Answers
The current area of Mr. Milstein's kitchen table is:
[tex]=17\frac{1}{2}\text{ square fe}e\text{t}[/tex]The new width of Mr. Milstein's kitchen table = 5 feet
The area of the new kitchen table if the length is l is given by
[tex]\text{ Area (A) = length x width = 5l}[/tex]Note that the area of the proposed kitchen table should be larger than the current one.
[tex]\begin{gathered} \text{ The current area = }17\frac{1}{2}\text{ square fe}e\text{t} \\ \text{ The new area = 5 x l = 5l} \\ \text{ Therefore,} \\ \text{ proposed area > new area} \\ \text{ 5l >}17\frac{1}{2}\text{ square fe}e\text{t} \end{gathered}[/tex]Therefore,
[tex]\text{ 5l >}17\frac{1}{2}\text{ square fe}e\text{t can be used to get the length of the new table}[/tex]The correct option is F
Related Questions
Write 0.00128 in scientific notation
Answers
Given:
[tex]0.00128[/tex]To write it in scientific notation:
It can be written as,
[tex]\begin{gathered} 0.00128=\frac{1.28}{1000} \\ =\frac{1.28}{10^3} \\ =1.28\times10^{-3} \end{gathered}[/tex]Hence, the scientific notation is,
[tex]1.28\times10^{-3}[/tex]The perimeter of the triangle and the perimeter of the square are equal. Create and solve an equation to find the value of x.
Answers
Answer: 16
Step-by-step explanation:
The perimeter of the triangle is [tex]2x+2x+x-8=5x-8[/tex].
The perimeter of the square is [tex]4(x+2)=4x+8[/tex].
Setting the perimeters equal to each other,
[tex]5x-8=4x+8\\\\x-8=8\\\\x=16[/tex]
I need help finding at least three solutions 10 8 7 6 4 = 2 you can add subtract and/or divide
Answers
You can only subtract or divide?
the figure above represents a closed cylindrical tank of height 15m.the radius of the Cross-section is 7m. Calculate a) the curved surface area of the tank. b) the volume of the tank. use π=22/7
Answers
Answer:
a) The curved surface area is;
[tex]660\text{ }m^2[/tex]b) The volume of the cylindrical tank is;
[tex]2310\text{ }m^3[/tex]Explanation:
Given that the cylindrical tank has height 15m and radius 7m.
[tex]\begin{gathered} h=15\text{ m} \\ r=7\text{ m} \\ \pi=\frac{22}{7} \end{gathered}[/tex]The curved surface area of a cylinder can be calculated using the formula;
[tex]A=2\pi rh[/tex]substituting the given values;
[tex]\begin{gathered} A=2\times\frac{22}{7}\times7\times15 \\ A=660m^2 \end{gathered}[/tex]Therefore, the curved surface area is;
[tex]660\text{ }m^2[/tex]The volume of the cylindrical tank can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\frac{22}{7}\times7^2\times15 \\ V=2310m^3 \end{gathered}[/tex]Therefore, the volume of the cylindrical tank is;
[tex]2310\text{ }m^3[/tex]Jonah picked 287 cherry tomatoes from his garden in May and 339 in June.
How many cherry tomatoes did Jonah pick in all?
The estimate by rounding to the nearest hundred. Then solve.
Answers
Answer:
600
Step-by-step explanation:
the total is 626 but round it to the nearest hundred is 600 because the rule 5 or more go up one more 4 or less stay at rest
Find BC.
Round to the nearest tenth.
C
12
A
87°
9
B
Answers
Answer:
C-10
A-90
B-10
Step-by-step explanation:
For rounding off to nearest tens, we compare the last digit.
The amount of cereal in a box is normally distributed with a mean of 24 oz. and a standarddeviation of 0.62 oz. If 7,500 boxes of cereal are packaged in one day, approximately how many boxeswould contain less than 22.9 oz.?
Answers
Given data:
The given mean is m=24.
The given standard devaition is s=0.62.
The given vallue is x=22.9.
The expression for the value of z is,
[tex]\begin{gathered} P(x<22.9)=P(z<\frac{x-m}{s}) \\ =P(z<\frac{22.9-24}{0.62}) \\ =P(z<-1.774) \end{gathered}[/tex]Refer the standard z-table.
[tex]P(x<22.9)=0.03836[/tex]The number of box required are,
[tex]\begin{gathered} N=7,500\times0.03836 \\ =287.7 \\ \approx288 \end{gathered}[/tex]Thus, the number of boxes are 288.
Please help??????????
Answers
Answer:
Equation: 2x +2x +x -8= 4(x +2)
x= 16
Step-by-step explanation:
The perimeter is the total length of the sides of a particular shape or figure.
Given that the triangle and square have an equal perimeter,
Perimeter of triangle= perimeter of square
Since a square has 4 equal sides,
2x +2x +x -8= 4(x +2)
Let's solve the above equation.
Simplify and expand:
5x -8= 4x +8
Move x terms to the left of the equation, constants to the right.
5x -4x= 8 +8
x= 16
Thus, the value of x is 16.
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Answer:
x = 16
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
As the sides of a square are equal in length, the perimeter of a square is four times the length of one side.
[tex]\begin{aligned}\implies \textsf{Perimeter of the square}&=4(x+2)\\& = 4x+8\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Perimeter of the triangle}&=2x+2x+(x-8)\\&=4x+x-8\\&=5x-8\end{aligned}[/tex]
If the perimeter of the triangle and the perimeter of the square are equal then:
[tex]\begin{aligned}\implies\textsf{Perimeter of the triangle}&=\textsf{Perimeter of the square}\\5x-8&=4x+8\\5x-8-4x&=4x+8-4x\\x-8&=8\\x-8+8&=8+8\\x&=16\end{aligned}[/tex]
Therefore, the value of x is 16.
What is the unit rate per bottle if a pack of 25 bottles of juice sells for $5
Answers
Answer:
Each bottle cost $0.20. That is the unit rate
Step-by-step explanation:
[tex]\frac{5.00}{25}[/tex]
The table shows the proportional relationship between the number of uniform shirts for a soccer team and the cost. Number of Uniform Shirts Cost (in dollars) 9 148.50 15 247.50 21 346.50 Determine the constant of proportionality. 99.50 54 16.50 6
Answers
The constant of proportionality that lies in all of the pairs of values that we have here is given as 17.5
What is the constant of proportionality?This is the term that is used to refer to the ratio that is known for the fact that it helps to relate two values that are given in a proportional way.
For instance we are to find the constant proportionality of (9, 148.50)
This is given as 9 + 148.5 / 9
= 157.5 / 9
= 17.5
Then the second pair is (15 ,247.50)
In the same way 15 + 247.50 / 15 = 17.5
Hence we can see that the constant of proportionality in all of the pairs is 17.5
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Answer:
its 16.50 i literally just took the test trust me.
Step-by-step explanation:
9 x 16.50 = 148.50
15 x 16.50= 247.50
21 x 16.50 = 346.50!
hope this helps! =)
HELP PLEASEEEEE!!!!!!
Answers
A rational number between the two given ones is -2/5, such that:
-1/3 > -2/5 > -1/2.
How to find a rational number between the two given ones?Rememeber that a rational number is any number that can be written as a quotient between two integer numbers.
Here we want to find a rational number between -1/3 and 1/-2, we can rewrite the second one as -1/2.
Now we want to find a number x such that:
-1/3 > x > --1/2
Remember that:
-1/3 ≈ -0.33...
-1/2 ≈ -0.5
So a number between these two is -0.4 which can be written as -2/5 (this is also rational).
That is the number we wanted to find.
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Sketch the graph of the line whose equation, in point-slope form, is y-3=9/5 (x+1). Also write the equation of this line in slope- intercept form .(y=mx+b )
Answers
Given the equation of the line in point-slope form:
[tex]y-3=\frac{9}{5}(x+1)[/tex]Based on this, one point of the line is (-1, 3). Now, the slope-intercept form of the equation is:
[tex]\begin{gathered} y-3=\frac{9x}{5}+\frac{9}{5} \\ y=\frac{9}{5}x+\frac{9}{5}+3 \\ \Rightarrow y=\frac{9}{5}x+\frac{24}{5} \end{gathered}[/tex]Then, another point of the line is (0, 24/5) = (0, 4.8). Finally, the graph of the equation is:
write an equation of the line in the point- slope form that passes through the given points in the table. Then write the equation in slope-intercept form. (10,80) (5,65)
Answers
To write the equation of the line that passes through (10,80) (5,65)
we will use the formula;
[tex]y-y_1\text{ =}\frac{y_{2-}y_1}{x_2-x_1}(x-x_1)[/tex]x₁ = 10 y₁ = 80 x₂ = 5 y₂ = 65
substituting the above into the formula;
[tex]y\text{ - 80 = }\frac{65\text{ - 80}}{5\text{ - 10}}(\text{ x - 10)}[/tex]we will go ahead and simplify
[tex]y\text{ - 80 = }\frac{-15}{-5}(x-10)[/tex]y- 80 = 3(x - 10)
y- 80 = 3x - 30
y -3x -80 + 30 = 0
y - 3x - 50 = 0
The above is the equation of the line.
To write in a slope-intercept form simply means to write it in the form;
y = mx + b
where m is the slope and b is the intercept
Hence;
y = 3x + 50
The above is the equation of the line in a slope-intercept form
1 i Solve the system of linear equations. y = -2x - 4 y = 2x - 4
Answers
In order to solve the system, we can compare both y values from each equation:
[tex]\begin{gathered} \begin{cases}y=-2x-4 \\ y=2x-4\end{cases} \\ -2x-4=2x-4 \\ 4x=0 \\ x=0 \\ \\ y=2x-4 \\ y=0-4 \\ y=-4 \end{gathered}[/tex]So the solution for this system is the pair (0, -4), that is, x = 0 and y = -4.
Cylinder 1 is congruent to cylinder 2. The dimensions of the cylinders are given inunits.Cylinder 1Cylinder 238What is the volume of cylinder 2?
Answers
Since the two cylinders are congruent, it means that their dimensions are exactly the same thing.
In other words, the radius of cylinder 1 is the same as that of cylinder 2, and the height of cylinder 2 is the same as that of cylinder 1. This is what it means for two solid shapes to be congruent.
Now, to find the volume of cylinder 2, we apply the frmula for the volume of a tyical cylnder:
[tex]\text{Volume}=\pi\times r^2\times h[/tex]Now,
radius of cylinder 2 = radius of cylinder 1 = 3
height of cylinder 2 = 8
Thus: r = 3, h= 8
Therefore:
[tex]\begin{gathered} \text{Volume}=\pi\times r^2\times h \\ \text{Volume}=\pi\times3^2\times8 \\ \text{Volume}=\pi\times9^{}\times8 \\ \text{Volume}=\pi\times72 \\ \text{Volume}=72\pi\text{ cubic units} \end{gathered}[/tex]Therefore the volume of cylinder 2 is 72pi cubic units (Option D)
The probability distribution for arandom variable x is given in the table.Find the probability that x>5
Answers
The probability that x≥5
P (x≥5) = P(5)+P(10)+P(15)+ P(20)
P (x≥5)= 0.1+0.25+0.1+0.15
P (x≥5)= 0.6
Carolyn leases a new Hyundai Elantra by paying $2400 up front and $167 a month over three years. The lease also stipulates he will be charged $0.12 per mile forevery mile over 36,000. If she puts 39,087 miles on the car, what will be the total cost of the lease?Round your answer to the nearest cent hundredth) but do not include a Sin your response
Answers
we have that
3 years=3(12)=36 months
so
$2,400+$167(36)=$8,412
and
39,087-36,000=3,087 miles
so
$0.12*(3,087)=$370.44
therefore
The total cost is
$8,412+$370.44=$8,782.44
the answer is $8,782.44D Question 6 6) sin A С 39 36 15 B 5 12 A) B) 12 13
Answers
B) 12/13
1) In this triangle, the sine of angle A is given by the opposite leg over the hypotenuse, so we can write it out. Since the hypotenuse is opposite to the right angle:
[tex]\begin{gathered} \sin (A)=\frac{36}{39} \\ \sin (A)\text{ = }\frac{12}{13} \end{gathered}[/tex]Note that we simplified that original ratio 36/39 dividing both numerator and denominator by 3
2) Hence, the answer is B) 12/13
Write the equation of the line that passes through the given points.
(0, 1) and (2, 2)
Answers
The equation of the line passing through points (0,1) and (2,2) will be y = ( 1 / 2) x + 1
What is an equation of the line?
An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope= 2-1 / 2-0 = 1 /2
Now pick one of the points and put in for y and x use (2,2).
2= 1/2(2) +b
2=1 + b
2-1 =1-1 +b subtract 1 from each side
1 = b This is your y-intercept
The equation will be written as:-
y = ( 1 / 2) x + 1
If EFGH is a parallelogram, what is the value of x?F(4-2)340HGA. 82B. 30.5cC. 36D. 37E. 34F. 9
Answers
x = 36° (option C)
Explanation:The adjacent angles in a parallelogram are supplementary. This means the sum of the angles is equal to 180 degrees
The adjacent angles in this paralllelogram are (4x + 2)° and 34°
(4x + 2)° + 34° = 180°
4x + 2 + 34 = 180
4x + 36 = 180
4x = 180 - 36
4x = 144
Divide both sides by 4:
4x/4 = 144/4
x = 36° (option C)
Find the slope of each line.
Answers
Given any line, to find the slope of the line, follow the procedure below:
First, pick any two points (x1,y1) and (x2,y2) on the line.
Then, substitute the points into the formula for slope below:
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]You can use this method to find the slope of any given line.
let x = 12; then y = 7/2(12) = 2 = 42 + 2 = 44
slope = m.... m = (y1 - y2)/(x1 - x2) then plug in the x & y values...
m = (30 - 44)/(8 -12) = -14/-4 = 7/2
thus, slope of line 'y' = 7/2
create your own systems of equations that has a solution of (-2,4)
Answers
In this case we have the point (-2,4), since this represents the x and y coordinates of the solution of the system of equations, then:
x= -2
y= 4
Let's create the pair of equations:
1. ax+by=c
2. ex+fy=g
Randomly let's define the values of the coefficients a, b, e and f:
a= 1
b=2
e= -1
f= 4
With these values and the known coordinates of the solution, let's replace into the expressions of the system of equations and solve for c and g, like this:
answer pls :DD
3x - 6 =42
Answers
49/3
X=16.3
Boom
Find the distance between: (6,12) and (7,-4)
Answers
The formula for determining the distance betwwen two points is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt{(y2-y1)^2+(x2-x1)^2} \\ \text{From the information given,} \\ x1\text{ = 6, x2 = 7} \\ y1\text{ = 12, y2 = - 4} \\ \text{Distance = }\sqrt{(-4-12)^2+(7-6)^2} \\ \text{Distance = }\sqrt{-16^2+1^2}=\sqrt{257} \\ \text{Distance = 16.03} \end{gathered}[/tex]The distance is 16.03
A jet flies at an average speed of 230
miles per hour. How long will it take to
fly from New York to Amsterdam, a
distance of 3,647 miles? (distance =
rate time)
.
Answers
Answer:
15
Step-by-step explanation:
Speed= 230 per hour
Distance=3,647
Formula
Time=Distance upon speed
divide 230 into 3,647=15 time
It costs $5,600 to manufacture a Jet Ski. If the desired percent markup based on cost is 48%, how much should each Jet Ski sell for?
Answers
Each Jet Ski should sell for $8288.
What is selling price?
The amount a buyer pays for a good or service is known as the selling price. It may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.
Let the selling price be x.
Therefore according to the question,
( x - 5600/ 5600) 100 = 48
=> x - 5600 = 48 . 56
=> x = 2688 + 5600
=> x = 8288
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PLEASE HELP!!!
In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
168°
102°
57°
12°
Answers
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168° so option (A) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠J + m∠L + m∠K = 180°
m∠K = 180° - 78° - 90°
m∠K = 12°.
The exterior angle of k = 180- 12 = 168°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠K is 168°".
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Given mn, find the value of x.
(x+14)°
(9x-4)º
Answers
Answer: x = 17
Step-by-step explanation:
We can tell that these two angles are supplementary angles because we can use corresponding angles. See attached.
(x + 14)° + (9x - 4)° = 180°
x° + 14° + 9x° - 4° = 180°
14°- 4° + x° + 9x° = 180°
10° + 10x° = 180°
10x° = 170°
x = 17
the income for selling x units of a video game is R=257x. The cost to produce the game is C =193x +5248. In order to make a profit the income must be greater than the cost. find the vaule of X
Answers
The value of x when the income for selling x units of a video game is R=257x is x > 82.
What is the value of x?From the information given, it was stated that the income for selling x units of a video game is R=257x and that the cost to produce the game is C =193x +5248.
To make a profit the income must be greater than the cost. The value of x will be:
257x > 193x + 5248
Collect like terms
257x - 193x > 5248
64x > 5258
Divide
x > 5248/64
x > 82
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a) Find the exact solution of
log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2)
While x = 1
Answers
The exact solution of log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2) While x = 1 is 0.954.
Given:
log 3(2x - 1) + log 3(2x + 1) = log 3(x + 2)
= log 3(x + 2)
putting x = 1
= log 3( 1 + 2 )
= log 3 . 3
= log 3 + log 3
= 0.477 + 0.477
=0.954
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