The probability that the hat was blue or was from Manufacturer B is 0.8677.
The P[tex](red)^{c}[/tex] is 0.6985.
The P(manufacturer B and Red) is 0.1640.
The P(Manufacturer B or Red) is 0.8456.
What are the probabilities?Probability is used to determine the odds that a random event would happen. The odds that the random event happens range from 0 to 1.
The probability that the hat was blue or was from Manufacturer B = (number of blue hats / total number of hats) + (number of hats from manufacturer B / total number of hats)
The probability that the hat was blue or was from Manufacturer B = (44 / 136) + (74 / 136) = 118/136 = 0.8677
The P[tex](red)^{c}[/tex] = complement of red = hats that are not red = (number of black hats + number of blue hats) / total number of hats
The P[tex](red)^{c}[/tex] = (51 + 44) / 136
The P[tex](red)^{c}[/tex] = 95 / 136
The P[tex](red)^{c}[/tex] = 0.6985
The P(manufacturer B and Red) = (number of hats produced by manufacturer B / total number of hats) x (number of red hats / total number of hats)
(74 / 136) x (41 / 136) = 0.1640
The P(Manufacturer B or Red) = (number of hats produced by manufacturer B / total number of hats) + (number of red hats / total number of hats)
(74 / 136) + (41 / 136) = 115 / 136 = 0.8456
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I need help with this please help me
The measurement of angles ∠1 is 126° and ∠2 is 154°.
According to the question,
We have the following information:
We have a figure of two triangles and some of the measurements of the angles are given.
We know that the sum of three angles of a triangle is 180°.
So, for the larger triangle, we have the following expression:
96+30+third angle = 180
Third angle = 180-126
Third angle = 54°
We know that sum of angles on a straight line is 180°.
So, we have:
∠1+54 = 180
∠1 = 180-54
∠1 = 126°
Now, finding the sum of angles in smaller triangle:
126+28+third angle = 180
Third angle = 180-154
Third angle = 26°
Now, angle 2 and this angle will make a straight line.
∠2+26 = 180
∠2 = 180-26
∠2 = 154°
Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.
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Solve the system of equations by graphing. List the coordinates.
u=v
4u=2v-12
By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).
What is a graph?A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
In order to plot the system of equations on a graph, we would simplify the second equation as follows:
4u = 2v - 12
Dividing both sides of the equation by 4, we have the following:
4u/4 = 2v/4 - 12/4
u = v/2 - 3
Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.
By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (−4,1)
Answer:
[tex]y=-43x-173[/tex]
Step-by-step explanation:
[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]
For questions 9-11, find the values of x and y if l || m.
The values of x and y using angle relationships are as follows:
x = 9, y = 13x = 22, y = 15x = 7, y = 24How to find angles in parallel line cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
Therefore, the angle relationship can be used to find the value of x and y in the diagram.
In the diagram, l and m are parallel lines and are cut by a transversal line.
Therefore,
10.
10x - 17 = 8x + 1(alternate exterior angles are congruent)
10x - 8x = 1 + 17
2x = 18
x = 18 / 2
x = 9
8x + 1 + 6y + 29 = 180(sum of angles on a straight line is 180 degrees)
72 + 1 + 29 + 6y = 180
102 + 6y = 180
6y = 180 - 102
6y = 78
y = 78 / 6
y = 13
11.
7x - 30 = 5x + 14(Corresponding angles)
Corresponding angles are congruent.
7x - 5x = 14 + 30
2x = 44
x = 44 / 2
x = 22
3y + 11 + 7x - 30 = 180(sum of angles on a straight line)
3y + 11 + 7(22) - 30 = 180
3y + 11 + 154 - 30 = 180
3y = 180 - 11 - 154 + 30
3y = 45
y = 45 / 3
y = 15
12.
7y - 23 = 23x - 16 (vertically opposite angles)
7y - 23x = 7
8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)
31x - 37 = 180
31x = 180 + 37
31x = 217
x = 217 / 31
x = 7
7y - 23(7) = 7
7y = 7 + 161
7y = 168
y = 168 / 7
y = 24
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if I make 11 dollars an hour and i worked 20 hours for 4 days, how much would I earn?
Answer: I think you would earn $8.35 per hour
Step-by-step explanation:
Answer: $880
Step-by-step explanation:
As I understand you are working 20 hours a day for 4 days.
[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880
Help please! 15 points!!!!! give me an answer!!!!!
Billy has 15 apples he eats 3 ands sells 4 for $4 dollars each, How many apples are left. And what's Billy's total profit at the end of the day?
Answer:
Step-by-step explanation:
7*5
Answer:
he got 8 apples left and made a profit of 16
Step-by-step explanation:
QUATIONS
Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make true equations of
the following. Use each digit once
The true equations are :
2 + 7 = 9
8 × 5 = 4 0
6 ÷ 3 = 2
2 - 1 = 1
We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.
The first true equation is 2 + 7 = 9.
The second true equation is 8 × 5 = 4 0.
The third true equation is 6 ÷ 3 = 2.
The fourth true equation is 2 - 1 = 1.
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Which integer makes the following sentence true? -10 < ? < -1
Answer:
Below
Step-by-step explanation:
Any of the following
-9 -8 -7 -6 -5 -4 -3 -2
Monica’s dose from the fluoroscopy tower, at a distance of 9 feet, is 100 mR/hr. What is the radiation intensity, in Roentgens, at 1 foot from the fluoroscopy tower?
The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr
How to the radiation intensity, in Roentgens?
Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray
The equation below relates the radiation intensity and distance:
I₁/I₂ = D₂²/D₁²
where: I₁ = intensity at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source
Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot
Using the formula:
100/I₂ = 1²/9²
100/I₂ = 1/81
I₂ = 100 × 81
I₂ = 8100 mR/hr
I₂ = 8100×10⁻³ R/hr (1 mR/hr = 1×10⁻³ R/hr)
I₂ = 8.1 R/hr
Therefore, the radiation intensity in Roentgens is 8.1 R/hr
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For the following, based on the information given which would you use to find the missing variable?
The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively
How to find the missing variables?We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
1st triangle
tan 25° = b/8 (tan = opp/adj)
b = 8 tan 25° = 3.73m
2nd triangle
sin 21° = x/22 (sin = opp/hyp)
x = 22 sin 21° = 7.88 units
3rd triangle
cos 47° = 28/x (cos = adj/hyp)
x = 28/cos 47° = 41.06 units
4th triangle
Use Pythagoras' theorem:
12² = 8² + y²
y² = 12² - 8²
y² = 144 - 64
y² = 80
y = √80 = 8.94 units
Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units
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Complete the table representing a linear function.
hint:Use the rate of change to find the missing values.
hint:Find the rate of change using change in y divided by change in x.
After finding the rate of change, this table representing a linear function can be completed as follows:
x y
1 0
2 10
5 40
10 90
What is the rate of change?Mathematically, the rate of change can be calculated by using this formula;
Rate of change, k = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, k = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x as follows:
Rate of change, k = (40 - 0)/(5 - 1)
Rate of change, k = 40/4
Rate of change, k = 10.
For the first blank, we have:
10 = (40 - y)/(5 - 2)
10 = (40 - y)/3
30 = 40 - y
y = 40 - 30
y = 10.
For the second blank, we have:
10 = (90 - 40)/(x - 5)
10 = (50)/(x - 5)
10x - 50 = 50
10x = 50 + 50
10x = 100
x = 10.
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The temperature in the United States last night was -9℃. It is now -3℃. What was the change in temperature?
The change in temperature in United States since last night is -6 degree centigrade.
Given the temperature in United States last night is = -9 degree C
Now the temperature is = -3 degree C
So the change in temperature is given by,
= Final Temperature - Initial Temperature
= -9 - (-3)
= -9 + 3
= -6 degree C
Hence the change in temperature in United States since last night is -6 degree centigrade.
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Find the perimeter and area of the polygon shown below 15 8 17 16
The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.
How to calculate the perimeter?It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:
= 16 + 15 + 16 + 8 + 17
= 72 feet
The area will be:
= Area of triangle + Area of rectangle
= (1/2 × base × height) + (length × width)
= (1/2 × 8 × 17) + (15 × 16)
= 68 + 240
= 308ft²
Therefore, the correct option is B.
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Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 4.6 kg.
Complete parts (a) through (c) below.
b. If 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is
(Round to four decimal places as needed.)
The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Amounts of weight that male college students gain during their freshman year are normally distributed
mean of μ = 1.1 kg and
Standard deviation of o= 4.6 kg.
Z score=x-μ/o
=25-1.1/4.6
=23.9/4.6
=5.196
Z score=x-μ/o
=25-1.1/0
=0
Z score=25-1.1/3
=23.9/3
=7.966
By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
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What is the end behavior of the graph of f(x) = x5 - 8x4 + 16x³?
O
O f(x)→→∞ as x→∞; f(x) →→∞ as x→ +∞
f(x)→∞ as x→-∞0; f(x) → +∞o as x→ +∞
O f(x) +∞o as x→-∞; f(x) →→→∞as x→ +∞
+∞o as x→∞0; f(x)→ +∞ as x→→ +00
O
f(x)
DONE
The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .
In the question ,
it is given that ,
the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,
In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .
In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .
that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞
let us find the roots of the function ,
f(x) [tex]=[/tex] 0
x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0
taking x³ common ,
x³(x² - 8x [tex]+[/tex] 16) = 0
x³(x² - 4x - 4x + 16) = 0 .... by using splitting the middle term method
x³(x(x - 4) - 4(x - 4)) = 0
x³(x - 4)(x - 4) = 0
which means x³ [tex]=[/tex] 0 and x-4 = 0
that is x=0 and x = 4 .
So , the roots of the function f(x) are x=0 and x=4 .
This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.
Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .
The given question is incomplete , the complete question is
What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?
(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞
(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞
(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞
(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞
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a sponsor of one person walking in a charity walkathon will donate 7 plus an additional .25 for each mile a person walks. which of the following functions , d, models the total amount , in dollars that the sponsor will donate to teh charity when the person walks m miles?
The function that models the total amount, in dollars, that the sponsor will donate to the charity when the person walks m miles is F(d) = 7 + 0.25m.
What is a function?Mathematically, a function is an expression involving two or more variables (independent and dependent) showing that a mathematical relationship exists between the expressions.
Functions use the equation symbol to show that the expressions are equal when the variables are substituted with integers.
Every function has a domain (input variable) and a range (output variable) or codomain.
Constant donation = $7
Variable donation per mile = $0.25
Function, F(d) = 7 + 0.25m
where d = the total amount donated
m = the total miles the person walks
Thus, the total donation made by the sponsor is represented by the function, F(d) = 7 + 0.25m.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each set of prices with the correct percent of increase or decrease.
11% decrease
11% increase
8.7% decrease
7.4% increase
8% decrease
12.4% decrease
9.9% increase
8% increase
original price: $63.00
new price: $56.07
arrowRight
original price: $98.00
new price: $108.78
arrowRight
original price: $37.50
new price: $34.50
arrowRight
original price: $12.25
new price: $13.23
arrowRight
Each set of prices should be matched with the correct percentage of increase or decrease as follows:
12.4% decrease = original price: $63.00 and new price: $56.07.11% increase = original price: $98.00 and new price: $108.78.8.7% decrease = original price: $37.50 and new price: $34.50.8% increase = original price: $12.25 and new price: $13.23.How to calculate percentage change?Mathematically, percentage increase can be calculated by using this formula:
Percentage increase = [original price - new price]/new price × 100
At original price: $63.00 and new price: $56.07, we have:
Percentage decrease = [63.00 - 56.07]/56.07 × 100
Percentage decrease = 6.93/56.07 × 100
Percentage decrease = 0.124 × 100
Percentage decrease = 12.4%.
At original price: $98.00 and new price: $108.78, we have:
Percentage increase = [108.78 - 98.00]/98.00 × 100
Percentage increase = 10.78/98.00 × 100
Percentage increase = 0.11 × 100
Percentage increase = 11%.
At original price: $37.50 and new price: $34.50, we have:
Percentage decrease = [37.50 - 34.50]/34.50 × 100
Percentage decrease = 3/34.50 × 100
Percentage decrease = 0.087 × 100
Percentage decrease = 8.7%.
At original price: $12.25 and new price: $13.23, we have:
Percentage increase = [13.23 - 12.25]/12.25 × 100
Percentage increase = 0.98/12.25 × 100
Percentage increase = 0.08 × 100
Percentage increase = 8%.
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Write an equation and solve:
Sandy has $60 and saves $10 a month. Randy has
$45 and saves $20 per month. After how many
months will they have the same amount of
money?
Answer:
3/2 month
Step-by-step explanation:
Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?
When x = months:
Sandy: 10x + 60
Randy: 20x + 45
You are looking for x when:
Sandy = Randy
10x + 60 = 20x + 45
subtract 45 from both sides:
10x + 60 - 45 = 20x + 45 - 45
10x + 15 = 20x
subtract 10x from both sides:
10x + 15 - 10x = 20x - 10x
15 = 10x
divide both sides by 10:
15/10 = 10x/10
x = 15/10
reduce:
x = 3/2
It will take 3/2 months of Sandy and Randy to have the same amount of money.
[3/2 month also equals 1.5 months, depending on the format of the answer you need]
At his most recent medical checkup, a boy was 40 inches tall. Currently, he is 46 inches tall. What percent taller is the boy now?
im not smart at this lol
Answer:
15%
Step-by-step explanation:
15%*40=46
Answer:
15%
Step-by-step explanation:
[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]
The boy was 40 inches tall so that means 40 inches is the old value
The boy is currently 46 inches tall now, so 46 is the new value
Plug these values into the equation:
[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]
Simplify:
[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]
[tex]Percent of change =\frac{600}{ 40} \\[/tex]
[tex]Percent of change =15[/tex]
I hope this answers your question :)
Question 6(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O 4, 8, 11
O 6, 8, 13
O√3, √5,8
O√3, √13, 4
K
The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d) .
In the question ,
four set of sides is given ,
we need to find the set of side that forms a right triangle ,
we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .
Option(a)
the sides are 4 , 8 , 11.
4 + 8 = 11
16 + 64 = 121
80 = 121
we know that 80 121 ,
So , the sides do not form a right triangle
Option(b)
the sides are 6 , 8 , 13
6 + 8 = 13
36 + 64 = 169
100 169
we know that 100 169 ,
So , the sides do not form a right triangle .
Option(c)
the sides are √3, √5 , 8
√3 + √5 = 8
3 + 5 = 64
8 = 64
we know that 8 64 ,
So , the sides do not form a right triangle .
Option(d)
the sides are √3, √13 , 4
√3 + √13 = 4
3 + 13 = 16
16 = 16
Yes , the sides form a right triangle .
Therefore , The sides {√3 , √13 , 4} forms a right triangle .
The given question is incomplete , the complete question is
Determine which set of side measurements could be used to form a right triangle ?
(a) 4, 8, 11
(b) 6, 8, 13
(c)√3, √5,8
(d)√3, √13, 4
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4. Using the Place Value Method, order the following from least to greatest.
.134
.2
.051
.46
Answer: 0.051, 0.134, 0.2, 0.46
Step-by-step explanation:
(18x³ - x² + 9x - 3) and (5x³ + 6x² - 14x +11) Add the polynomials (Provide only the coefficients. If a coefficient is negative, include the negative sign on the left side of the number. Do not type 'plus' sign)
Answer: put it in a caculator
Step-by-step explanation:
Combine 18x^3 and 5x^3.
23x³ - x² + 9x-3 + 6x² - 14x+11Combine x^2 and 6x^2.
23x³ + 5x² + 9x -3 - 14x + 11Combine 9x and −14x.
23x³ + 5x² + -5x -3 + 11Add −3 and 11.
23x³ + 5x² -5x + 8Triangle EFG is similar to triangle HIJ. Find JH. Round your answer to
the nearest tenth if necessary. Figures are not drawn to scale.
The length of the side JH in the triangle ΔHIJ is 97.9.
We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.
Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".
IJ ∝ FG
IJ = k*FG
k = IJ/FG
k = 47/12
The side JH is proportional to the side GE.
JH = k*GE
x = (47/12)*25
x = 97.9
Hence, the length of the side JH is 97.9 units.
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Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, after h hours
The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let the number of hours be given as h.
Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:
c = 3 + (5 × h)
c = 3 + 5h
where c = total cost
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NO LINKS! Please help me with this problem #3
Answer:
b) f(x) = -16x² + 8x + 30
Step-by-step explanation:
When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.
The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.
If a > 0, the parabola opens upwards.If a < 0, the parabola opens downwards.Therefore, f(x) = -16x² + 8x + 30 could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.
If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).
Kathleen’s grandfather has a very old pet tortoise. He told Kathleen that the tortoise was 61 years old when she was born 10 years ago. Kathleen is amazed and wants to know how old the tortoise is now. Write an equation Kathleen can use to find the tortoise’s age t and solve.
Answer:
t - 10 = 61
Step-by-step explanation:
We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61
so t = 71.
2*8/3 give me answer
Answer:
Exact Form: 16/3
Decimal Form: 5.3
Mixed Number Form: 5 1/3
Step-by-step explanation:
A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4 .
write 28 plus 24 as a product of two factors
Answer:
4(13)
Step-by-step explanation:
[tex]28+24=7(4)+6(4)=\boxed{4(13)}[/tex]
Why does completing the square always result in a perfect square trinomial?
Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.
When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.
Hope this helps.
Step-by-step explanation:
can you help me use compatible numbers to find two estimates of 478/12 i will give you 100000 points
Answer:
48
Step-by-step explanation: