768 cm'^2 is the trapezoid’s area.
What is isosceles trapezoid?
Isosceles trapezoids have equal length non-parallel sides, hence the name "isosceles" which means "equal legs". The "legs" are another name for these equal sides.
Let 50 cm = the bottom base
We can find the area of one of the triangles that comprise the area of the trapezoid.....its sides are 30, 40 and 50 cm
Let s be the semi-perimeter of one of the triangle = [ 50 + 40 + 30 ] / 2 = 60 cm
And the area of of this triangle = sqrt [ s ( s - a) (s - b) ( s -c) ] where a,b, c are the sides
So...we have sqrt [ 60 ( 60 - 30) (60 - 40) (60 - 50) ] = sqrt [ 60 * 30 * 20 * 10 ] =
sqrt [ 1800 * 200] = sqrt [ 3600 * 100] = 60 * 10 = 600 cm ^2
Now the base of this triangle = 50 and the height can be found as
follows :
Area = (1/2) 50 * height
600 = 25 * height
height = 24 cm and this is the height of the trapezoid
Now....the top base can be found as 50 - 2 sqrt [ 30^2 - 24^2 ] = 14 cm
So....the area of the trapezoid = (1/2) height ( sum of the bases) = (1/2) (24) ( 50 + 14) = 12 ( 64) = 768 cm'^2
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A runner’s times (in minutes) in three races are 6.9, 6.6, and 6.5. The runner will run two more races and wants the average time of all five races to be less than 6.8 minutes. Describe the average time needed in the two races to achieve this goal. The average time in the two races must be less than minutes.
The average time in two races must be less than 7 minutes.
Given,
Runner's times in three races = 6.9 minutes, 6.6 minutes, 6.5 minutes.
Runner will run two more races.
The average time of all five races = less than 6.8 minutes
We have to find the average time needed in the two races:
Now,
(6.9 + 6.6 + 6.5 + x + y) / 5 < 6.8
Here, x and y are the time in two races.
Let's assume the average as 6.5 which is less than 6.8.
Then,
(6.9 + 6.6 + 6.5 + x + y) / 5 = 6.5
(6.9 + 6.6 + 6.5 + x + y) = (6.5 × 5)
x + y = (6.5 × 5) - (6.9 + 6.6 + 6.5)
x + y = 32.5 - 20
x + y = 12.5
Now, we have to find the average of two races:
That is, (x + y) / 2 = 12.5 / 2 = 6.25.
Above is a solution required by an assumption. By this solution we came to know that the average of two races must be less than 7 minutes.
So, let's conclude like:
The average time in the two races must be less than 7 minutes.
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each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100. full data set sample of size 5 sample of size 12 sample of size 30 . . . question content area right part 1 for each data set, compute the mean and median. what is the mean of the sample of size 5? enter your response here (type an integer or decimal rounded to one decimal place as needed.)
All the above data were obtained by entering them in excel format and obtaining it using standard methods.
What is the standard deviation?A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a wider range. The standard deviation is a measure of variance or dispersion in statistics. Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lowercase Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
For sample size 5, Mean = 117.6 and Standard Deviation = 9.2
For sample size 12, Mean = 103.5 and Standard Deviation = 8.6
For sample size 30, Mean =104.6 and Standard Deviation = 8.7
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what is the answer for J(-3,2) and K(9,2)
The distance between points J(-3,2) and K(9,2) is 12 units.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
The given points are
J(-3,2) and K(9,2)
[tex]x_{1} =-3\\\\x_{2} =9\\\\y_{1} =2\\\\y_{2} =2[/tex]
According to given question we have
By the use of distance formula we have
[tex]\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2}} \\\\=\sqrt{(9 -(-3) )^{2}+ (2 -2 )^{2}}\\\\=\sqrt{(12 )^{2}}\\\\=12[/tex]
Therefore, the distance between points J(-3,2) and K(9,2) is 12 units.
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Distance between is missing in question
the right triangle shown below with hypotenuse 13 inches long and vertical leg 5 inches long is rotated 360c around the vertical leg to form a right circular cone. what is the volume of this cone, in cubic inches?
The cone has a volume of (D) 288in3.
What do we mean by volume?A volume is a unit of measure of occupied three-dimensional space. It is frequently quantified numerically using SI-derived units (such as cubic meters and liters) or various imperial modules (such as the gallon, quart, and cubic inch). The definition of volume is related to the definition of length (cubed). The volume of a container is generally recognized to be its capacity; that is, the quantity of fluid (gas or liquid) that it can hold, rather than the amount of space that it occupies.To find the volume:
Given:
Radius = 6 inheight =?g = 10 inVolume =?Formula:
Volume of a cone = πr²h / 3The Pythagorean theorem is used to calculate height.
height² = 10² - 6² = 100 - 36 = 64 height = 8The volume of the cone:
Volume = π(6)²(8) Volume = π(36)(8) Volume = 288π in³Therefore, the volume of the cone is (D) 288in³.
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The complete question is given below:
Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?
A. 32
B. 96
C. 128
D. 288
E. 384
consider a group of hundred students. out of them, eighty students can speak either english or spanish. suppose twenty-five students can speak only english. how many students can speak spanish?
the product of two consecutive integers is 272. which quadratic equation can be used to find x, the smaller number? x2 1
Quadratic equation which is x² + x - 272 = 0 can be used to find the product of two consecutive integers.
What is a quadratic equation?An algebraic equation of a second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
Let one number be x,
second number will be - (x+1)
so, the product of two numbers will be -
x(x+1) = 272
x² + x = 272
x² + x - 272 = 0
The quadratic equation, used to find the numbers is x² + x - 272 = 0.
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4. (40 Pts) The Vacation Times website rates recreational vehicle campgrounds
using integers from 0 to 15. Last year they rated over 1,000 campsites. The
ratings were normally distributed with mean 7.6 and standard deviation 1.7.
a. How high would a campsite's rating have to be for it to be considered in
the top 10% of rated campsites? Round to the nearest hundredth.
b. Find the z-score for a rating of 5. Round to the nearest hundredth.
Using the normal distribution, it is found that:
a) The rating would have to be of at least 9.78.
b) The z-score for a rating of 5 is of -1.53.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given by:
[tex]\mu = 7.6, \sigma = 1.7[/tex]
For item a, we have to find the 90th percentile, which is X when Z = 1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
1.28 = (X - 7.6)/1.7
X - 7.6 = 1.28 x 1.7
X = 9.78.
The rating would have to be of at least 9.78.
For item b, we have to find Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (5 - 7.6)/1.7
Z = -1.53.
The z-score for a rating of 5 is of -1.53.
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Find the value of sin S rounded to the nearest hundredth, if necessary.
30
R
16
S
The value of sin S is = 5/13
Given a right triangle with hypotenuse BD = 13 & BC = 12, Find CD,
By, Pythagoras theorem
BD2 = BC2 + CD2
132 = 122 + CD2
CD2 = 132 - 122
CD2 = 169 – 144
CD2 = 25
CD =
CD = 5
We know that,
Sin = opposite side/hypotenuse
Sin S = 5/13
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Hence, these triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
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[tex]3x+6=4x+7[/tex]
Question 7 (5 points)
What are the coordinates of the vertices of the image after a 90-degree counter-
clockwise rotation about the origin?
Answer:
Explanation ↓
Step-by-step explanation:
The origin is the rotation’s set point unless expressed otherwise. In a coordinate plane, when the point (x, y) is revolved in a 90-degree clockwise directive, the projected vision will have a coordinate of (y, -x).
PLEASE HELP V=1/3a^2h solve for h
Answer: h=3V/a^2
Step-by-step explanation:
V=1/3a^2h
V=1/3 * a^2 * h
V*3=3*1/3 * a^2 * h
3V=a^2 * h
h=3V/a^2
The end points of ab are A (-7,3) and B (1,0) find the coordinates of the midpoint M.
Answer: M(-3,1.5)
Step-by-step explanation:
A(-7,3) B(1,0)
[tex]\displaystyle\\M(x,y)=(\frac{x_A+x_B}{2} ,\frac{y_A+y_B}{2} )\\\\M(x,y)=(\frac{-7+1}{2},\frac{3+0}{2} )\\\\M(x,y)=(\frac{-6}{2},\frac{3}{2} )\\\\M(x,y)=(-3,1.5)\\\\Thus,\\\\M(-3,1.5)[/tex]
. If the lesser of two consecutive even integers is five more than half the greater,
what are the two integers?
Answer:
12 and 14
Step-by-step explanation:
You want two consecutive even integers such that the lesser is five more than half the greater.
SetupLet x represent the lesser of the integers. Then x+2 is the greater, and we can write the given relation as ...
x = (x+2)/2 +5 . . . . . lesser is 5 more than half the greater
SolutionMultiplying by 2 gives ...
2x = x +2 +10
x = 12 . . . . . . . . subtract x
x+2 = 14
The two integers are 12 and 14.
what is the sum of x and 16 is less than 32?
Answer:
I don't know the exact question you're asking, but the solution for x would be x16.
3/5evaluate the expression and name the poperty used in each step. [5/(3times1)] 3/5
Evaluate expression and Name the property used in each step.
= { [5/(3 times 1)] } 3/5
= {[5/(3.1)]} 3/5
We can write,
Multiplicate identity,
= [5/3] 3/5
Substitution,
= (5/3) (3/5)
Cancel the numerator and denominator values,
So,
We can write,
= 1 Multiplicative Inverse
Therefore,
3/5evaluate the expression and name the property used in each step. [5/(3times1)] 3/5 is = 1 Multiplicative Inverse.
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with explanation needed. a and b
a)
Solution,
According to fuel gauge,the petrol left is exactly between 1/2 and 3/4 part of the 40 litres.
i.e. Left fuel = (1/2 + 3/4)/2 litres
Here,
1/2 of 40l = 1/2×40l
= 20l
3/4 of 40l = 3/4×40l
= 30l
Then,
Left fuel = (20l + 30l)/2
= 50l/2
= 25l
Consumed fuel = 40l - 25l
= 15l
Therefore,15 litres of petrol is used to travel 240km
b)
Solution,
Consumed fuel = 15l
Distance covered = 240km
Then,
Fuel consumption rate = 240km/15 l
= 16km/l
Therefore,the rate of petrol consumption is 16km/l of his car for this journey
Melinda has 5 cousins. She called each one on the phone 4 times this month. How many phone calls did she make to her cousins this month
Answer:20
Step-by-step explanation:5*4=20 hope this helps
belinda received a 3+ points on a problem on a quiz what is the absolute value of the number of points she received
Answer:
3
Step-by-step explanation:
the absolute value is distance of a number from 0 so +3 absolute value is 0
Members of a lacrosse team raised $1775-50 to go to a tournament. They rented a bus
for $901.50 and budgeted $46 per player for meals. Write and solve an equation
which can be used to determine x, the number of players the team can bring to the
tournament.
Considering the definition of an equation and the way to solve it, the equation is 901.5 + 46x= 1775.50 and the number of players the team can bring to the tournament is 19.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it and the equality must be true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of players the team can bring to the tournament, and knowing that:
Members of a lacrosse team raised $1775.50 to go to a tournament. They rented a bus for $901.50 and budgeted $46 per player for meals.the equation in this case is:
901.5 + 46x= 1775.50
Solving:
46x= 1775.50 - 901.5
46x= 874
x= 874 ÷ 46
x=19
Finally, the equation is 901.5 + 46x= 1775.50 and the number of players the team can bring to the tournament is 19.
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Jen was the leading scorer on her soccer team. She scored 120 goals and had 20 assists in her high school career. a. The number of points awarded for goals is given by 2g where g is the number of goals scored. How many points did Jen earn for goals? b. The point total is given by n + a where a is the number of assists. Use your answer from part (a) to find Jen's point total. mirum
a. The number of points that Jen earned will be 240 points.
b. The point total where a is the number of assists is 260 points.
How to compute the function?The number of points that Jen earned will be:
= 2g
where g = number of goals scored
= 2 × 120
= 240
b. The point total is given by n + a where a is the number of assists.
Therefore, the point total will be:
= Goals + Assist
= 240 + 20
= 260 points.
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A 1,600 deposit for 15 years at a compound interest rate of 12%
Answer:
$8,758
I hope this helps!
If John's credit card has a balance of $1,329.64 balance and he charged $528.44 in new purchases, what
is the new balance?
Answer: 801.2
Step-by-step explanation:
What is the approximate value of √8?
Answer:
the approximate value should be 2.83
a phrase that describes a set of real numbers is given. express the phrase as an inequality involving an absolute value. all real numbers x more than 2 units from 0
The inequality will be - {x ∈ R: x > x+2} that describes a set of all real numbers x more than 2 units from 0.
What is an inequality?Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols <,>,=,etc.
What is an example of inequality?The equation-like form of the formula 5x - 4 > 2x + 3 has an arrowhead in lieu of the equals sign. It is an illustration of inequity. This shows that the left half, 5x - 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Given,
all real numbers x more than 2 units from 0
So, the inequality representing the the information will be -
{x ∈ R: x > x+2}
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5 less than 10 times a number is 2 times than number plus 6
Group of answer choices
11/8
11
8
6
of relation.
Jess and Marie share money in the ratio of 3:5. If they have 64 dollars, how much does Marie have?
valve
======================================================
Explanation:
The ratio 3:5 is equivalent to 3x:5x after multiplying both parts by x.
Jess has 3x dollars and Marie has 5x dollars
3x+5x = 64
8x = 64
x = 64/8
x = 8
Therefore,
Jess has 3x = 3*8 = 24 dollarsMarie has 5x = 5*8 = 40 dollarsThe ratio 24:40 reduces to 3:5 after dividing both parts by the GCF 8.
---------------------------
Another way to solve:
m = amount Marie has
64-m = amount Jess has
3/5 = (64-m)/m
3m = 5(64-m)
3m = 320-5m
3m+5m = 320
8m = 320
m = 320/8
m = 40 dollars is the amount Marie has
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
Each side is 2 centimeters.
Hope this helps :)
Step-by-step explanation:
A square has sides that are all equal. So in this case the area is 4 square centimeters, and in order to find that we had to multiply 2 sides in which they are equal to each other. All the sides were 2 centimeters. We get 2 sides and multiply to get the area of the square chip.
2 cm × 2cm = 4 square centimeters
Solve equation.
3/5b=-2
To solve the equation, multiply both sides by 5/3. The solution is b = -10/3.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction or addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.The given problem:
Solve 3/5 b = -2
Notice that the variable, b, is already isolated on the left side.
Multiply both sides by 5/3:
3/5 b . 5/3 = -2 . 5/3
b = -10/3 (solved)
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what is the problem 10.5-9.67
Answer:
0.83
Step-by-step explanation:
10.5-9.67 the answer is 0.83
Answer:The answer is 0.83
Step-by-step explanation:Please give brainliest if right.I hope this helps.
Question 2 (1 point)
To find which number is one thousand times larger than 2.3 x 10^2, you would do the following steps.
a
Ob
Oc
Od
Change 1,000 to Scientific notation and then subtract from (2.3 x 10^6)
Change 1,000 to Scientific notation and then divide by (2.3 x 10^6)
Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6)
Change 1,000 to Scientific notation and then add to (2.3x10^2)
Answer:
d
Step-by-step explanation:
bc i think it is
To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
The correct answer choice option C
Scientific notationThis is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.
which number is one thousand times larger than 2.3 x 10²
Change 1,000 to Scientific notation and then multiply by (2.3 x 10²)1000 to scientific notation
= 10³
2.3 x 10² × 1000
= 2.3 x 10² × 10³
= 2.3 × 10^5
Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.
Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
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