[tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
It is given that:
Total students are 80
32 pupils use the swimming pool
43 pupils use the gym
19 pupils use neither the swimming pool nor the gym
To know the pupils who use both add 32+43 = 75
75-61= 14 pupils use both
32-14 = 18 pupils use only the swimming pool
43-18= 29 pupils use only the gym
Hence, [tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
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A car manufacturer has parked some new cars in 2 car parks.In the first car park there are 60 cars in the ratio 1 red car for every 2 blue cars and 3 silver cars.In the second car park there are 80 cars in the ratio 2 blue cars for every 3 red cars and 5 silver cars.
11. How many red cars are there altogether?
12.How many blue cars are there altogether?
13.How many silver cars are there together?
The total number of red cars is 34, the total number of blue cars is 36, and the total number of silver cars is 70.
How do we solve ratio problems?
The ratio problems can be solved as follows:
11. The total number of red cars can be calculated as follows:
Number of red car in the first car park = (1 / (1 + 2 + 3)) * 60 = 10
Number of red car in the second car park = (3 / (2 + 3 + 5)) * 80 = 24
Total number of red cars = 10 + 24 = 34
12. The total number of blue cars can be calculated as follows:
Number of blue car in the first car park = (2 / (1 + 2 + 3)) * 60 = 20
Number of blue car in the second car park = (2 / (2 + 3 + 5)) * 80 = 16
Total number of blue cars = 20 + 16 = 36
13. The total number of silver cars can be calculated as follows:
Number of silver car in the first car park = (3 / (1 + 2 + 3)) * 60 = 30
Number of silver car in the second car park = (5 / (2 + 3 + 5)) * 80 = 40
Total number of silver cars = 30 + 40 = 70
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Select the correct answer.
Identify the end behavior and the zeros of function h.
h(1) = -1³ - 91² +41 +96
Based on these key features, which statement is true about the graph representing function h?
A.
The graph is negative on the intervals (- infinity, -8) and (-4, 3).
B. The graph is positive on the intervals (-8, -4) and (3, infinity).
OC. The graph is negative on the intervals (-3, 4) and (8, ∞).
D. The graph is positive on the intervals (-infinity ,-8) and (-4, 3).
Based on the key features, the end behavior and the zeros of function h [h(x) = -x³ - 9x² +4x +96], the statement that is true of the above graph is: "The graph is positive on the intervals (-8, -4) and (3, infinity) (Option B)"
A function's "end behavior" refers to how the function's graph behaves at its "ends" on the x-axis.
In other words, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞ ), the end behavior of a function represents the trend of the graph.
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The graph below have the same shape.what is the equation of the blue graph?
Answer:
g(x) = (x - 5)²
Step-by-step explanation:
This is an example of the transformation of functions.
In this example, we see the graph f(x) has been moved 5 in the positive direction on the x-axis.
Due to the fact that we are working with the x-axis, our transformation will be placed inside the bracket, and it will do the opposite of what we expect.
This means that our transformation will be set out in this format:
[tex]g(x) = f(x-5)[/tex]
We know that:
[tex]f(x) = x^2[/tex]
Therefore,
[tex]g(x) = f(x-5) = (x-5)^2[/tex]
So, [tex]g(x) = (x-5)^2[/tex].
It was reported that uninsured drivers caused 1 in 20 accidents. About 682,494 car crashes were reported. About how many of these drivers were uninsured?
What is the slope of a line that is perpendicular to the line y = -1/2x+5
-2
-1/2
1/2
2
Step-by-step explanation:
please mark me as brainlest
Answer:
slope = 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and
there is a 10% sales tax
How much will she pay altogether?
44 QUES
25% of $40.00 is $
Select
After using the coupon, the sale price is $
Select...
The 10% tax on the sale price is $
Select
The final price is $
Select
A percentage is a way to describe a part of a whole. The amount that Kelly will pay for the dress is $33.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and there is a 10% sales tax. Therefore, the amount she will pay is,
25% of $40.00 is,
0.25 × $40 = $10
After using the coupon, the sale price is,
$40 - $10 = $30
The 10% tax on the sale price is,
0.10 × $30 = $3
The final price is $
$30 + $3 = $33
Hence, the amount that Kelly will pay for the dress is $33.
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What is the square root of -1
Answer:
Step-by-step explanation:
Negative numbers don't have real square roots since a square is either positive or 0. so it doesn't exist
Answer:
i
Step-by-step explanation:
the square root of negative one is not real.
It is classed as an imaginary number denoted by i , that is
[tex]\sqrt{-1}[/tex] = i
8
the probability that a biased coin lands on heads is 0.47
13
the probability that a biased dice lands on an even number is
20
samira flips the coin and rolls the dice.
find the probability that the coin lands on tails and the dice
lands on an even number.
The probability that the coin lands on tails and the dice lands on an even number is 0.3455
How to determine the probability?Let A represents a biased coin lands on heads and B represents a biased dice lands on an even number
So, we have:
P(A) = 0.47
P(B) = 13/20
The required probability is:
P(A' and B) = P(A) * P(B)
This gives
P('A and B) = (1 - 0.47) * 13/20
Evaluate
P('A and B) = 0.3455
Hence, the probability that the coin lands on tails and the dice lands on an even number is 0.3455
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PLEASE HELP ASAP
If "x" varies directly with "y," and
x = -19 when y = 14, what is
"x" when y = 2?
Enter the number that belongs in the green box.
Reduce to simplest form.
X = -
Notice that the negative sign has already been entered.
The value of x when y = 2 is -19/7
How to solve for x?A direct variation from x to y is represented as:
x = ky
Where k represents the variation constant.
x = -19 when y = 14.
So, we have:
-19 = 14k
Make k the subject
k = -19/14
Substitute k = -19/14 in x = ky
x = -19y/14
When y = 2, we have:
x = -19 * 2/14
Evaluate
x = -19/7
Hence, the value of x when y = 2 is -19/7
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What is 108+259+301+405
Answer:
1073
Step-by-step explanation:
it's simple addition
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
What is 8 Divided by 231 to the nearest thousandth
Answer:
0.346
Step-by-step explanation:
brainiest pls ty
Answer:
.,..
Step-by-step explanation:
0.346 ............ I'm..............
Which of the following is most likely the next step in the series?
Answer:
I think the answer is B
Step-by-step explanation:
The steps for multiplying the linear expressions –2n and three-fourths n are shown. A 2-column table with 4 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3. Second column is labeled Step with entries (negative 2 n) (three-fourths n), negative 2 times three-fourths times n times n, (negative 2 times three-fourths) times (n times n), negative three-halves n squared. What is the mathematical reasoning for Step 1? associative property commutative property distributive property simplify
The mathematical reasoning for the first step is; Distributive Property
How to use Algebra Properties?We want to multiply the linear expressions; -2n and ³/₄n.
The first step will be to express them with the multiplication sign to get and factorize;
-2n × ³/₄n
Now, since n is common to both terms, we will factorize it out to get;
n(-2 × ³/₄)
Now, that operation above is termed as a distributive property because we know that the algebra distributive property is;
a(b + c) = ab + ac
Or a(b × c) = ab × ac
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Answer:
communitave property i think
Step-by-step explanation:
Can someone help me out on this problem ?
16-2t=3/2t+9 solve for t
answer: t=2
steps:
16-2t = 3/2t+9
7 = 3/2t + 2t
2 is 4/2
7 = 3/2t + 4/2t
7 = 7/2t
7/2t = 7
(2/7)7/2t=7(2/7)
t=7(2/7)
t=2
A day is chosen from a week.
1. What are the possible outcomes?
2. What is the chance of choosing Wednesday?
3. Find the probability of selecting weekends.
Answer:
1. the possible outcomes are any of the seven days of the week
2. 1/7 chance of choosing Wednesday
3. 2/7 chance of choosing Saturday or Sunday
[tex]\mathbb{PROBLEM:}[/tex]
[tex] \\ [/tex]
A day is chosen from a week.
1. What are the possible outcomes?
2. What is the chance of choosing Wednesday?
3. Find the probability of selecting weekends.
[tex] \\ [/tex]
=======================================
[tex]\mathbb{SOLUTION:}[/tex]
[tex] \\ [/tex]
1. What are the possible outcomes?
a day is chosen from a week, possible outcomes are Monday, Tuesday, Wednesday, Thursday, Friday,, Saturday or Sunday2. What is the chance of choosing Wednesday?
because there is only one day in a week on Wednesday, the choice of choosing Wednesday is 1/7[tex]\tt\underline\red{ \: \: \frac{1}{7} \: \: }[/tex]
3. Find the probability of selecting weekends.
because there one two days in a week on selecting weekends, the probability of selecting weekends is 2/7[tex]\tt\underline\red{ \: \: \frac{2}{7} \: \: } [/tex]
=======================================
♥️
can anybody help meee
Answer:
a.) f(2) = 3
b.) if f(x) = 2
x=3
Step-by-step explanation:
Here you must notice that on the graph where x is 2, y or f(x) is at 3. This means that the answer where in the function of x, where the input 2, the output or y/f(x) is 3
And if the output is 2, the input is 3 as proven above.
Answer? Having trouble understanding this question
Answer:
[tex]\frac{k+5}{k-2}[/tex]
Step-by-step explanation:
[tex]\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }[/tex]
multiply numerator and denominator by k² to eliminate fractions
= [tex]\frac{k^2-25}{k^2-7k+10}[/tex] ← factor numerator and denominator
------------------------------
k² - 25 ← is a difference of squares
= (k - 5)(k + 5)
k² - 7k + 10
= (k - 5)(k - 2)
------------------------------
= [tex]\frac{(k-5)(k+5)}{(k-5)(k-2)}[/tex] ← cancel (x - 5) on numerator / denominator
= [tex]\frac{k+5}{k-2}[/tex]
The mass of Jupiter is 1.898x10^27 kg, while the mass of Earth is 5.972x10^24 kg. How many times greater is the mass of Jupiter compared to the mass of the Earth? Round the answer in standard form to the nearest whole number.
Answer:
318
Step-by-step explanation:
(1.898×10^27)÷(5.972×10^24)=317.82=318
dawn simplified a power correctly and came up with a value of 64. which could have been the original exponential form of the expression dawn simplified? check all that apply.
Answer:
below
Step-by-step explanation:
the second option is the only expression that came up with the value of 64
(2^6)
Answer:2,⁶ (–8)² and (–2)⁶ hope I helped. : )
Step-by-step explanation:
hi :)
Which of the following best describes how the y values are changing over each interval?
X
y
1
4
2
8
3
12
4
16
5
20
They are increasing by 4 each time.
O They are increasing by 6 each time.
O They are being multiplied by 2 each time.
O They are being multiplied by 4 each time
Answer:
y=ax+b
a=-0.6020457867
b=-2.256697516 <------- There is your value for b, which is the answer to the problem.
You can use these values for a and b to generate an equation in slope-intercept form, which you can then enter under Y= and view the graph.
Step-by-step explanation:
The value of y is multiplied by 2 each time when the value of x increases by 1 and this can be determined by using the arithmetic operations.
What is an mathematical expression?Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
Given that,
Table -- x y
1 20
2 40
3 80
4 160
5 320
The following steps can be used in order to describe how the y values are changed over each interval:
Step 1 - When value of (x = 1) and the value of (y = 20).
Step 2 - When value of (x = 2) and the value of (y = 40).
Step 3 - When value of (x = 3) and the value of (y = 80).
Step 4 - When value of (x = 4) and the value of (y = 160).
Step 5 - From the above steps, it can be concluded that the value of y is multiplied by 2 each time when the value of x increases by 1.
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Carl scored a total of 24 points by making 6 two-point baskets and some three-point baskets. Which equation can be used to find the number of three-pointers he scored, and how many three-point shots did Carl score?
A. 3p + 12 = 24
Carl made 12 three-point baskets.
B. 3p + 12 = 24
Carl made 4 three-point baskets.
C. p + 6 = 24
Carl made 18 three-point baskets.
D. p + 6 = 24
Carl made 30 three-point baskets.
Answer:
A.3p+12=24
Step-by-step explanation:
carl Made 12 three-pint baskets.
Directions: Find the inverse of each number.
Additive
-2 =
18 =
-30 =
2/5 =
Multiplicative
8/9 =
12/15 =
-6 =
10 =
Answer:
Additive
-2 = 2
18 = -18
-30 = 30
2/5 = -2/5
Multiplicative
8/9 = 9/8
12/15 = 15/12
-6 = -1/6
10 = 1/10
Step-by-step explanation:
an additive inverse is a number you must add to another number to get 0
(think of it as the negative version of the number)
{but WHY? In math, you can imagine comparing numbers on a number line. If we are finding the opposite of a number, we want to find the same distance from 0, but on the opposite side of 0. So, 2 would be two to the right of 0, -2 would be two to the left of 0}
-2 + 2 = 0
18 - 18 = 0
-30 + 30 = 0
2/5 - 2/5 = 0
a multiplicative inverse is a number that you multiply by another number to get 1.
We are finding the "reciprocal" of a number; you are essentially flipping it as a fraction
(reciprocal of 2 = 1/2 {remember, 2 is the same thing as 2/1 } ; reciprocal of 1 / 8 = 8)
note: reciprocal is being used interchangeably with multiplicative inverse here
8/9 · 9/8 = 1
12/15 · 15/12 = 1
-6 · -1/6 = 1 {-6 = -6/1}
10 · 1/10 = 1 {10 = 10/1}
hope this helps!! have a lovely day :)
Answer:
Additive: number that you add to get 0
2
-18
30
-2/5
Multiplicative: number that you multiply to get 1
9/8
15/12
-1/6
1/10
hope this is helpful!! ^u^
Evaluate (10 – 4i) ÷ (5 + i)
Answer:
the answer would be 23/13 - 15/13i
Step-by-step explanation:
The result of the complex expression (10 – 4i) ÷ (5 + i) is [tex]\frac{23}{13} - i\frac{15}{13}[/tex] .
Given, complex expression (10 – 4i) ÷ (5 + i)
Complex roots: When the roots are complex in nature then they appear in complex conjugate pair.
Complex roots: a ± ib
Complex number pair : a ± ib
i = iota(imaginary number)
a = real part
b = imaginary part
Value of iota :
[tex]i = \sqrt{-1}\\ i^2 = -1[/tex]
Complex expression : (10 – 4i) ÷ (5 + i)
Apply rationalization,
Use formula [tex](a^2 - b^2) = (a+b)(a-b)[/tex].
[tex]\frac{ (10 - 4i) }{(5 + i)} \times \frac{5-i}{5-i} \\\\= \frac{(10 - 4i) \times (5-i) }{(5+i)(5-i)} \\\\=\frac{50 -30i -4}{5^2 - i^2}\\ \\= \frac{46 - 30i}{25 +1 } \\\\= \frac{46 - 30i}{26} \\\\[/tex]
[tex]= \frac{23}{13} - i\frac{15}{13}[/tex]
The real part is positive and imaginary part is negative.
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PLS HELP!!! 50 POINTS!!!
Part C:
In the section describing the survey methods, the report states, “Each sample of national adults includes a minimum quota of 60% cell phone respondents and 40% landline respondents.” Do you think this is a good minimum quota for this survey? Should it be lower or higher?
Part D:
The report begins by showing three bulleted highlights from the survey. At the end of the article, you can click a link to view the complete question responses and trends. Click the link and interpret the results of question 5. Use your interpretation of the statistics to write one more bullet point that could be added as a fourth bullet at the beginning of the report.
This is not a good minimum quota for this survey. For us to have a good minimum quota, there must be equality. i,e 50% for cell phone respondents and 50% for landline respondents.
What is the survey method in Statistics?Survey methodology is the study of the sampling of discrete units or groups from a population and the procedures used to gather survey data, including the design of questionnaires and approaches for increasing survey response rates and precision.
A good minimum quota for this survey should be 50% for cell phone respondents and 50% for landline respondents.
It implies that the quota for cell phone respondents should be 10% lower and 10% higher for landline respondents.
For us to answer Part D, kindly provide or repost the complete question since we cannot see any link added.
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Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answer:
(5, 20)
Step-by-step explanation:
Which of these four sets of side lengths will form a right trangle?
Set 1
4 cm 5 cm 6 cm
Set 3
10 mm 20 mm 30 mm
O Set 1
O Set 2
O Set 3
O Set 4
Set 2
8 in, 12 in 20 in
Set 4
12 R 16 R 20 R
answer:
set 4
Step-by-step explanation:
because when you divide the numbers 12,16 and 20 by 2 you'll get 6,8 and 10 which is a Pythagoras family....and it will form a right angle triangle
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
From the power rules, the matching of each expression with its equivalent expression is:
[tex]5^{-3}=\frac{1}{125}[/tex]
[tex]-5^{-3}=-\frac{1}{125}[/tex]
[tex](-5^{-3})^{-1}=-125[/tex]
[tex](-5^{-3})^{0}=1[/tex]
Power RulesThere are different power rules, see some them:
1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent. See the examples:
[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]
2. Power. For this rule, you should repeat the base and multiply the exponents. See the example, [tex](2^{2})^3=2^6=64[/tex].
3. Zero Exponent. When you have an exponent equals to zero, the result must be 1. See the example, [tex]2^0=1[/tex].
From this for your question, you have:
[tex]5^{-3}=\frac{1}{5^3}=\frac{1}{125}[/tex][tex]-5^{-3}=-\frac{1}{5^3}=-\frac{1}{125}[/tex][tex](-5^{-3})^{-1}=(-5)^{3}=-125[/tex][tex](-5^{-3})^{0}=(-5)^{0}=1[/tex]Read more about power rules here:
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In a carnival drawing, a green ticket wins $1, a yellow ticket wins $5, and a blue ticket wins $10. There are 20 green tickets, 10 yellow tickets and 5 blue tickets. In simplest form, what are the odds against winning less than $10?
A. 1:4
B. 1:5
C. 1:6
D. 6:1
A ratio shows us the number of times a number contains another number. The correct option is C.
What is a Ratio?A ratio shows us the number of times a number contains another number.
For winning less than $10, a person needs to take out a green ticket or a yellow ticket. Therefore, the odds against winning less than $10 are,
(Number of blue tickets) : (Number of green and yellow tickets)
5: 30
1: 6
Hence, the correct option is C.
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