The area of triangle ABC is 17.5 or 35/2
To solve this, we need to know the base and height of the triangle.
In this case, the base is the side AB, and the height is the side BC
Now we can count the units to get the lenght of the sides:
AB is 7 units long
BC is 5 units long.
Now we can use the formula for the area of a triangle:
[tex]A=\frac{bh}{2}[/tex]Where A is the area, b is the base and h is the height.
Putting the values of b and h:
[tex]A=\frac{7\cdot5}{2}=\frac{35}{2}=17.5[/tex]Then the area is 35/2 or 17.5 square units
4. In a school of 120 students, 41 studied Maths, 48 studied Chemistry and 42 studied Physics, 16 studied both Chemistry and Maths, 14 studied Maths and Physics, 18 studied Chemistry and Physics and 9 studied all the three subjects. Find how many of them studied:
(i) Exactly one subject.
(ii) At least one subject.
(iii) None of the subjects
Answer:
i) 62
ii) 92
iii) 28
Step-by-step explanation:
i) 19+23+20
=62
ii) 23+9+9+7+19+5+20
=92
iii) 120-23-9-9-7-19-5-20
or
120-92
=28
What is the volume of this rectangular prism? 1/4 cm 1/2 cm 1/3 cm
The formula of the volume of a rectangular prism
[tex]V=l\times w\times h[/tex]we substitute the values given
l=length= 1/3cm
w=width=1/2cm
h=height=1/4cm
[tex]V=\frac{1}{3}\times\frac{1}{2}\times\frac{1}{4}=\frac{1}{24}cm^3[/tex]If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected high school students will say that they exercise regularly. Would you consider this event likely or unlikely to occur?
Very unlikely to occur
1) In this problem, let's find the binomial probability of that event to take place.
[tex]\begin{gathered} P(X=5)=\binom{5}{5}(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=1\cdot(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=0.37^5\mleft(0.63\mright)^{5-5} \\ P(X=5)=0.0069343957 \end{gathered}[/tex]2) Note the binomial probability of that event happening is very very low.
3) So we can state that this event is very unlikely to occur
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
The value of the 1 digit in 13,089 is how much greater that the value of the digit one in 30,124
For 13,089 - the value of the digit 1 is ten thousand or 10,000
For 30,124 - the value of the digit 1 is one hundred or 100
Therefore:
[tex]\frac{10000}{100}=100[/tex]Answer: the value of the digit 1 in 13,089 is 100 times greater than the value of the digit 1 in 30,124
Lin drew the following dilation of triangle AED and she made triangle ABC
What is The center of dilation is ?
The Scale factor for triangle AED to triangle ABC is?
1. A, as A is the shared vertex of both triangles. and 2. The original is ABC, and the dilated version is AED. as triangle ABC's half is represented by triangle AED.
How do you calculate a triangle's dilation?The following is a basic formula to determine a dilated figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.
What is the triangle's center of dilation?A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
The center, which may be found within, outside, or on a figure, is the only invariant (constant) point under a dilation (k 1).
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Help please!!!!!!!!!!!!!
in
ABC, ABC is a right angle AB=3 units, and BC=2 units &ABC is dilated by a scale factor of 0.5 with point 8 as the center of dilation, resulting
in the image AABC. Which statement about AB is true?
OA AB is 15 units long but lies on a different line than AB
OB AB is 3 units long but lies on a different line than AB
OC AB is 3 units long and lies on the same line as AB
OD. AB is 1.5 units long and lies on the same line as AB?
Answer:
A'B' is 1.5 units long and lies on the same line as AB.
Step-by-step explanation:
If AB = 3 units, BC = 2 units and a scale factor of 0.5 is applied, then A'B = 3*0.5 = 1.5 and B'C = 2* 0.5 = 1. Given that the point B is taken as the center of dilation then, segments A'B lies on the same line as AB and B'C lies on the same line as BC.
What is the sign of (-2)³? What is the sign of (-3)²? Justify your answers.
Based on the given bases with powers, the sign of (-2)³ is negative.
The sign of (-3)² can be found to be positive.
The justification for the signs can be found below.
How to find the sign?When multiplying two negative numbers, the result would be a positive number. When multiplying positive number by a negative number, the result would be negative.
(-2)³ is the same as -2 x -2 x -2 which is:
= -2 x -2 x -2
= 4 x -2
= -8
4 became positive but then became negative when multiplied by another -2.
(-3)² is 3 x 3:
= 3 x 3
= 9
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Which inequality is represented by the number line below?
The inequality that is represented by the number line is C. x ≤ 7.
What is an inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line. A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.
It should be noted that from the number line, we can see that the arrow starts from -7 and then moves backwards. This shows that it's x ≤ 7.
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What is the net salary for someone with a gross of $150 000 a year if they must pay a tax of 30%?
Gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
As given in the question,
Gross salary of an individual is $150 000 a year
Percentage of tax on gross salary =30%
Amount of tax is equal to
= 30% of $150 000
= (30/100)× 150 000
= $45000
Net salary per year
= $(150 000 - 45000)
= $105000
Net salary per month
= $(105000/12)
= $8750
Therefore, gross salary of an individual is $150 000 a year if they pay a tax of 30% then net salary is equal to $8750 per month and $105000 per year.
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A school event requires 4 adults for every 35 kids. 12 adults are available. How many kids can attend?
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
therefore
Answer:
105 and five kids can attend
Step-by-step explanation:
12 divide by 4=3
this means that 3 groups of kids can go
so 35 x 3=105
So the answer is 105
How do u determine the value of the ratio?
Answer:
Step-by-step explanation:
Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.
The owners of a house want to knock down the wall between the kitchen and the family room.
The area of the family room is x² + 10 + 24 and the area of the kitchen is x² + 7x + 12. Write an
expression that represents the area of the new combined space.
Answer:
[tex]2x^2+7x+46[/tex]
Step-by-step explanation:
[tex](x^2+10+24)+(x^2+7x+12) \\ \\ =x^2+34+x^2+7x+12 \\ \\ =2x^2+7x+46[/tex]
Answer the question.
A juice drink contains 24% real fruit juice. Find the amount of real fruit juice in 8 ounces of the drink. (Include units in your answer. More information.)
Answer:
i think it is 24.76% of real jucie
Step-by-step explanation:
because the rest is not real jucie
You invested $28,000 in two accounts paying 3% and 6% annual interest, respectively. If the total interest earned for
the year was $1590, how much was invested at each rate?
The amount invested at 3% is $
The mount invested at 6% is $
Answer: 6000 at 3% and 22000 at 6%
Step-by-step explanation:
x + y = 28,000
0.3x + 0.6y = 1500
multiply everything in the first equation by 0.3 since we want to be able to eliminate the variable x from both equations.
0.3x +0.3y = 840 then subtract second equation to just get one variable
0.3x + 0.6y =1500
-0.3y = -660
y = 22000
28000 - 22000 = 6000 which is x
So 6000 is invested at 3% and 22000 is at invested at 6%
fing the square root of 225 with process class 5
The Square root of 225 is 15
What is division ?The act of repeatedly subtracting is called division. It functions in the opposite way to how multiplication works. Forming equal groups is how it is described. When dividing numbers, we split a larger number into smaller ones so that the product of the multiplication of those smaller numbers equals the larger number that was divided. As an illustration, 4 2 = 2. This knowledge can be expressed as the multiplication 2 x 2 = 4.
Given that :Square root of 225
225 = 3 × 75
225 = 3 × 3 ×25
225 = 3 ×3 × 5 ×5
225 = 3² × 5²
225 = (3 × 5)²
225 = 15²
√225 = 15
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Please help I’ll mark you as brainliest if correct!!
The sequences are :
a. 2 , 16 , 18 , 54 , 162 is Geometric progression
Three terms : 486, 1458, 4374.
b. 1, 6 , 11, 16, 21 is arithmetic progression
Next three terms 26, 31., 36..
What is geometric progression?In a geometric progression, each element following the first is created by multiplying it by a number known as the common ratio, which is represented by the symbol r.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).The terms in the sequence that result if the same number is added to or removed from each term of an A.P. are also in an A.P. with the same common difference.To learn more about : Progression
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You drive 2 hours to the lake. Driving home on the same route, you decrease your speed by 25
miles per hour, increasing your drive time by 2 hours. Write and solve an equation to find how
fast you were driving to the lake.
Equation:
Solution:
Velocity differs from speed. Distance divided by time is the dimension of speed.
The speed of the vehicle while driving from home to the lake was 50 miles per hour.
What is Speed?The speed of an object, sometimes known as "v" in daily speech and kinematics, is a scalar quantity that measures how much its position changes over time or how much it changes per unit of time. The distance traveled by an object during a time interval is equal to the duration of the interval divided by the object's speed, with the instantaneous speed being the upper limit of the average speed as the interval's duration becomes closer to zero. Velocity differs from speed. Distance divided by time is the dimension of speed. The meter per second (m/s) is the SI unit of speed, although the kilometer per hour (km/h) or, in the US and UK, miles per hour, is the most widely used measure in daily life (mph). The knot is a popular choice for air and sea travel.From Home to Lake,
Let the speed of driving be 'x' miles per hour,
Time taken = 2 hours
Speed = Distance/Time
⇒ Distance = Speed x Time = 2x ..................(1)
From Lake to Home,
Distance will be the same (as the same route is taken),
Speed = (x-25) miles per hour
Time = 2 + 2 = 4 hours
So, Distance = Speed x Time = 4(x-25) ....................(2)
On equating (1) and (2),
2x = 4(x-25)
simplifying the above equation, we get
⇒ 2x = 4x - 100
⇒ 4x - 2x = 100
⇒ 2x = 100
⇒ x = 100/2
⇒ x = 50
Therefore, the speed of the vehicle while driving from home to the lake was 50 miles per hour.
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heyyyyyyyyyyyyyyyyyyy
The statement says that Kristen read a total of 18 books over 3 months.
And then ask us to calculate the numbers of books that he will read in a period of 5 months.
In order to calculate that, we must determine first how many books Kristen read in a month.
# of books that Kristen read in a month = 18 books / 3 months = 6 books / month
So, in order to calculate the number of books that Kristen read in 5 month, we just multiply:
5 months * 6 books/month = 30 books (answer)
Find the length of AC¯¯¯¯¯¯¯¯A. 33.13B. 377.19C. 378.63D. 2.89
The trigonometry ratios are
[tex]\begin{gathered} SinD=\frac{AK}{KD} \\ \\ tanD=\frac{AK}{AD} \\ \\ tanK=\frac{AD}{AK} \\ \\ cosK=\frac{AD}{KD} \end{gathered}[/tex]AD = 31
AK = 24
Since we do not have the length of KD, then
The value of sinD and cosK are wrong
Let us find tanD and tanK to check which one is right
[tex]tanD=\frac{24}{31}[/tex]But the given value is 31/24, then tanD is wrong
[tex]tanK=\frac{31}{24}[/tex]It is the same with the given value
The correct option is C
h(1) = -2
h(2) = 1
h(n) = h(n-2) + h(n-1)
Answer:
h(1)=h(1-2)+h(1-1)
h(1)=h(-1)+h(0)
h(-1)-h(-1)=0
h(0)=h(0)
To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $6 per hour. The chemistry club wants to spend at most $67
on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
By estimating the linear inequality, the possible numbers of hours the chemistry club could rent the meeting room exists 9 hours.
What is meant by Linear inequalities?In mathematics, an expression with uneven sides is referred to as an inequality. When a relationship leads to a non-equal comparison between two expressions or two numbers, it is referred to as an inequality in mathematics.
In this case, the equal sign "=" is replaced with any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol ().
Strict inequalities are denoted by the symbols "" and ">," whereas slack inequalities are denoted by "" and "". A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.
To rent a certain meeting room, a college charges a reservation fee of $19 - 16 and an additional fee of $6 per hour. The chemistry club wants to spend at most $67 - 70
Given that, college charges a reservation fee of $19 and an additional fee of $6 per hour.
The chemistry club wants to spend at most $67.
To estimate the possible numbers of hours the chemistry club could rent the meeting room:
The governing inequality is
19 + 6t < 67
The solution is
t < (67-19)/6
simplifying the above equation, we get
t = 8 hours.
Therefore, the value of t = 8 hours.
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A candy company developed a new consumer product that is expected to earn $3,000 in profit each year if consumer demand is low, $19,000 per
year if consumer demand is moderate, and $31,000 per year if consumer demand is high. The probability of low, moderate, and high demand is
35%, 45%, and 20%, respectively. Determine the expected monetary value (EMV) for the new product.
The most appropriate choice for probability and profit will be given by:
Expected monetary value is $15800
What is probability and profit?
Probability of an event is the chance of occurance of that event.
Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes
Probability varies from 0 to 1.
If the selling price of an item is more than its cost price, difference between the selling price and the cost price gives the profit.
Profit if consumer demand is low = $3000
Profit if consumer demand is moderate = $19000
Profit if consumer demand is high = $31000
Probability of low demand = 35%
Probability of moderate demand = 45%
Probability of high demand = 20%
Expected monetary value = $([tex]3000 \times \frac{35}{100}+19000 \times \frac{45}{100}+ 31000 \times \frac{20}{100}\\[/tex])
= $([tex]1050 + 8550+6200[/tex])
= $[tex]15800[/tex]
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12 eggs cost 3 dollers how much is one egg
Work Shown:
12 eggs = 3 dollars
12/12 eggs = 3/12 dollars
1 egg = 0.25 dollars
1 egg = 25 cents
Answer:
.25 cents
Step-by-step explanation:
3/12= .25
.25 x 12= 4.00
This graph shows a proportional relationship.500450400350300Words2502001501005023455670010Time (minutes)What is the unit rate shown by the graph?75 minutes per word1.25 minutes per word1.25 words per minute75 words per minute
In the graph we can see that the person wrote 300 words after 4 minutes. so the rate is:
[tex]\frac{300}{4}=75[/tex]75 words per minute
(2x+1)(3x+2)=6xsquare+7x+2
Factorization of the given equation : 6x² + 7x +2 is equal to
(2x +1 ) ( 3x +2 ).
As given in the question,
Given equation is
6x² + 7x +2
Using the sum and the product pattern we get
Product of extreme terms is 6 × 2=12
Factors of 12 are 1, 2, 3, 4, 6,12
4 ×3=12(product of extreme terms)
4 +3 = 7(middle term)
Factorize the equation by splitting middle term
6x² +7x +2
=6x²+ 4x +3x +2
=2x( 3x+2)+1(3x+2)
=(2x+1)(3x+2)
Therefore, factorization of the given equation : 6x² + 7x +2 is equal to
(2x +1 ) ( 3x +2 ).
The complete question is :
Factorize the given equation : 6x² + 7x +2 .
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Which calculation correctly uses prime factorization to write in simplest form?
Marked
Price
$320.00
Rate of
Discount
20%
Discount
Sale Price
$
$
(Simplify your answers. Type whole numbers or decimals.)
Answer: 64 is the answer
Step-by-step explanation:
I had a question like this and got it right! Hope this the correct answer for you!
well, we know that the regular price is 320 bucks, but is discounted by 20% so
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 320}}{\left( \cfrac{20}{100} \right)320}\implies 64~\hfill \underset{\textit{discount price}}{\stackrel{320~~ - ~~64}{\text{\LARGE 256}}}[/tex]
You deposit $200 in an account earning 2% interest compounded annually. How much will you have in the account in 20 years?
Answer:
221
Step-by-step explanation:
Interest goes up 5 dollar each year