The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
Amount to spend by the taxi driver ≤ 10.50.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The taxi company only has $10.50 to spend.
This means that,
The maximum amount to spend is $10.50.
We can also represent as:
Amount to spend by the taxi driver ≤ 10.50.
Thus,
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
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A band expects to put 16 songs on their next CD. The band writes and records 62.5% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD?
Answer:
songs in the final CD 13
Step-by-step explanation:
the 100% = 16
-------------------
16/x=100/62.5
(16/x)*x=(100/62.5)*x
16=1.6*x
16/1.6=x
10=x
x=10
This is the 62.5% of 16
---------------------
now the new 100% is 10 + 16 = 26
but during the editing process 50% are removed
and the 50% of 26 (half of it) is = 13
how many units apart are -6 and 4 on the number line
In any triangle the sum of the measures of the angles is 180°. And ABC is three times as large as B and also 16° larger than C. Find the measure of each angle
The measures of the each angle of the triangle is 84, 28 and 68 degrees.
How to find the measure of angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The triangle has the sum of the measures of the angles as 180°.
Angle A is three times as large as angle B and also 16° larger than C.
Therefore,
let
angle A = x
Angle B = x / 3
Angle C = x - 16
Therefore,
x + x - 16 + x /3 = 180
7 / 3 x - 16 = 180
7 / 3 x = 180 + 16
7 / 3 x = 196
cross multiply
7x = 196 × 3
7x = 588
divide both sides by 7
x = 588 / 7
x = 84
Therefore,
A = 84 degrees
B = 84 / 3 = 28 degrees
C = 84 - 16 = 68 degrees
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you would like to create a rectangular vegetable patch with an area of 32 sq. ft. to grow oranges. the fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. what are the dimensions of the vegetable patch with the least expensive fence? let the variable x denote the length of the east and west sides of the garden and let the variable y denote the length of the north and south sides of the garden. you and your friends individually set up a solution for the optimization problem using these variables. who set up the problem properly?
The maximum and minimum measurements are 5 and -3 respectively.
f ( x ) = -x^3 +3x^2+ 45 x + 10
f' l x ) = 0
0 = - 3x^2 +6x +45
x = 5,- 3.
f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174
f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58
f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1
+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185
Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}
= 185 at x=5
Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}
= - 71 at x= -3
In light of this, the maximum and minimum values are 5 and -3, respectively.
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Hello I just need the answers for 31 and 32 I just answered a math equation to a few minutes ago so I’d like a final answer again please I need it ASAP thank you and have a great day
The value of n is A. -1/2
The inequality that does not represent the position of 2 numbers on a number line is A. 4 1/2 > 25/4
What is number line?A number line is a horizontal representation of number parts with equal intervals
The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values
n is the negative side of the line and it is half (1/2) way between 0 and -1 hence should be -1/2
for the inequality, 4 1/2 > 25/4
4 1/2 = 4.5
25/4 = 6.25
4.5 should less than 6.25, and hence do not represent the correct position of two numbers
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Help!! Direct and Inverse Variations
The value of y is 24 when x is -2.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
There are direct variations
y= 24 when x=2
We need to find value of y when x =-2
This can be found by forming an equation.
Let the value of unknown y be a
2/24=-4/a
Apply cross multiplication
2a=24(-2)
2a=-48
We need to divide by 2 on both sides
a=-24
Hence the value of y is 24 when x is -2.
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Which rational number is equivalent to 0 . ¯¯¯¯¯¯ 36 ?
The rational number is equivalent to 0.36 is 9/25
How to determine the equivalent rational number?From the question, we have the following decimal number that can be used in our computation:
Decimal number = 0.36
To start with, we need to express the decimal number as a fraction
This is represented as follows:
So, we have the following representation
Decimal number = 36/100
Change the label of the above representation to rational number
Rational number = 36/100
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 18/50
Simplify the rational number (divide the numerator and the denominator by 2)
Rational number = 9/25
Hence, the equivalent rational number is 9/25
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There are 40 coins in a roll of nickels .there are 50 coins in a roll of dimes and 20 coins in a roll of half -dollars.alondra has 3 rolls of coins. she has a total of 90 coins. make an organized list to show all the combinations of coin rolls. what coins does alondra have?
Answer:
she has 2 half dollors and 1 dimes
Step-by-step explanation:
2 half dollors means 2x20=40 coins
1 dimes means 1x50=50 coins
when you total it you get 50+40=90
so it is 3 rolls and it totally has 90
find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height 12 cm.
The volume of the cone is 15393.80 cm³
The curved surface area of a cone is 4068.36 cm²
The total surface area of the cone is 7916.81 cm²
Given parameters;
The base radius( r ) of the cone is 35cm
The height( h ) of the cone is 12cm
Case (I): To find the volume of the cone;
The volume of the cone = [tex]\pi r^{2}\frac{h}{3}[/tex]
= π *(35)² * 12/3
= 15393.80 cm³
Case (II): To find the curved surface area of the cone;
The curved surface area of the cone = πrl
We know that;
Slant height l = [tex]\sqrt{(r^2 + h^2)}[/tex]
By substituting the values;
l = [tex]\sqrt{35^2 + 12^2}[/tex]
l = 37
We know that;
The curved surface area of a cone = πrl
= π * 35 *37
= 4068.36 cm²
Case (III): The total surface area of the cone;
The total surface area of the cone = πr(l + r)
= π * 35 * (37 + 35)
= 7916.81 cm²
Therefore,
The volume of the cone is 15393.80 cm³
The curved surface area of a cone is 4068.36 cm²
The total surface area of the cone is 7916.81 cm²
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A positive integer M divided by six gives a remainder of three. Another positive integer N divided by six gives a remainder of five. What is the remainder when the sum M+N is divided by six?
When the sum M+N is divided by 6 , the remainder is 8
What is Remainder?The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). We always have remainder when the denominator is a factor of numerator.
For example 5/2, diving 5 with 2, 2 is not a factor of 5,
There are 2 2s in 5 with remainder 1.
M/6= x y/6
where is the factor and y is the remainder
therefore m/6= (6x+y)/6
y= 3,. m/6= (6x+3)/6
N/6= (6x+5)/6
therefore dividing both sides by 6
m= 6x+3
n= 6x+5
adding m and n
m+n= 12x+8
dividing m+n by 6
(m+n)/6 = (12x+8)/6
relating (12x+8)/6 with (6x+y)/6
y = 8
Therefore the remainder is 8
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What is the correct standard form for 400+3+0.07+0.001
What is the correct standard form for 400+3+0.07+0.001
403.071
Answer:
=4.03071×10²
Step-by-step explanation:
400+3=403
=403+0.07=403.07
=403.07+0.001=403.071
so 403.071 to standard form is 403.071 divide by 100 is 4.03071 and 10 and and also change to 2 zeros and Chang it to powers so =4.03071×10²
What is the probability that a randomly selected person is a girl given they are an 8th grader?
Answer:
76
Step-by-step explanation:
1. Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope
Label each line with its slope. HELP IM REALLY STUCK ON THIS
Factor x^2 -2x -35 please
How to solve for x step by step 3x-1=20
Answer:
x = 7
Step-by-step explanation:
Given equation,
→ 3x - 1 = 20
Now the value of x will be,
→ 3x - 1 = 20
→ 3x = 20 + 1
→ x = 21/3
→ [ x = 7 ]
Hence, the value of x is 7.
graph each function for the given domain 2x-y=3; d: (-2,0,1,3)
The range values for the domain of the functions are as follows
x y
-2 7
0 3
1 1
3 -3
How to complete the tables for the graphThe domain are the input values of the graph the output values are solved using the given functions
The given function 2x-y=3
rearranging gives
y = 3 - 2x
solving for the range values using the domain values: (-2,0,1,3)
= 3 - 2x = 3 - 2 * -2 = 7
= 3 - 2 * 0 = 3
= 3 - 2 * 1 = 1
= 3 - 2 * 3 = -3
The graph is attached
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Two sailboats are sailing up a river. The relationship between the distance (d ), in miles, from the starting point to the time (t ), in hours, it takes to sail a distance d for each boat is given.
The correct statement regarding the proportional relationships is given as follows:
Boat A travels at a faster rate than Boat B.
What is a proportional relationship?A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
The function for boat A is:
d = 10.5t.
Hence the rate is:
10.5 miles per hour.
From the graph, the rate for boat B is obtained as follows:
k = 90/10 = 9 miles per hour.
A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.
Missing InformationThe problem is given by the image shown at the end of the answer.
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One of the support wires for a radio tower is
100 feet long. One end of the wire is 40 feet from
the base of the tower, as shown in the diagram
below.
Support wire
Note: The figure is not drawn to scale.
What angle (x), in degrees, does the support wire
make with the ground?
Using the trigonometry ratio, the value of angle x is 66.42°.
In the given question,
One of the support wires for a radio tower is 100 feet long.
One end of the wire is 40 feet from the base of the tower.
We have to find the angle (x), in degrees, that the support wire make with the ground.
To find the angle of x we use trigonometry ratio.
According to the ratio cosine is the ratio between base and hypotenuse.
So the formula is Cos x= B/H
where H = Hypotenuse
B = Base
From the given figure we know that, H=100 feet, B=40 feet
Now putting the value
Cos x= 40/100
Simplifying
Cos x = 2/5
Cos x = 0.4
So x = arccos(0.4)
x = 66.42
Hence, the value of angle x is 66.42°.
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-13-7=
+
?
Write as addition.
Answer:
As addition: -13+(-7)=-20
"Solve the Equation."
if the equation only has one solution, enter "NS" (No Solution) .
if the equation has Infinite Many solutions, enter "IM"
1. 6(x+5)=6x+5
2. -4x=7x-33
The equation 6(x + 5) = 6x + 5 has NS (No Solution) and the equation -4x = 7x - 33 has IM (Infinite Many solutions).
Let us take the given equation
6(x + 5) = 6x + 5
⇒ 6x + 30 = 6x + 5
⇒ 6x - 6x = 5 - 30
⇒ 0 = -25
Hence, the given equation has No Solution (NS)
Let us take the given equation
-4x = 7x - 33
-4x - 7x = -33
-11x = -33
x = 3
Hence, the given equations has Infinite Many solutions (IM)
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Use prime factorization to find the exponent. Show all of your work in good form.
625 as a power of 5
343 as a power of 7
216 as a power of 6
169 as a power of 13
256 as a power of 4; as a power of 2
729 as a power of 9; as a power of 3
The use of prime factorization to find the exponents of the given numbers gives 625 = 5⁴, 343 = 7³, 216 = 6³, 169 = 13², 256 = 4⁴; 256 = 2⁸ and 729 = 9³; 729 = 3⁶
How to express numbers as a product of prime factors?
When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2
An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴
Thus, you can use prime factorization to find the exponent of the given numbers as follows:
625 as a power of 5
625 = 5×5×5×5 = 5⁴
343 as a power of 7
343 = 7×7×7 = 7³
216 as a power of 6
216 = 6×6×6 = 6³
169 as a power of 13
169 = 13×13 = 13²
256 as a power of 4; as a power of 2
256 = 4×4×4×4 = 4⁴
256 = 2×2×2×2× 2×2×2×2 = 2⁸
729 as a power of 9; as a power of 3
729 = 9×9×9 = 9³
729 = 3×3×3×3×3×3 = 3⁶
Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and 729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively
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A line passes through points
(8, - 2) and
(-5, 7). Which ratio can be used to determine the slope of the line?
7+2/
8+5
7-2/
-5-8
8+5/
-2+7
7+2/
-5-8
Answer:
7+2/8+5
Step-by-step explanation:
I have a lot of trouble with dividing does anyone have a tip for it
Answer:
Divide by Three Trick
This is a fun trick. If the sum of the digits in a number can be divided by three, then the number can as well.
Examples:
1) The number 12. The digits 1+2=3 and 12 ÷ 3 = 4.
2) The number 15. The digits 1+5 = 6, which is divisible by 3. It turns out that 15 ÷ 3 = 5
Mrs. Wong is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Lakeside Florist charges $19 for each smaller arrangement, plus $50 for the large centerpiece. Spencer's Flowers, in contrast, charges $42 for the large centerpiece and $23 per arrangement for the rest. If Mrs. Wong orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?
Step-by-step explanation:
so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.
cost1(x) = 19x + 50
cost2(x) = 23x + 42
to get the value for x we know that the cost is the same either way.
that means
cost1(x) = cost2(x) = 19x + 50 = 23x + 42
19x + 50 = 23x + 42
50 = 4x + 42
8 = 4x
x = 2
so, she orders 2 small arrangements.
the total cost is
19×2 + 50 = 38 + 50 = $88
cross check with the other function :
23×2 + 42 = 46 + 42 = $88
correct
rationalise the denominator [tex]\frac{1}{4-\sqrt-{11} }[/tex]
Answer:
[tex]\frac{4+\sqrt{11} }{5}[/tex]
Step-by-step explanation:
to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.
the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then
[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL
= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]
= [tex]\frac{4+\sqrt{11} }{5}[/tex]
given that £1 = $1.62
how much is £650 in $
Answer:
$1053
Step-by-step explanation:
If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.
To do this multiplication, we can break 1.62 down simply into $1.00 +$0.6+$0.02
650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.
When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053
What is the effect on the graph of y = 2x + 2
when it is changed to y = 2x-2?
Answer:
shifted down 4 units
Step-by-step explanation:
You want to know the effect on the graph of changing y=2x+2 to y=2x-2.
Y-interceptThe constant in the equation y=2x+2 is the y-intercept. The line described by this equation crosses the y-axis at y=2.
When the equation is changed to y=2x-2, the y-intercept changes from +2 to -2, a shift down of 4 units. The shifted line has the same slope as the original, so is parallel to it.
The effect on the graph is to move it down 4 units.
9. If mBED=(15x-47) and mBD = (9x-1), find m/CBD.
125° is the angle of CBD
An angle pair that forms a straight line is referred to as a straight angle pair. This pair's sum of any two or more angles is always equal to 180°.
What is the straight-angle angle?A straight angle has a 180° angle.
The two angles are from a straight line, and they sum to 180 degrees.
A + B + C = 180
8x -41+ 9x+17 = 180
Conjoin similar terms
17x -24 = 180
24 more on each side
17x -24+24 = 180 +24
17x = 204
multiply by 17
17x/17 = 204/17
x =12
We desire CBD angled.
CBD = 9x+17
= 9*12+17=108+17
= 125
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for each of the following determine the n -unit percent change. the 19-unit percent change is 45 %. what is the 17-unit percent change? % the 16-unit percent change is 43 %. what is the 12-unit percent change? % the 20-unit percent change is -25 %. what is the 18-unit percent change? % the 5-unit percent change is -50 %. what is the 8-unit percent change?
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
Given, that
The 19-unit percent change is 45 %
Now, 1-unit percent change is 45/19
17-unit percent change is (45/19)×17%
= 40.26%
The 16-unit percent change is 43 %
Now, 1-unit percent change is 43/16
12-unit percent change is (43/16)×12%
= 32.25%
The 20-unit percent change is -25%
Now, 1-unit percent change is -25/20
18-unit percent change is (-25/20)×18%
= -22.5%
The 5-unit percent change is -50 %
Now, 1-unit percent change is -50/5
8-unit percent change is (-50/5)×8%
= -80%
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
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help i have no clue what this even means
Case 1: largest surface area: 2120 sq. in.
Case 2: smallest surface area: 1380 sq. in. of the wooden block.
What is defined as the cuboid?A three-dimensional shape called a cuboid is described as having six rectangular face, eight vertices, and twelve edges.Twelve edges plus eight vertices and corners to up a cuboid.For the given question, the dimensions of the wooden block are given.
Length l = 50 inchesWidth w = 5 unitsHeight h = 2 unitsSurface area of a cuboid is = 2lw + 2lh + 2 hw
Case 1: largest surface area.
To get the largest surface area, join the wooden cube along length 50 cm.
Total length = 50 + 50 + 50 = 150 inches.
Put in formula.
Surface area = 2×150×5 + 2×5×2 + 2×2×150
Surface area = 2120 sq. in.
Case 2: smallest surface area.
To get the smallest surface area, join the wooden cube along height 2 cm.
Total length = 2 + 2 + 2 =8 inches.
Put in formula.
Surface area = 2×8×50 + 2×50×5 + 2×5×8
Surface area = 1380 sq. in.
Thus, the smallest surface area of the wooden cube is found as 1380 sq. in.
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The correct question is-
There are 3 identical wooden blocks that are 50 inches long, 5 inches wide and 2 inches thick. If you glue them together , what is the largest and smallest outer surface area can get?
