Answer:
You would save $18
Step-by-step explanation:
(27/3)*2 = $18
The dimensions of Square A are three times The dimensions of Square B. The area of Square A is 1,296 cm2. What is the area of Square b?
Square B Area = 144cm²
Square B = X
The dimensions of Square A are three times The dimensions of Square B
Square A = 3 * Square B
Square A = 3X
The area of Square A is 1,296 cm2.
Square A Area = (3X)² = 1296
Square B Area = X²
Solve to find X.
(3X)² = 1296
3X = 36
X = 36/3 = 12
Square B Area = 12² = 144
Square B Area = 144cm²
Final answer:
The area of Square B is 144 cm², calculated by dividing the area of Square A (1,296 cm²) by 9, because the area of a square scales with the square of its linear dimensions.
Explanation:
The area of Square A is given as 1,296 cm². Since the dimensions of Square A are three times the dimensions of Square B, we can find the area of Square B by understanding that area scales in proportion to the square of the linear dimensions. This means that if one dimension is three times another, the area will be nine times (3² = 9) larger.
To find the area of Square B, we simply divide the area of Square A by 9:
Area of Square B = Area of Square A / 9
Area of Square B = 1,296 cm² / 9
Area of Square B = 144 cm².
Therefore, the area of Square B is 144 cm².
Solve the equation. Round to the nearest hundredth. Show work.
[tex]8^{-x+7} = 3^{7x+2}[/tex]
Answer:
Final answer is approx x=1.27.
Step-by-step explanation:
Given equation is [tex]8^{-x+7}=3^{7x+2}[/tex].
Now we need to solve equation [tex]8^{-x+7}=3^{7x+2}[/tex] and round to the nearest hundredth.
[tex]8^{-x+7}=3^{7x+2}[/tex]
[tex]\log(8^{-x+7})=\log(3^{7x+2})[/tex]
[tex]\left(-x+7\right)\cdot\log\left(8\right)=\left(7x+2\right)\cdot\log\left(3\right)[/tex]
[tex]-x\cdot\log\left(8\right)+7\cdot\log\left(8\right)=7x\cdot\log\left(3\right)+2\cdot\log\left(3\right)[/tex]
[tex]-x\cdot\log\left(8\right)-7x\cdot\log\left(3\right)=2\cdot\log\left(3\right)-7\cdot\log\left(8\right)[/tex]
[tex]x\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)=\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)[/tex]
[tex]x=\frac{\left(2\cdot\log\left(3\right)-7\cdot\log\left(8\right)\right)}{\left(-\log\left(8\right)-7\cdot\log\left(3\right)\right)}[/tex]
Now use calculator to calculate log values, we get:
[tex]x=1.26501646392[/tex]
Round to the nearest hundredth.
Hence final answer is approx x=1.27.
An artist wants to paint a mural. She mixes blue paint and red paint to make paint that is a certain shade of purple. The ratio of blue paint to red paint should be 3 to 2. She needs 20 gallons of the purple paint. How much more blue paint than red paint does she need?
Answer:
She needs 4 more gallons of blue paint than red paint
Step-by-step explanation:
Since the ratio is 3 to 2, 3 + 2 = 5.
The artist needs 20 gallons of purple paint, so 20/5 = 4
The amount of blue and red paint needed is 4x3 to 4x2, or 12 to 8.
She needs 12 gallons of blue paint and 8 gallons of red paint.
12 - 8 = 4
She needs 4 more gallons of blue paint than red paint.
Answer:
ok!
Step-by-step explanation:
blue = 8 gallons
red = 12 gallons
At a football game, the ratio of filled seats to empty seats was 7 to 3. The maximum capacity of the stadium is 70,580 seats. How many seats were filled for the game?
Add the two numbers in the ratio: 7 +3 = 10
Divide total capacity by 10:
70,580 / 10 = 7,058
Multiply that by the ratio of filled seats:
7,058 x 7 = 49,406
49,406 seats were filled.
What is the value of 6x squared+ 4x + 8 when x=7? Please answer this I really need help!
If 3(r+300)=6, then what would be the value of r+300-2?
Solve for r in the first equation:
3(r+300) = 6
Use the distributive property:
3r + 900 = 6
Subtract 900 from both sides:
3r = -894
Divide both sides by 3:
r = -894 / 3
r = -298
Now you have r, replace r in the second equation and solve:
r +300 -2 =
-298 + 300 - 2 = 0
The answer is 0.
Answer:
0 is the value of r+300-2
Solve for r in the first equation:
3(r+300) = 6
Use the distributive property:
3r + 900 = 6
Subtract 900 from both sides:
3r = -894
Divide both sides by 3:
r = -894 / 3
r = -298
Now you have r, replace r in the second equation and solve:
r +300 -2 =
-298 + 300 - 2 = 0
The answer is 0.
(a) What is the difference between a sequence and a series? A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers. A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is an unordered list of numbers. A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. (b) What is a convergent series? What is a divergent series? A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent. A series is divergent if the sequence of partial sums is a convergent sequence. A series is convergent if it is not divergent. A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent. A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent.
Answer:
a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A series is convergent if the sequence of partial sums is a convergent sequence.
Step-by-step explanation:
A sequence is a pattern. It is an ordered list of objects, such as numbers, letters, colors, etc.
A series is a sum of a sequence.
A divergent series is one that is not convergent.
A convergent series is one in which the sequence of partial sums approaches a limit; this means the partial sums form a convergent sequence.
60 POINTS!!! Please Help ASAP
Question:
Find the distance between the points (1, 4) and (-5, -4) on the coordinate plane. Show your work to justify your answer and earn full credit.
ANSWER
The distance is 10 units.
EXPLANATION
Let us use the distance formula to find the distance between,
[tex](x_1,y_1)=(1,4)[/tex]
and
[tex](x_2,y_2)=( - 5, - 4)[/tex]
The distance formula is given by,
[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} [/tex]
We plug in the values to get,
[tex]d = \sqrt{( - 5-1)^2 + ( - 4-4)^2} [/tex]
[tex]d = \sqrt{( -6)^2 + ( - 8)^2} [/tex]
[tex]d = \sqrt{36+ 64} [/tex]
[tex]d = \sqrt{100} [/tex]
[tex]d = 10[/tex]
How many times greater is the value of the 4 in 64781 than the value of the 2 in 25409
64,781 --- 4,000
25,409 --- 400
4,000÷400=10
If cos x = 2 / 3 and x is in quadrant 4, find:
a. sin(x / 2)
b. cos(x / 2)
c. tan(x / 2)
Answer:
A
Step-by-step explanation:
cos(x)=2/3 in Q 4
sin(x/2)=+√(1-cos(x))/2
√(1-cos(x))/2=√(1-[2/3]/2=√(1/3)/2=-√(1/6) because sin is negative in Q 4
Answer:
See below.
Step-by-step explanation:
Because cos x = 2/3 the adjacent side = 2 and hypotenuse = 3 so the length of the opposite side =
√(3^2 - 2^2) = -√5 (its negative because we are in Quadrant 4).
So sin x = -√5/3.
(a) sin (x /2) = - √ [ (1 - cos x)/2 ]
= -√(1 - 2/3)/ 2)
= -√(1/6). or -0.4082.
(b) cos (x/2) = √ [ (1 + cos x)/2]
= √ 5/6 or 0.9129.
(c) tan (x /2) = ( 1 - cos x) / sin x.
= ( 1 - 2/3) / -√5/3
= -0.4472.
It takes Ebru 13 minutes to bike to school. If she walks, it takes her twice as long. Ebru leaves for school at 7;15 What time will Ebru get to school if she walks?
Answer:
[tex]7;41[/tex]
Step-by-step explanation:
Let
x----> the time it take Ebru to walk to the school
we know that
[tex]x=2(13)=26\ min[/tex]
so
[tex]7;15 +26\ min=7;41[/tex]
Ebru takes 26 minutes to walk to school, twice as long as biking. Leaving at 7:15 AM means she would arrive at school by walking at 7:41 AM.
If Ebru bikes to school, it takes her 13 minutes. Walking takes her twice as long, which would be 26 minutes. If Ebru leaves her house at 7:15 AM, we can calculate the time she will get to school by walking by adding 26 minutes to the departure time.
7:15 AM + 20 minutes = 7:35 AM7:35 AM + 6 minutes = 7:41 AMTherefore, if Ebru walks to school, she will arrive at 7:41 AM.
a bag contains 'p' white balls 'Q' red balls and 'R'
Blue Balls A ball is drawn at the random find the probability of getting blue ball
Answer:
probability is r/p+q+r
Step-by-step explanation:
to find the probability, you take the number of desired balls (blue in this case )
and divide it by the total number of balls in the problem (add them all up) to get your answer
I hope that answered your question!!
The red object below, is best defined as a
Answer:
Where is the red object?
Step-by-step explanation:
I CANT SEE THE RED OBJECT U DIDNT PUT ITTT
Which expression is equivalent to 8(a-6)
a. w>36
b w<36
c.w>5
d.w<5
Answer:
8a - 48
Step-by-step explanation:
An equivalent expression is an expression which is equal to 8(a-6). You can expand or simplify an expression to make an equivalent expression. Apply the distributive property to form a new equivalent expression by multiplying 8 into each term. 8(a-6) = 8*a - 8*6 = 8a - 48. The options listed below do not connect to this problem since they do not use the same variable as the expression.
Question part points submissions used use newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (round your answer to four decimal places.) 2x3 − 3x2 + 2 = 0, x1 = −1
Set [tex]f(x)=2x^3-3x^2+2[/tex]. Find the tangent line [tex]\ell_1(x)[/tex] to [tex]f(x)[/tex] at the point when [tex]x=x_1[/tex]:
[tex]f'(x)=6x^2-6x\implies f'(x_1)=12[/tex] (slope of [tex]\ell_1[/tex])
[tex]\implies\ell_1(x)=12(x-x_1)+f(x_1)=12(x+1)-3=12x+9[/tex]
Set [tex]x_2=-\dfrac9{12}[/tex], the root of [tex]\ell_1(x)[/tex]. The tangent line [tex]\ell_2(x)[/tex] to [tex]f(x)[/tex] at [tex]x=x_2[/tex] has slope and thus equation
[tex]f'(x_2)=\dfrac{63}8\implies\ell_2(x)=\dfrac{63}8\left(x+\dfrac9{12}\right)-\dfrac{17}{32}=7x+\dfrac{151}{32}[/tex]
which has its root at [tex]x_3=-\dfrac{151}{224}\approx-0.6741[/tex].
(The actual value of this root is about -0.6777)
Theres 5 boxes of candle. One box has 16 candles Four boxes has 24 candles each How many candles do the five boxes have altogether?
Answer:
112 candles
Step-by-step explanation:
We can simply add up the 5 numbers of candles, or we can take advantage of the invention of multiplication to replace repeated addition. The number of candles altogether is the sum of the numbers of candles in each of the 5 boxes.
16 + 4×24 = 16 +96 = 112
The total number of candles is 112.
the question and answers are below on the picture
Answer:
[tex]\large\boxed{B)\ 16x^2-25}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (a-b)(a+b)=a^2-b^2[/tex]
[tex](4x-5)(4x+5)=(4x)^2-5^2=16x^2-25[/tex]
Find a number less than 100 that is increased by one-fifth of its value when its digits are reversed.
Lets say the number is ab. Its value is 10a + b
When it is reversed it is 10b + a = 12a+1.2b (from the condition its value should increase 0.2 times).
11 a = 8.8b
a/b = 8.8/11 = 0.8/1 = 8/10 = 4/5 ( we do this because a and b should be natural numbers less than 10).
answer is 45.
A two-digit number less than 100 that increases by one-fifth of its original value, when its digits are reversed, can be found by setting up an equation. By defining the tens digit as 'a' and the unit digit as 'b', the equation 6a = 9b is derived. Solving for the digits within their possible values, the number 12 is found.
Explanation:To find a number less than 100 that increases by one-fifth of its value when its digits are reversed, we need to set up an equation. Let's call the tens digit a and the units digit b. The number can be written as 10a + b. When the digits are reversed, the number becomes 10b + a. The problem states that reversing the digits increases the number by one-fifth of its original value, which gives us the equation:
(10a + b) + \frac{1}{5}(10a + b) = 10b + a
Now solving the equation:
6a = 9b
As a and b are digits, their possible values range between 0 and 9. We find that a = 1 and b = 2 satisfy the equation. Hence, the number is:12
When we reverse the digits, we get 21, which is greater than 12 by \frac{1}{5} of 12, as required.
Learn more about Reversing Digits Problem here:https://brainly.com/question/34687674
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Store A sells 12 juice bottles for $4 and store B sells 18 juice bottles for $6 are the rates equivalent
Answer:
Yes
Step-by-step explanation:
Mateo wants to make a toy sailboat. He has two pieces of wood to choose from.
His first piece of wood is a block that measures 18'' x 10" x 8". It weighs 46.65 lbs.
His second piece of wood is a log of wood measuring 21" long, with an average circumference of 25.12". It weights 39.25 lbs.
The sailboat needs to float, but both blocks of wood are denser than wood usually is, and he's not sure either piece of wood will float. He doesn't want to get the water wet before he's applied a sealant, so he isn't willing to just drop them in the water to find out.
2a. Which common solid can he use to represent the block? Which common solid can he use to represent the log? (2 points)
2b. What is the density of the block in pounds per cubic inch? Give the formula for density and show your work. (3 points)
2c. What is the density of the log in pounds per cubic inch? Give the formula for density and show your work. Use 3.14 for π. (Hint: you can determine the radius from the circumference.) (3 points)
2d. Water has a density of about 0.0361 pounds/cubic inch. Anything rarer will float, and anything denser will sink. Which of the pieces of wood are suitable for making a toy boat that will float? (2 points)
Answer:
wut is it
Step-by-step explanation:
A baseball infield is in the shape of a square within the bases and home plate. The area of the infield is 8,100 square feet. What is the length of one side of the infield?
a scientist is growing bacteria in a lab for study one particular type of bacteria grows at a rate of y=2t^2+3t+500 a different bacteria grows at a rate of y=3t^2+t+300 in both of these eqiations y is the number of bacteria after t minutes when is there an equal number of both types of bacteria
Please help me with this...
3x+4=5x-50
54=2x
27=x
Answer:
x = 27
Step-by-step explanation:
The diagonals of a rectangle are congruent, hence
BD = AC ← substitute values
5x - 50 = 3x + 4 (subtract 3x from both sides )
2x - 50 = 4 ( add 50 to both sides )
2x = 54 ( divide both sides by 2 )
x = 27
NEED HELP ASAP! PLEASE HElp!!
the answer should be C
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given byP(x) = p(1-p)^(x-1)where p is the probability of success on any one trial.Assume that the probability of a defective computer component is 0.34. Find the probability that the first defect is found in the second component tested.(Round answer to four decimal places.)P(2) =
Answer:
0.2312
Step-by-step explanation:
Using the formula given,
[tex]P(x) = p(1-p)^{x-1}[/tex],
we use 0.34 for p and 2 for x:
[tex]P(2) = 0.34(1-0.34)^{2-1}\\\\P(2) = 0.34(0.68)^1\\\\P(2) = 0.34(0.68) = 0.2312[/tex]
Which function has the graph shown?
Answer:
y = csc(x) -1
Step-by-step explanation:
The vertical offset of -1 is your first clue. Your second clue is that the range does not include (-2, 0), typical of cosecant and secant functions (offset by -1).
_____
Comment on answer choices
Apparently the cosine choices are intended to be confused with the cosecant choice. The cosine function has a range of [-1, 1], so will not show any vertical asymptotes anywhere, regardless of scaling or translation.
A counterexample for the expression sin y tan y= cos y is 0.
Answer:
True
Step-by-step explanation:
To answer this question we must evaluate
y = 0° on both sides of the equation.
For the left side we have:
[tex]sin(0\°) tan(0\°)[/tex]
We know that [tex]tan(0\°) =\frac{sin(0\°)}{cos(0\°)}[/tex]
We know that [tex]cos(0\°) = 1[/tex] and [tex]sin(0\°) = 0[/tex].
Therefore [tex]tan(0\°) = 0[/tex].
Then the left-hand side of the equals is equal to zero.
On the right side we have:
[tex]cos(y)[/tex]
When evaluating [tex]cos(y)[/tex] at [tex]y = 0[/tex]
We have to [tex]cos(0\°) = 1[/tex].
0 ≠ 1
The equation is not satisfied. Therefore y = 0 ° is a counterexample to the equation
Answer:true
Step-by-step explanation:
edge
the graph of F(x), shown below, has the same shape as the graph of G(x)=x^2. but it is shifted up 4 units and to the right 3 units. What is its equation
Answer:
C
Step-by-step explanation:
The equation is y = a(b(x-c))+d
So for it to move right three units, it would be x - 3.
For it to move up 4 unites, it would be x+4.
So the equation would be y = (x - 3)^2 + 4
The correct answer is C
First you would substitute the expression moving it to the left then you change the signs the power function with an even exponent is always a positive or 0 but there is no x intercept.
In your own words, summarize how the Jacksonian Era was characterized?
Answer: Actually The Jacksonian Era was characterized by the thought that each individual also equally have right and he or she is important and that all should be able to have a say or participate in any government activities.
All in all i think its actually giving greater right to the common man.
Use the x-intercept method to find all real solutions of the equation.
x^3-6x2+3x+10=0
Answer:
Three solutions were found :
x = 5
x = 2
x = -1
Step-by-step explanation:
Answer:
d. [tex]x=-1,2,\:or\:5[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-6x^2+3x+10=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator.
The corresponding function is
[tex]f(x)=x^3-6x^2+3x+10[/tex]
The solution to [tex]x^3-6x^2+3x+10=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(2,0) and (5,0).
Therefore the real solutions are:
[tex]x=-1,2,\:or\:5[/tex]