When faced with an unknown variable in a maths problem, it is advised to find the subject formula and then use it to solve the equation to find the answer.
What is an Unknown Variable?This refers to the type of variable in a given equation that has to be solved for because its properties or value is not known.
Hence, we can see that when faced with an unknown variable in a given math problem, it is better to find the subject formula, then input the value of this into an equation, to find the value of the variable.
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Transportation officials tell us that 60% of drivers wear seat belts while driving. Find the probability that more than 562 drivers in a sample of 900 drivers wear seat belts.
The probability that more than 562 drivers is 0.9328
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given: p = 0.60
n = 900
Let X denote the number of drivers that wear a seat belt,
P(X > 562)
[tex]\mu[/tex] = n*p = 900(0.60) = 540
[tex]\sigma^{2}[/tex]= n*p*(1-p)
=900*0.60*0.40
=216
P(X >562) = Pr( Z > 1.4976)
= 0.9328
Hence, the probability that more than 562 drivers is 0.9328
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If a 103 pound man can have 1292 mg of a medicine in a day, how much can a 102 pound woman have? (round answer to one decimal place) She can have mg
Answer:
1279.5mg
Step-by-step explanation:
103 pound man takes -1292mg of medicines
102 pound woman will take -xmg of medicine
cross multiply
102x1292=103x
131784=103x
x=131784/103
x=1279.5mg
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Women will have 1279.5mg of medicine in a day.
How much can a 102-pound woman have?103-pound man takes -1292mg of medicines.
102-pound woman will take x mg of the medicine.
By cross multiply
102x1292=103x
131784=103x
x=131784/103
x=1279.5mg
What is an example of a word problem?Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
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10% of an amount is 6.2 . Wirk out the original account
Answer:
the original amount was 62
Step-by-step explanation:
You can use the part over whole formula like this:
[tex]\frac{part}{whole} = ( \frac{6.2}{?} * \frac{10}{100})\\ ? = 62[/tex]
why?
because we know that 10% = 10/100, we can easily find out the answer by cross multiplying
? * 10 (let's use x, instead of ?)
=10x
6.2 * 100
= 620
Now we have an equation that looks like this: 10x = 620
By using the inverse operation tool (dividing each side by 10 to isolate x) we have:
x (or ?) = 62
What 2 numbers add up to 37 and multiply to 210?
Answer: 30 and 7
Step-by-step explanation: 30 plus 7 is 37, 30 times 7 is 210
There is a 50% chance of rain here and a 25% chance of rain on Mars. Therefore, there is a 75%
chance that it will rain here or on Mars. Explain why this is a false statement.
There is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
There is a 50% chance of rain here and a 25% chance of rain on Mars. Therefore, there is a 75% chance that it will rain here or on Mars.
The probability that it will rain here:
P(rain here) = 50%
P(rain on mars) 50%
P(not rain here) = 100 - 50 = 50%
P(not rain on mars) = 100 - 50 = 50%
P(rain here and not on mars) = 0.5×0.5 = 0.25 or 25%
Thus, there is a 75% chance that it will rain here or on Mars is false because there is a 25% chance that it will rain here and not on Mars.
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which system of the equation is represents by the graph?
Each statement describes a transformation of the graph of y = log2x. Which statement correctly describes the graph of y = log2(x + 3) - 9?
The transformation of a function may involve any change in the initial function. The correct option is C.
The complete question is:
Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?
It is the graph of y = log2x translated 3 units down and 9 units to the left.It is the graph of y = log2x translated 9 units down and 3 units to the right.It is the graph of y = log2x translated 9 units down and 3 units to the left.It is the graph of y = log2x translated 3 units up and 9 units to the left.How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]Given the initial function y = log2x, now if the function is needed to be transformed to y = log2(x + 3) - 9, then the function is needed to be shifted left by 3 units and down by 9 units.
Hence, the correct option is C.
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5
14
6
3
1
2
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If
it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a
probability of winning.
B. Yes. Each friend has a
probability of winning.
C. No. Andrew has a probability of winning and Liz has a
probability of winning.
D. No. Andrew has a probability of winning and Liz has a
probability of winning.
The question is incomplete. Below you will find the missing figure.
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a 1/4 probability of winning.
B. Yes. Each friend has a 1/6 probability of winning.
C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.
D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.
The correct option is Option A: Yes. Each friend has 1/4 probability of winning.
Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.
P = no. of favorable outcome/ total no. of outcome
Here given in the question,
If the spinner touches region 2 or 3, Andrew wins
If the spinner touches region 4, Liz wins.
This is fair play because both have the same size of region for winning.
If we cut the circle into 8 pieces,
as region 1 is the sum of 2 sub-parts of the circle,
possibility of spinner touching region 1= 2/8= 1/4
possibility of spinner touching the small region = 1/8
So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4
Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4
possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4
Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.
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pls help i forgot how to do this :)
Answer:
in picture
Step-by-step explanation:
added in the picture
The graph of the function f(x) = -(x+3)(x-1) is
shown below.
-6
-4 -2
6
A
2
-2
4
-6
2
4
6 X
What is true about the domain and range of the
function?
O The domain is all real numbers less than or equali
to 4, and the range is all real numbers such that -31
≤x≤ 1.
The domain is all real numbers such that-3≤x≤
1, and the range is all real numbers less than or
equal to 4.
The domain is all real numbers, and the range is all
real numbers less than or equal to 4.
The domain is all real numbers less than or equal
to 4, and the range is all real numbers.
Using the concepts of domain and range of a function, the correct statement regarding the graph of the function f(x) = -(x + 3)(x - 1) is given by:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.The graph of f(x) = -(x + 3)(x - 1) is given at the end of the answer, hence:
The domain is all real values, as the function keeps going to infinity.The range is all values of y that are less than or equal to 4.Hence the correct statement is:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
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7. What is the ratio of the interior angles of a pentagon and a decagon?
Answer:
A pentagon has 5 sides.
Sum of the interior angles = ( n - 2) x 180
Sum of the interior angles = ( 5 - 2) x 180
Sum of the interior angles = 540°
STEP 2: Find one interior angle:
one interior angle = 540 ÷ 5 = 108°
STEP 3: Find the sum of interior angles of a decagon
A decagon has 10 sides
Sum of the interior angles = ( n - 2) x 180
Sum of the interior angles = ( 10 - 2) x 180
Sum of the interior angles = 1440°
STEP 4: Find one interior angle:
one interior angle = 1440 ÷ 10 = 144°
STEP 5: Find the ratio:
Pentagon : Decagon = 108 : 144
Simplify:
Pentagon : Decagon = 3 : 4
Answer: The ratio is 3 : 4
Please answer! Will give the brainliest!
Answer: K. 3
Step-by-step explanation:
There are 30 students in total. What I did is I added everything that was in the Venn diagram and subtracted that from 30.
[tex]12+5+10=27[/tex]
[tex]30-27=3[/tex]
Therefore, there are 3 students who didn't like either English or math.
I hope this helps! Pls give brainliest!! :)
Is 3^20 times 2^14 a factor of 3^22 Times 2^12
Answer:
no
Step-by-step explanation:
In order for one number (A) to be a factor of another (B), the exponents of the primes in the prime factorization of A cannot exceed those of the prime factorization of B.
__
A = 2^14 × 3^20
B = 2^12 × 3^22
The exponent of the factor 2 in A is 14, which exceeds the exponent of the factor 2 in B (12). Therefore, A cannot be a factor of B.
(3^20)(2^14) is not a factor of (3^22)(2^12)
manual spent 4.56 on a sandwich and 2.98 on a drink How much did he spend in all? If he paid with a 10$ bill how much change did he get
Manual paid with a $10 bill and he got $2.46 as a change.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.
Money spent on sandwich=$4.56 and money spent on drink=$2.98.
We need to find out how much did he spend in all.
That is, the total money spent=4.56+2.98=$7.54
He paid with a $10 bill, he gets change as 10-7.54=$2.46
Hence, he paid with a $10 bill and he got $2.46 as a change.
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Convert:
3½ kilograms to grams
Step-by-step explanation:
3 1/2 = 3,5 kg → ? g
1 kg = 1.000 g
• Convert kg to g.
= 3,5 kg
= 3,5 × 1.000
= 3.500 grams IS THE ANSWER
If x = 3, then 3x – 4 = 5. x = 3 law of detatchment
Answer:
3x-4=5
Step-by-step explanation:
it is correct
A table is in the shape of a regular
hexagon. The perimeter of the table is 12
feet. What is the length of each side of
the table?
A 1 ft
B 2 ft
C 3 ft
D 4 ft
Answer:
B
Step-by-step explanation:
A hexagon has 6 sides. If you divide the perimeter(12) by the number of sides(6), you get the length of one side(2).
The perimeter of a standard-sized rectangular rug is 24 ft. The length is 2ft longer than the width. Find the dimensions.
The length and width of the rectangle are equal to: 7 ft and 5 ft, respectively
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.
For this question, the length is 2ft longer than the width - L=2+W. Thus,
24=2*(2+W)+2W
24=4+2W+2W
24-4=4W
20=4W
W=5 ft
If W=5, L will be 2+5=7 ft.
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What is the partial fraction decomposition of StartFraction 7 x squared + 14 Over (x squared + 3) squared EndFraction?
The final decomposition of the given partial fraction is; 7 + (-7/(x² + 3))
How to decompose partial fractions?We are given the polynomial fraction (7x² + 14)/(x² + 3) to decompose.
Now, due to the fact that the degree of the numerator is not less than the degree of the denominator, we will perform polynomial long division to get;
(7x² + 14)/(x² + 3) = 7 + (-7/(x² + 3))
Now, the second term (-7/(x² + 3)) cannot be decomposed further and as such, we say that our final decomposition of the given partial fraction is;
7 + (-7/(x² + 3))
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12. A bag contains 12 red, 9 green and 5 black markers. If Cooper randomly selects 7 markers, how many
ways could this be done if EXACTLY 6 are to be the same color?
Answer:
Step-by-step explanation:
7 marks
6 same colors
from 12 red 6 same exactly the same
12 x 11 x 10 x 9 x7 x6
1 remainig
from 9 green 6 saem exactly the same
9 x 8 x 7 x 6 x5 x4
1 remaining
add the results above to get your final answer
26 markers in total
6 to be chosen of the same color from 7
What is the simplified form of StartRoot 100 x Superscript 36 Baseline EndRoot ?
10x Superscript 18
10x Superscript 6
50x Superscript 18
50
The simplified form of the expression √(100x³⁶) will be 10x¹⁸. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ √(100x³⁶)
Then the simplified form of the expression will be
⇒ √[(10x¹⁸)²]
⇒ 10x¹⁸
Then the correct option is A.
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Answer:
Step-by-step explanation:
Expert-Verified Answer
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The simplified form of √(400x¹⁰⁰) is;
D; 20x⁵⁰
We want to find the simplified form of √(400x¹⁰⁰)
Now, according to laws of indices;
√ab = √a × √b
Thus;
√(400x¹⁰⁰) = √400 × √(x¹⁰⁰)
⇒ 20√(x¹⁰⁰)
Also according to law of indices;
a⁴ = a² × a²
Thus;
x¹⁰⁰ = x⁵⁰ × x⁵⁰
Thus;
√(x¹⁰⁰) = √(x⁵⁰ × x⁵⁰)
⇒ x⁵⁰
Our final answer is;
20x⁵⁰
What is 6289 round off to the nearest 1000 (thousand)????
Answer:
6230 will be answer I think
Mark me as Brainliest
Answer:
Well, it's to the nearest thousand, and we know that 6289 is 6 thousand 2 hundred and 89. So, you look at the number next to the thousand which is the hundreds, and as we can see that is 2. Therefore it will be 6000, as 6289 cannot be rounded to 7000 since 2 doesn't exceed 5.
So, the answer is 6000
(I don't mind being marked brainliest for this I'd just like to help someone. :)
What is the value of the expression
(12+x) +
4+x
when X= 4 and y=-8?
OA) 4
OB)
OC)
OD 10
Step-by-step explanation:
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The value of the expression x
4
−8x
3
+18x
2
−8x+2, when x=2+
3
, is:
Medium
Solution
verified
Verified by Toppr
Correct option is B)
Let f(x)=x
4
−8x
3
+18x
2
−8x+2
Substituting x=2+
3
, we get
f(2+
3
)=(2+
3
)
4
−8(2+
3
)
3
+18(2+
3
)
2
−8(2+
3
)+2
=(2+
3
)
2
((2+
3
)
2
+18)−8(2+
3
)((2+
3
)
2
+1)+2
=(7+4
3
)(4
3
+25)−8(2+
3
)(8+4
3
)+2
=175+48−128−96+2
=1
Hence, option B is correct.
Large eggs weigh 1/1/2 pounds per dozen. Dawn bought eight large eggs. How much did the eggs weigh
Answer: 1 pound
Step-by-step explanation:
Because 12 eggs= 1.5 pounds. So, you divide 1.5/12 = 0.125. And the 0.125 times 8 = 1 pound
Answer:
1 lb
Step-by-step explanation:
Since 1 dozen(12) eggs weigh 1 1/2 or 3/2 lbs, each egg weights 3/2 ÷ 12 = 3/24 lb
So 8 eggs would weight 8 x 3/24 = 1 lb
Graph the equation by plotting three points. If all three are correct, the line will appear. -3y=2x-7 ....... 20 POINTS
First lets simplify to slope intercept (y=mx+b)
y=[tex](2x-7)/-3[/tex]
y=-2/3x+7/3
Point 1: (0,7/3) as when x is 0, y=7/3.
Point 2: lets plug x in as 3 to cross cancel.
[tex]\frac{-2}{3} *\frac{3}{1} = \frac{-2}{1}[/tex]
So (3,-2).
Lets do point 3: plug in -3.
[tex]\frac{-2}{3} *\frac{-3}{1} = \frac{2}{1} = 2[/tex]
So (-3,2).
Your three points are (0,2.33 repeat) or (0,7/3), (3,-2) and (-3,2)
Hopefully this helps you out, heart if it was helpful and please do not hesitate to ask any questions. I have also attached an image of the line
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the funtions f(x) and g(x) are shown on the graph f(x)=x^2
what is g(x)?
Answer:
C
Step-by-step explanation:
A reflection of a graph on the x axis simply adds the opposite sign to the x^2, in this case, since f(x) = x^2 is positive, a reflection would mean that g(x) would be -x^2. As g(x) is also vertically translated down 2 units, the equation would then become g(x) = -x^2 - 2 and the correct answer would be C.
A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. The correct option is D.
What is a relative frequency table?A relative frequency table is a chart that depicts the popularity or pattern of a specific piece of data based on the population sampled. When we look at relative frequency, we are comparing the number of times a given event occurs to the overall number of events.
The complete question is mentioned in the below image with the relative frequency table.
As per the relative frequency table, the value 0.2 highlighted in the table represents that 20% of his customers ordered cheese but no chili on their hot dogs.
Hence, the correct option is D.
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These tables of values represent continuous functions. For which function
will the y-values be the greatest for very large values of x?
y
1 7
2 21
3 63
4 189
5 567
B. x
y
17
2 207
3 407
4 607
5 807
C.xy
1 325
2 400
3 475
4 550
5625
Y
1 565
2 570
3 575
4 580
5585
What is the answer??
Answer: the answer is a
Step-by-step explanation:
A club organises a lottery, selling tickets at 25 cents each. The club will be giving a prize of
€58
to the winner but also plans to make a profit of
€150
from the whole event. What is the least number of tickets that the club needs to sell?
Using proportions, it is found that the club needs to sell at least 832 tickets to make their desired profit.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The prize is of €58, with the event making a profit of €150, hence the amount of money they have to earn from tickets is given by:
A = 150 + 58 = €208.
The tickets are sold at €0.25, hence the number of tickets they have to sell is:
n = 208/0.25 = 208 x 4 = 832.
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|4x + 7| − 4 = 20
Can anyone help me with this
Answer:
x = -31/4 or x = 17/4
Step-by-step explanation:
|4x + 7| − 4 = 20
⇔ |4x + 7| − 4 + 4 = 20 + 4
⇔ |4x + 7| = 24
⇔ 4x + 7 = 24 or 4x + 7 = -24
⇔ 4x = 24 - 7 or 4x = -24 - 7
⇔ 4x = 17 or 4x = -31
⇔ x = 17/4 or x = -31/4
Answer:
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
Step-by-step explanation:
| | is notation for absolute value
absolute value - the distance that a number is from 0
> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |
if we have | x | = 20, we could really have (without the | | ) two versions of x
either | x | = 20 ; or | -x | = 20 {because a negative x inside of the | | has the same value as positive x}
we set this up as two equations:
x = 20 or -x = 20
^ {multiply by -1}
x = 20 or x = -20
now, let's plug our understanding into the equation
|4x + 7| - 4 = 20
first, we should simplify our equation to:
|4x + 7| - 4 = 20
+ 4 + 4
|4x + 7| = 24
now, let's separate this absolute value equation into two separate equations:
4x + 7 = 24:
- 7 - 7 {subtract 7 from both sides to isolate x}
4x = 17
÷4 ÷4 {divide both sides by 4 to get 1x}
x= [tex]\frac{17}{4}[/tex]
or,
4x + 7 = -24:
- 7 -7 {subtract 7 from both sides to isolate x}
4x = -31
÷4 ÷4 {divide both sides by 4 to get 1x}
x = [tex]-\frac{31}{4}[/tex]
so, we know that
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
hope this helps!!
