanation:
Two functions f(x) and g(x) are said to be inverse of each other if:
fog(x)=gof(x)=x
i.e. the composition of two functions give identity no matter what the order is.
A)
[tex]f(x)=\dfrac{x}{12}+15[/tex] and [tex]g(x)=12x-15[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x[/tex]
Hence, option: A is incorrect.
B)
[tex]f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x[/tex]
Hence, option: B is incorrect.
D)
[tex]f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)[/tex]
[tex]fog(x)=9+\sqrt[3]{9-x^3}\neq x[/tex]
Hence, option: D is incorrect.
C)
[tex]f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})[/tex]
[tex]fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x[/tex]
Similarly,
[tex]gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x[/tex]
Hence, option: C is the correct option.
Answer:
D.f(x)=8x³+6 and g(x)=³x-6/8
Step-by-step explanation:
apex
Hidemi is a waiter. He waits on a table of 4 whose bill comes to $90.27. If Hidemi receives a 15% tip, approximately how much will he receive?
$4.50
$103.50
$13.50
$13.05
Hidemi will receive a tip approximately amount of $13.50 which is the correct answer would be option (C).
Hidemi works as a waiter. He serves a table of four with a bill of $90.27. If Hidemi gets a 15% tip which is given in the equation.
What is the percentage?The percentage is defined as a ratio stated as a fraction of 100.
For example, if Shekharaman received a 57% on his quiz, she received a 67 out of 100. It is written as 57/100 in fractional form and 57:100 in ratio form.
We have to determine the evaluation of 15% of $90.27.
⇒ 15% of 90.27
15% is described as 15/100 in fractional form
⇒ (15/100)(90.27)
15/100 is expressed as 0.15 in decimal form
⇒ (0.15)(90.27)
Apply the multiplication operation, and we get
⇒ 13.540 ≈ 13.50
Therefore, He will receive a tip approximately amount of $13.50.
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he coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .
Which statement correctly describes the relationship between △JKL and △J′K′L′ ?
△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a translation 1 unit up followed by a reflection across the y-axis, which is a sequence of rigid motions.
△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a reflection across the x-axis followed by a reflection across the y-axis, which is a sequence of rigid motions.
△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.
△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.
Answer:
As Given :The coordinates of the vertices of △JKL are J(3, 0) , K(1, −2) , and L(6, −2) . The coordinates of the vertices of △J′K′L′ are J′(−3, 1) , K′(−1, 3) , and L′(−6, 3) .
⇒As we can see the two triangles are congruent because length of sides are equal.i.e By SSS ΔJKL and ΔJ'K'L' are congruent.
⇒ As you can see from the figure depicted below the triangle JKL is rotated by an angle of 180° then translation of y coordinate by 1 unit up has taken place.
So , Option (3) is correct which is :△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 180° about the origin followed by a translation 1 unit up, which is a sequence of rigid motions.
Solve the inequality. g – 6 > –1
Answer:
g>5
Step-by-step explanation:
g-6>-1
+6 to both sides
g is left alone :)
Find the area of triangle QRS. Round the answer to the nearest tenth. A. 19.4 square units B. 91.2 square units C. 1,040.5 square units D. 1,052.4 square unts
Answer: Letter B.
Step-by-step explanation:
what will be the result of substituting 2 for x in both expressions below?
Answer:
the anwser is A
Step-by-step explanation:
if you didnt understand the top
Ricky bought flowers for Susan he spent a total of $14.85 and bought 13 flowers if you knows Lillys cost $1.25 and tulips cost $.90 how many of each flower did he buy Susan
Write an expression for the sum of four consecutive odd integers where 2n +1 represents the smallest odd integer.
Casey bought sandwiches and bags of chips. Each sandwich cost three times as much as a bag of chips. She bought 5 sandwiches for $6 each and spent $42. How many bags of chips b did she buy?
Answer:
She bought 6 bag of chips.
Step-by-step explanation:
Let the price of bag of chips be s.
Each sandwich cost three times as much as a bag of chips.
Cost of sandwich = 3s
She bought 5 sandwiches for $6.
That is cost of sandwich = 3s = 6
s = 2$
Cost of bag of chips = s = 2$
Price of 5 sandwiches = 5 x 6 = 30 $.
She spent $42, remaining money = 42 - 30 =12 $
Number of bag of chips can be bought with 12 $
[tex]n=\frac{12}{2}=6[/tex]
She bought 6 bag of chips.
Which expression is a difference of cubes?
A.9w^33 - y^12
B.18p^15 - q^21
C.36a^22 - b^16
D.64c^15 - d^27
The expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is 64c¹⁵-d²⁷. the expression will be written in the power of a cube as below:-
64c¹⁵-d²⁷ = (4c⁵)³ - (d⁹)³
Therefore, the expression 64c¹⁵-d²⁷ having a difference of cube will be (4c⁵)³ - (d⁹)³. The correct option is D.
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535 students of the senior class voted to take a field trip ir 3/4 of the class voted, how many students voted for the trip? Round your answer to the nearest whole number.
Answer:
401 students voted for the trip .
Step-by-step explanation:
As given in the question
535 students of the senior class voted to take a field trip[tex]\frac{3}{4}[/tex] of the class voted .
Thus
[tex]Students\ voted\ for\ the\ trip = \frac{3}{4}\times Total\ students[/tex]
Put value in the above
[tex]Students\ voted\ for\ the\ trip = \frac{3\times 535}{4}[/tex]
[tex]Students\ voted\ for\ the\ trip = \frac{1605}{4}[/tex]
= 401
Therefore 401 students voted for the trip .