Answer:
There are 23 students
-- 9 students play neither sport
-- therefore, 23 - 9 = 14 students play at least one of the two sports; some play both sports.
Inclusive or: the probability will be: 14 / 23 that a student chosen at random will play at least one of the two sports.
Exclusive or: we need to first find how many students play both sports.
Since 14 persons play sports and since 7 play basketball and 12 play baseball, this requires 7 + 12 = 19 students.
Subtracting 19 - 14 = 5 give the number of students who play both sports.
If we eliminate these 5 persons as well as the 9 who play neither sport, we have to eliminate 5 + 9 = 14 persons.
This gives 23 - 14 = 9 persons who play only one of the two sports.
The probability will be: 9/23 play a sport, but only one sport.
Step-by-step explanation:
The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
To find the probability that a student does not play an instrument given that they play a sport, we need to use conditional probability.
Let A be the event that a student plays a sport and B be the event that a student plays an instrument.
We want to find P(not B | A), which is the probability that a student does not play an instrument given that they play a sport.
We know that,
P(A) = 7/23, P(B) = 9/23, and P(A and B) = 3/23.
Using the formula for conditional probability, we have:
P(not B | A) = P(A and not B) / P(A)
We can find P(A and not B) by using the fact that,
P(A and B) = P(B) - P(A and not B).
P(A and not B)
= P(B) - P(A and B)
= 9/23 - 3/23
= 6/23
Substituting into the formula, we get:
P(not B | A) = (6/23) / (7/23) = 6/7
Therefore,
The probability that a student does not play an instrument given that they play a sport is 6/7 or approximately 0.857.
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8. Each day, Amy walks to school. She leaves her home
and walks south 7 blocks to her friend's house. They then
turn to the west and walk 12 blocks to the school. At the
end of the day, Amy walks directly from the school to
her home.
a) To the nearest tenth (one decimal place), how many
blocks does Amy walk on her way home?
<+
-10
-10
Home s
-5
Friend's house
-5
-10
5
10
School
S
b) How many blocks does Amy walk in one day for her round trip to the school and back
home? Round to the nearest tenth.
Answer:
(a) 13.9 blocks (nearest tenth)
(b) 32.9 blocks (nearest tenth)
Step-by-step explanation:
The given scenario can be modeled as a right triangle.
If Amy walks south 7 blocks, one leg of the triangle is 7.
If Amy then walks west 12 blocks, the other leg of the triangle is 12.
Part (a)To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):
[tex]\implies 7^2+12^2=c^2[/tex]
[tex]\implies 49+144=c^2[/tex]
[tex]\implies 193=c^2[/tex]
[tex]\implies c=\sqrt{193}[/tex]
[tex]\implies c=13.8924439894...[/tex]
Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.
Part (b)To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:
[tex]\implies 7 + 12 + 13.9 = 32.9[/tex]
Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
The three statements that are always true regarding this diagram are:
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 + m∠5 = 180°
m∠2 + m∠3 = m∠6
Here's why:
The sum of the measures of the interior angles of a triangle is always 180°. Therefore, m∠2 + m∠3 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠4 = m∠2 + m∠5, and m∠3 + m∠4 + m∠5 = 180°.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Therefore, m∠6 = m∠2 + m∠3.
The other two statements are not always true. For example, if m∠5 = 100° and m∠3 = 80°, then m∠5 + m∠3 = 180°, but m∠4 ≠ 0°. Similarly, if m∠5 = 100° and m∠6 = 80°, then m∠5 + m∠6 ≠ 180°.
Step-by-step explanation:
round to the nearest ten
Answer:
A
Step-by-step explanation:
The given dimensions:
Height = 12 in
Radius = 9 in
Recall the cylinder volume formula: [tex]V=\pi r^2h[/tex]
where r = radius and h = height
Using the dimensions stated above, plug in the values into the formula
[tex]V=\pi 9^212\\9^2=81\\81\pi =254.4690049\\254.4690049*12=3053.628059\\V=3053.628059[/tex]
Finally, round answer to the nearest tenth
Your answer would be A.3053.6
Estimate 11,319+4,865 by first rounding each number to the nearest thousand.
Answer:
16,000
Step-by-step explanation:
11,319 rounded to the nearest thousand is 11,000.
4,895 rounded to the nearest thousand is 5,000.
11,000 + 5,000 is equal to 16,000.
Where did Nathan make a mistake?
In Step 1, Nathan did not multiply
both terms in parentheses by-3.
In Step 2, Nathan did not simplify
5x 3x correctly.
In Step 3, Nathan did not divide
by the correct number.
In Step 4, Nathan did not simplify
correctly.
<->) -24
8
Answer:
The question is not detailed enough
Answer:
In step 2, Nathan did not simplify 5x - 3x correctly.
Step-by-step explanation:
In step 2, Nathan was one number off the correct simplification.
6) This weekend, Eric makes sandwiches for 5 hours and delivers orders for
4 hours. How much money does he save?
6) Eric saves $
this weekend.
Answer:
$53
Step-by-step explanation:
You can just substitute the values in the equation
The amount Eric saves this weekend is $53.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
Sandwiches= $10
Order delivery= %14
Now,
To find how much money he saves this weekend, you need to substitute s = 5 and d = 4 into the expression and simplify. Here are the steps:
1/2(10s + 14d)
= 1/2(10(5) + 14(4))
= 1/2(50 + 56)
= 1/2(106)
= 53
Therefore, by the expression the answer will be $53.
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What is the greatest common factor of 20 and 65
Answer:
5
Step-by-step explanation:
Answer:I believe it would be 5
Step-by-step explanation:
because if you do it on a table chart you reach five first as the same number
The value of a brand new car is \$25,000$25,000 and the value depreciates 17% every year. Write a function to represent the value of the car after tt years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent.
Answer:
25,000 - .17t
Step-by-step explanation:
I don’t under this pls help thank you
Answer: 8%
Step-by-step explanation:
the instructions are on the image please help me and please hurry!
The elements in matrix X is attached below
What is MatrixMatrix is a mathematical construct consisting of an array of numbers, symbols, or expressions, arranged in rows and columns. It is most often used to represent linear relationships between two or more variables. Matrices are commonly used in science and engineering to represent systems of equations and in computer programming for representing data and performing operations on it.
In this problem, we can easily find x by reversing the variables and solve.
A - X = B
X = A - B
The elements in the matrix can be solved easily using an online calculator.
The value of x is attached below
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The vertex form of the equation of a parabola is y = 7(x-3)2 + 4. What is the standard form of the equation?
A. y = 7x2 - 42x+67
B. y = 7x2 - 6x + 22
C. y = 14x2 - 6x + 22
D. y = 14x2 - 12x + 44
Answer:
the standard form of the equation is: a. y=7x^2-42x+67
Write the ratio for Tan M.
Answer:
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPP
30
I DONT KNOW BUT THAT'S MY ANSWER HOPE IT HELP
Step-by-step explanation:
Is it +30 or - 30
If it was -ve under root it will be complex or imaginary number but it is a easy question
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Orange marble selection has a 0.33 experimental probability.12 over 60 is the experimental probability of landing on a number smaller than 2
what is probability ?Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.
given
In each of the three studies, Sandy's experimental probability matched the theoretical probability to the letter.
The theoretical likelihood of landing on orange is one-fourth, but the actual likelihood is 20%.
Orange marble selection has a 0.33 experimental probability.
12 over 60 is the experimental probability of landing on a number smaller than 2.
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There are three modes of transporting material from New York to Florida, namely, by land, sea, or air. Also land transportation may be by rail or highway. About half of the materials are transported by land, 30% by sea, and the rest by air. Also, 40% of all land transportation is bay highway and the rest is by rail shipments. The percentage of damaged cargo are, respectively. 10% by highway, 5% by rail, 6% by sea, and 2% by air. (a) What percentage of all cargos may be expected to be damaged
Answer:
5.7%
Step-by-step explanation:
% Prob (Land) = Half ie 50% ; % Prob (Sea) = 30%
% Prob (Air) = Remaining ie 100% - 50% - 30% = 20%
Prob (Land highway) = 40% of land = 40% of 50% = 20%
Prob (Land rail) = remaining ie 60% of land = 60% of 50% = 30%
Pr (Damage by Land) = 10% of rail + 5% of rail = 10% of 20% + 5% of 30% = 2% + 1.5% = 3.5%
Prob (Damage by Sea) = 6% of sea = 6% of 30% = 1.8%
Prob (Damage by Air) = 2% of air = 2% of 20% = 0.4%
Total Prob (Damage) = 3.5% + 1.8% + 0.4%
= 5.7%
what is the greatest common factor of 30b^2, 80b^, 20b^3?
Answer:
10b^2
Step-by-step explanation:
30b^2: 5 * 2 * 3 * b^2
80b^2: 5 * 2 * 2 * 2 *2 * b^2
20b^3: 5 * 2 * 2 * b^2 * b
The highest common factor is in bold script. It is 10b^2
Can anyone help me fill in the other blanks
On solving the problem we got that, 17yds and 11yds are its length and width
What does perimeter mean?The circumference of an item is known as its perimeter. For instance, your home has a yard that is enclosed. The length of the fence is the perimeter. The length of your fence is 200 feet if the yard is 50 feet by 50 feet.
length =L
width = W
length is 6 yd longer than its width,
L = 6 + W
perimeter is 56yds:
[tex]56= 2(L + W) \\ = > 68 = 2(6 + W) + 2W\\= > 12+ 2W + 2W = 56\\= > 4W = 44\\= > W = 11 yds\\= > L = 11+6 = 17 yds[/tex]
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What is the value of sin(7pi/4)? See attached.
Answer:
-sqrt(2)/2 , the last option of your document.
Step-by-step explanation:
sin(7pi/4) = -sin(7pi/4 - pi)
= -sin(7pi/4 - 4pi/4)
= - sin(3pi/4)
sin(3pi/4) is a special angle , which is sqrt(2)/2
Hence, sin(7pi/4) = -sin(3pi/4)
= -sqrt(2)/2
Answer:
-sqrt(2)/2
Step-by-step explanation:
did the test
what is 3 1/2 x 2 1/3
Answer:
8 1/6
Step-by-step explanation:
The product of fractions 3 1/2 × 2 1/3 = 49/6 or can also express it as a mixed fraction: 8 1/6.
To multiply mixed fractions like 3 1/2 and 2 1/3, follow these steps:
Step 1: Convert the mixed fractions into improper fractions.
3 1/2 = (3 × 2 + 1) / 2 = 7/2
2 1/3 = (2 × 3 + 1) / 3 = 7/3
Step 2: Multiply the numerators and denominators of the fractions.
(7/2) × (7/3) = (7 × 7) / (2 × 3) = 49/6
Step 3: Simplify the resulting fraction, if possible.
49/6 cannot be simplified further.
Therefore, 3 1/2 × 2 1/3 = 49/6 or can also express it as a mixed fraction: 8 1/6.
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Only answer question 2
100 points please answer
The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C
What are trigonometric identities?Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.
These involve certain functions of one, two or more angles.
They also are different from triangle identities, which involves angles and side lengths of a triangle.
To verify a trigonometric identity, we take the following steps;
Convert the equalities to terms of sine and cosine.Solve the identities at possible timesThen, simplify the left-hand side of the equation, before simplifying the right-hand side.Hence, the best option is C
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What is an equation for the linear function whose graph contains the points (9, 7) and (4, −8)?
Enter your answers in the boxes.
y−
=
(x−9)
The line that passes through these two points is y=x-2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here function whose graph contains the points (9, 7) and (4, −8)
Thus using the two point formula for a line we get the equation as
y-7=(x-9)
y=x-2
Hence, The line that passes through these two points is y=x-2
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what does a duck say
Answer:
theres three possible answers, they either QUACK, HONK, or hum
Step-by-step explanation:
19.
A box contains only quarters and dimes. If there were 10% more quarters, the total
value of the money in the box would increase by 7.5%. What is the ratio of the number of quarters to the
number of dimes in the box? Express your answer as a common fraction.
Answer:
The ratio of the number of quarters to the number of dimes in the box is 9:10
Step-by-step explanation:
Show instructions
Question 1 (1 point)
The base of the rectangular prism is shaded in the sketch below. What is the lateral surface area of
the rectangular prism?
15 cm
28 cm
34 cm
A 1,904 cm
B 1,860 cm?
C 3,764 cm?
D 14,280 cm?
shdudbdhxbdhxbsbdyshs
Answer:
C 3674cm²
Step-by-step explanation:
1) (34×15)×2= 510×2= 1020cm²
2) (28×15)×2= 420×2= 840cm²
3) (34×28)×2= 952×2= 1904cm²
4) Total of all areas (surface area): 1020+840+1904= 3764cm²
75 yd
40 yd
What is the length of the hypotenuse.
Help
PLEASE help test due !!!!
Use the two-way frequency table to answer questions #14-19
Answer:
14. 1/13
15. 14/15
16. 1/13
17. 15/30=1/2
18. 12/13
19. 12/15
If you are happy with my answers, please give brainliest :)
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
75
Step-by-step explanation:
Answer:
75 km
Step-by-step explanation:
Use the Pythagorean Theorem
c² = a² + b²
c² = = 72² + 21²
c² = 5,184 + 441
c² = 5,625
Take the square root of both sides
c = 75 km
jakie pole ma prostokąt o wymiarach 50cm x 16dm?
Solution
16 dm=160 cm
50 cm* 160 cm= 8000 cm²= 0,8 m²
odp C
Two piggy banks have a sum of $36.50. The first piggy bank has $13.75. How much does the second piggy bank have in it?
Answer:
22.75
Step-by-step explanation:
ur welcome hOWdAy