Yes, her strategy was correct.
What is BODMAS?When compared to operations involving just two numbers, solving an arithmetic expression that includes multiple operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets as well as multiple operations, as well as how to make a bracket simpler? Let's review the BODMAS rule as well as discover how brackets can be made simpler. For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, as well as Subtraction, is also known as BODMAS in some areas. Thus, the following figure illustrates the order in which BODMAS and PEMDAS operate.
Simplification is done following BODMAS rule.
266-39 gives 227.
Hence, her strategy was correct.
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The expressions (x²-ax-b) and (2x² + b) have a common factor (x + c),
where a, b and c #0
(i) Show that b=2ac/3
(ii) Given that a = -b = -3c, find the common factors.
Given (x+ c) is a common factor of (x^2- ax- b )and (2x^2+b)
x= -c is a root of x^2- ax- b= 0 and x^2+ b= 0
Concept used
Quadratic equationQuadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Quadratic Formula-b±√b²-4ac/2a
i) 1- 2a+b= 0
ii) 4+ b^b- 2a= 0
4- 2a+b=0,4+ b- 2a= 0
2a+b= 2c+d
2(c−a)= b−d
(c−a)/ (b−d)= 2
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26. HOW DO YOU SEE IT?
The graph represents the height / of a
projectile after / seconds.
Height of a Projectile
Height (feet)
20
15
10
5
0
0.5 1 1.5 2 2.5
Time (seconds)
a. Is h a function of t? Explain.
b.
Approximate the height of the projectile after
0.5 second and after 1.25 seconds.
c. Approximate the domain and range.
d. Is t a function of h? Explain.
We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.
(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.
(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.
(c)The domain of the function is [0,2.5] and the range of the function is [0,30].
(d) t is not a function of h.
Therefore a) h is a function of t. (b) Approximate height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.
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You invest $8,000 in 3 investment accounts. The accounts are: paper, metal and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
The following investments were done:
Metal account: $ 1,500Glass account: $ 3,000Paper account: $ 3,500How much money has a person invested in three accounts?
In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:
Metal: x
Glass: 2 · x
Paper: 8,000 - 3 · x
And the yield function is equal to:
280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)
280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x
120 = 0.08 · x
x = 1500
The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.
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Find the quotient of 0.744 by 6
[tex]0.744\div6[/tex]
Simplify:
[tex]\frac{0.744}{6}[/tex]
[tex]=0.124[/tex]
Make 'r' as the subject of the formula
m (n + r) = 5p
The equation written when r is the subject is:
[tex]\displaystyle{r=\dfrac{5p}{m}-n}[/tex]
To make the term r as the subject of equation means to isolate r-term. In order to do that, we will apply properties of equality.
What are Properties of Equality?Properties of equality are properties regarding equations/equality where states that when either sides are done by something (addition, subtraction, multiplication, division, etc.) then the other sides will also act the same as the acted side.
Example
Suppose we are given an equation of x = y. In this case, x and y are equal to each other. If x = 1 then y = 1. If we decide to add +2 to x we’d have to add it to y too so the result will be x + 2 = y + 2.
Same also applies to other equations!
SolutionIsolating r-term, first, we will apply division property where we divide both sides by m-term:
[tex]\displaystyle{\dfrac{m(n+r)}{m}=\dfrac{5p}{m}}\\\\\displaystyle{n+r=\dfrac{5p}{m}}[/tex]
Next, we use subtraction property to subtract both sides by n:
[tex]\displaystyle{n+r-n=\dfrac{5p}{m}-n}\\\\\displaystyle{r=\dfrac{5p}{m}-n}[/tex]
Please let me know if you have any questions!
The PayDay loan company lends you $500. After 2 weeks pay you pay back $520. What is the simple interest rate? Note that the times is a fraction of a year.
Answer:
Explanation:
• Loan Amount = $500
,• Time = 2 weeks
,• The amount paid pack = $520
We want to determine the simple interest rate.
First, find the amount paid as interest:
[tex][/tex]Which fraction is closest to 1/2?
a. 1/6
b.3/8
c.3/4
d.-1/2
Answer:
A. 1/6 would be the answer I think
a salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b. altogether, how many forms did he use?
The salesman used 460 order forms in total, when he used three types of order forms: a, b, c.
Given that,
A salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b
A = 50
B = 4A + 0.5C = 200+ 0.5C .......... (i)
C = A + 0.5B = 50 + 0.5 B .......... (ii)
multiply (ii) with 2
B = 2C -50 .......... (iii)
B = 0.5C + 160 ...........(i)
subtract (i) from (iii)
0 = 1.5C -210
C = 420/3 = 140
put in (i)
B = 200 + 0.5(140) = 270
Total forms = A+B+C = 50 + 270 + 140 = 460
Therefore, he used 460 forms altogether.
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How tall is a building that casts a 71-ft shadow when the angle of elevation of the sun is 29 degrees.Round to the nearest foot
Solution
We will draw a diagram to illustrate the information
Using the concept of SOHCAHTOA
We are given adjacent and we want to find opposite
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan29=\frac{H}{71} \\ cross\text{ multiply} \\ H=71tan29 \\ H=39.35594265 \\ H=39ft \end{gathered}[/tex]Therefore, the answer is
[tex]undefined[/tex]3. there are 27 tasks available. you will be randomly assigned 12 of them. there are 10 of them that you want to do. (a) what is the probability that you will be assigned none of the tasks that you want? (b) what is the probability that you will be assigned exactly 7 of the tasks that you want? (c) what is the probability that you will be assigned at least 1 of the tasks that you want? (d) what is the probability that you will be assigned at least 7 of the tasks that you want?
On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049
a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %
b) The probability that I am assigned exactly 7 of the tasks that I want
p = 10C7 * 17C5 / 27C12 = 0.0427 = 4.27%
c) The probability that I am assigned at least one of the tasks I want
p = 1 - 17C12 / 27C12 where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.
Thus, p = 1 - (7/19665) = 0.9996
d)Probability that I am assigned at least 7 of the tasks I want
p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12
⇒ p = 17 / 345 = 0.049 = 4.9%
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Solve for x to the nearest tenth.
Answer:
x = 11,2 inchs
Step-by-step explanation:
I infer that the units are in inches.
8-3 = 5
Then:
By the Pythagorean Teorem:
x² = 10² + 5²
x² = 100 + 25
x² = 125
√x² = √125
x = 11.18
to the nearest tenth:
x = 11.2 inches
a. Plot the data for the functions f(x) and g(x) on a grid.
b. Identify each function as linear, quadratic, or exponential, and use complete sentences to explain your choices.
c. Describe what happens to the function values in each function as x increases from left to right.
d. At what value(s) of x are the function values equal? If you cannot give exact values for x, give estimates.
For the given tables, we have that:
a. The grids are given at the end of the answer.
b. The functions are classified as follows: f(x) exponential, g(x) linear.
c. When x increases by one unit from left to right, we have that:
f(x) is multiplied by 4.g(x) is increased by 1.d. The functions are equal for a value between 1 and 2, as at x = 1 g(x) is greater while at x = 2 f(x) is greater.
Exponential and linear functionsThe difference between exponential and linear functions is in the rate of change, as:
Linear functions change by a constant amount when x changes by 1.Exponential functions change by a common ratio when x changes by 1.Hence the functions are classified as follows:
f(x) exponential: when x increases by 1, y is multiplied by 4.g(x) linear: when x increases by 1, y increases by 1.We have one exponential and one linear function, so it is quite difficult to solve an equation to verify where they are equal. We have that:
At x = 1, g(x) > f(x).At x = 2, f(x) > g(x).This means that at one point between x = 1 and x = 2, they intersected, that is, they had the same function values.
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study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 3 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. (b) find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.
The probability that their hospital stay is greater than 6 days is equal to 0.67724 and the probability that their hospital stay is from 5 to 6 days is equal to 0.108
Mean (μ) = 7.37
Standard deviation (σ) = 3
we need to calculate probability that their hospital stay is from 5 to 6 days i.e.
⇒ P(5 < X < 6) = P(X < 6)-P(X < 5)
Here we will use standard normal distribution where,
Z-score = (X -μ )/ σ = (6 - 7.37)/3 = -0.46
Z-score = (5 - 7.37)/3 = -0.79
from Z table we found p-value
⇒P(5<X<6) = P(X<6) - P(X<5) = 0.32276 - 0.21476 = 0.108
So there is 0.108 probability that their hospital stay is from 5 to 6 days.
we need to calculate probability that their hospital stay is greater than 6 days i.e.
We get: P(X > 6) = 1 − P(X < 6)
Here we will use standard normal distribution where,
Z-score = (X - μ)/σ = (6 - 7.37)/3 = -0.46
from Z table we found p-value
P(X > 6) = 1 - P(X<6) = 1 - 0.32276 = 0.67724
So there is 0.67724 probability that their hospital stay is greater than 6 days.
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For 10 weeks Dolly wrote down everything she ate as well as weighed herself each morning. For two separate weeks during the 10-week period when her car was broken down and she was walking to work, she was running late each day so she did not have a chance to write down what she ate.
At the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight. She concluded that for this experiment NOT writing down what she ate would help her lose weight.
Which mistake did Dolly have in her conclusion?
Responses
Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.
B Confusing an experiment with an observational study. Confusing an experiment with an observational study.
C Confusing causation with correlation.Confusing causation with correlation.
D She did not make any mistakes in her conclusion.
The mistake that Dolly have in her conclusion is A. Her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks. That her experiment lasted for 10 weeks since she did not record what she ate for 2 weeks.
How to illustrate the information?An experiment is carried out in order to get more information about a particular thing.
In this case, at the end of the 10 weeks, she graphed her weight over time and noticed that for the two weeks she didn't write down anything she lost weight.
Therefore, this caused the mistake that was noticed.
In conclusion, the correct option is A.
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Please help me on this question.
 how many years  did Joe serve in prison  if his sentence of 5 year was reduced by three for good behavior 
Answer: 2 years
Step-by-step explanation: If Joe was meant to serve 5 years but then his sentence got shortened by 3 years, that means we need to use subtraction. 5 minus 3 equals 2. Therefore, the answer is 2 years.
shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound
The number of pounds when company A and B have same amount is 16 pounds.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
In this case, shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound.
Let each pound be represented by p.
Company A will be 7 + 0.50p
Company B will be 11 + 0.25p
We will equate both equations.
7 + 0.50p = 11 + 0.25p
Collect like terms
0.50p - 0.25p = 11 - 7
0.25p = 4
Divide
p = 4 / 0.25
p = 16
The number of pounds is 16 pounds.
The complete information is given below.
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shipping company A charges a flat fee of $7 plus $0.50 for each pound shipping company B charges a flat fee of $11 plus $0.25 for each pound. How many pounds will give an equal amount?
Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 89 km/h slower than the other. If the two planes are 3254 kilometers apart after 2 hours, what is the rate of each plane?
Answer:
769 and 858
Step-by-step explanation:
Every hour, the distance between the two planes increases by 2x + 89
2 hours = 4x + 178
3254 = 4x + 178
4x = 3076
x = 769
=What is 623 divided by 7
623 / 7 = 89
Result = 89
Please help.
Is the answer ASA, SSS, AAS, or HL
Answer:
SSS
Step-by-step explanation:
We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.
-6 = -2/5y solve for y and simplify your answer as much as possible
Answer: y = 15
Step-by-step explanation:
Combine multiplied terms into a single fraction
-6 = -2y/5
Then, multiply both sides by 5 to get:
-30 = -2y
Last, you divide both sides by -2 to get:
15 = y or y = 15
Hope this helps!
Draw of a modelled object
Emily is designing a t-shirt logo for her company. The t-shirt printing company offers 11 colors to choose from for the logo design. If any number of colors can be chosen, how many different color combinations are possible?
39,916,800 color combinations are possible
Here, we want to get the possible number of color combinations possible.
Since any number of colors can be chosen, there are no restrictions here
That means the number of possible color combinations will be;
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800 color combinations
a researcher is told that the average age of respondents in a survey is 49 years. she is interested in finding out if most respondents are close to 49 years or not. the measure most appropriate to answer this question is:
The measure that would most correctly answer this question is standard deviation.
What is standard deviation?
The standard deviation is measure of how spread out data from mean.
Step-by-step explanation:
Average age of respondents in a survey is [tex]49[/tex] years. Researcher interested in finding out if most respondents are close to [tex]49[/tex] years or not.
Hence here measures of dispersion fact will be used.
Measures of dispersion are range and standard deviation.
Range is nothing but the difference between maximum and minimum values of the data.
Standard deviation gives proper idea about how far the data values are scattered from the mean point [tex]49[/tex] years.
Therefore the correct option is standard deviation.
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what is 3b= 39 can you pleasee help me
Answer: b=13
Step-by-step explanation:
b=39/3
b=13
Answer: its 13
Step-by-step explanation
Simplify one over x raised to the negative eighth power.
Answer:
1/x to the -8 power simplified would be x^8
Step-by-step explanation:
When there is a negative exponent you put the fraction under 1
[tex]\frac{1}{\frac{1}{x^{8} } }[/tex] and its the same as x^8
The simplified expression is [tex]x^8[/tex].
What is exponent?Exponent is the power of the variable or constant to which it is raised.
The expression 1 over x is denoted by 1/x.
The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].
The exponents of the denominator change from negative to positive when they move from denominator to numerator.
[tex]\frac{1}{x^{-8}}=x^8[/tex]
Thus, the simplified expression will be x raised to the power 8.
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The equation for line s can be written as x - y = -2. Line t is perpendicular to lines and passes through (-4, 1). What is the equation of line t?
=========================================================
Explanation:
Anything perpendicular to Ax+By = C is of the form Bx-Ay = D
The given equation is x-y = -2 showing that A = 1, B = -1 and C = -2.
So Bx-Ay = D will update to -x-y = D
Plug in the coordinates of (-4,1) to find D.
-x-y = D
D = -x-y
D = -(-4)-1
D = 4-1
D = 3
We go from -x-y = D to -x - y = 3
Then multiply both sides by -1 to end up with x + y = -3
a farmer needs to enclose three sides of a meadow with a fence (the fourth side is a cliff wall). the farmer has 34 feet of fence and wants the meadow to have an area of 140 sq-feet. what should the dimensions of the meadow be? (for the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side). additionally, the length should be as long as possible.)
The dimensions are Width = 7 feets ; length = 20 feets
As given,
Meadow area is 140 square feet.
Height = W (smaller dimension and 2 sides)
Height = L (longer dimension and 1 side)
Fence yards equal 34 feet;
Hence,
L + W = 34
L + 2W = 34
L = 34 - 2W - - - (1)
Recall:
Area = L * W = 140
Substitute value of L
140 = (34 - 2W) * W
140 = 34W - 2W²
2W² - 34W + 140 = 0
W² - 17W + 70 = 0
W² - 10W - 7W + 70 = 0
W(W - 10) - 7(W - 10) = 0
(W - 10) = 0 or (W - 7) =0
W = 10 or W = 7
We choose the shorter width because length should be as long as possible:
W = 7
L + 2W = 34
L = 30 - 14
L = 20 feets
Therefore, The measurements are 7 feet wide and 20 feet long.
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2x-4<6
what is the solution to this inequlity
Answer:
x < 5
Step-by-step explanation:
[tex]2x - 4 < 6[/tex]
[tex]2x < 10[/tex]
[tex]x < 5[/tex]
.........................................................
Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. The speed of the tennis ball is...
The speed of the tennis ball is 6.2 metres per seconds.
How to find the speed of the tennis?Speed is measured as the ratio of distance to the time in which the distance was covered.
Therefore, speed can be represented mathematically as follows;
speed = distance / time
Hence, the table tennis travels 12.4 metres south in 2 seconds.
The speed of the tennis can be computed as follows:
distance = 12. 4 metres
time = 2 seconds
Therefore,
speed = 12.4 / 2
speed = 6.2 meters per seconds.
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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.
Given that,
Katie and her best friend Liam play tennis every Saturday morning.
When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.
The speed of the tennis can be found by using formula
speed=distance/time
distance = 12. 4 metres
time = 2 seconds
Now speed=12.4/2
speed=6.2
Hence speed of the tennis ball is 6.2m/s
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2x+14= -21-5x
Need to find out what x is but a step by step explanation please
Answer:
Step-by-step explanation:
solve for x
2x+14=-21-5
2x+14=-26
subtract 14 from both sides
2x+(14-14)=-14-26
2x=-14-26
2x=-40
divide both sides of 2x = -40 by 2
[tex]\frac{2x}{2} =\frac{-40}{2}[/tex]
2/2=1
x=[tex]\frac{-40}{2}[/tex]
x= -20