I need help question 6 of math statistic
The area of the triangle ABC is 6√6 cm².
Triangle ABC is depicted in the given diagram, where AB = 7 cm, BC = 6 cm, and AC = 5 cm.
Heron's formula, which claims that the area is provided by: for a triangle with sides of lengths a, b, and c, can be used to determine the triangle's area.
(s(s-a)(s-b)(s-c)) = area
where s is the triangle's semi perimeter and is determined by:
s = (a + b + c)/2
Here are the facts:
7 cm for a and 6 cm for b.
c = 5 cm
The semi perimeter is as follows:
s = (7 + 6 + 5)/2 = 9
When we apply Heron's formula, we get:
Area = √(9(9-7)(9-6)(9-5)) = √(9 × 2 × 3 × 4) = √216
When we reduce the square root, we obtain:
= 6√6 cm²
As a result, the triangle ABC has a 6√6 cm² area.
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13) A cutlery manufacturer packs 200 teaspoon into boxes holding either 4 spoons or six spoons.there are 48 full boxes.
are 48 full boxes,
a) If there are a four-spoon boxes and y six spoons boxes use the information to find two equations relating to x and y
relating x and y.
b) How many boxes hold four spoons
Answer:
Step-by-step explanation:
890
Select all that apply Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply. Chebyshev's theorem applies to any set of values. Chebyshev's theorem works for symmetrical, bell-shaped distributions. Both work for skewed distributions. ClChebyshev's theorem applies only to symmetrical, bell-shaped distributions
Ther statement that is true regarding the application of Chebyshev's theorem and the Empirical Rule is B.Chebyshev's theorem works for symmetrical, bell-shaped distributions.
What is Chebyshev's theorem and the Empirical Rule?The Empirical Rule is an approximation that only works with data sets that have a relative frequency histogram with a bell-shaped distribution. The percentage of measurements that fall within one, two, and three standard deviations of the mean is estimated.
It is true that Chebyshev's Theorem holds true for all conceivable data sets. Both do not require a sample standard deviation for the data.
Therefore, option B is correct.
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PLEASE HELP ME
If Gen Z's debt increases by 67.2% per year. and their current debt is 16,000. How long would it take for Gen Z to be 140,000 in debt? Could you also please explain how you got the answer.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140000\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 67.2\%\to \frac{67.2}{100}\dotfill &0.672\\ t=years\\ \end{cases}[/tex]
[tex]140000 = 16000(1 + 0.672)^{t} \implies \cfrac{140000}{16000}=1.0672^t\implies \cfrac{35}{4}=1.0672^t \\\\\\ \log\left( \cfrac{35}{4} \right)=\log(1.0672^t)\implies \log\left( \cfrac{35}{4} \right)=t\log(1.0672) \\\\\\ \cfrac{\log\left( \frac{35}{4} \right)}{\log(1.0672)}=t\implies 33.35\approx t\qquad \textit{about 33 years and 128 days}[/tex]
Taxi company a charges 4$ plus 0.5x per mile and taxi company b charges 5 $ plus 0.25x per mile
Graph it do they intersect?
The graphs of the linear equations will intercept at the point (4, 6)
Do the graphs intercept?We know that taxy company a charges $4 plus $0.5 per mile, so the cost for x miles is:
A = 4 + 0.5x
While taxy company be charges $5 plus $0.25 per mile, so the cost for x miles will be:
B = 5 + 0.25x
The graphs will intersect at the x value such that the two linear equations are equal:
A = B
This happens when:
4 + 0.5x = 5 + 0.25x
0.5x - 0.25x = 5 - 4
0.25x = 1
x = 1/0.25 = 4
And the cost is:
B = 5 + 0.25*4 = 6
So the graphs intercept at the point (4, 6)
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I REQUEST HELP! PLS HELP ME W THIS Q!!! WILL GIVE BRAINLIEST!
Answer:
[tex]x\geq 5\\x > 4\\[/tex]
Answer:
x ≥ 5
x > 4
x < 6
Step-by-step explanation:
The inequalities for which 5 is the lowest integer value that x could take are:
x is greater than or equal to 5. (Since x can be 5 in this case.)x > 4. (Since 5 is the lowest integer value for x, and 5 is not greater than 4, x must be greater than 4.)x is less than 6. (Since 5 is less than 6, and x is the lowest integer value that is less than 6, x must satisfy this inequality.)Therefore, the correct options are:
x is greater than or equal to 5.
x > 4.
x is less than 6.
Two identical rectangular prisms and two identical cubes are joined.
Answer the questions to find the new solid’s surface area.
The new solid's surface area, which is 490 cm², is created by combining two identical cubes, each of which has a surface area of 294 cm².
What is the Total Surface Area of a Cube?The total area of a cube's faces that cover it is the surface area of the object. The cube's surface area is calculated as six times the square of its side lengths. 6a², where an is the cube's side length, serves as its representation. In essence, it is the overall surface area.
Total surface area of a cube = 6a², where a is the length of each of the sides.
Let the surface area of each identical cube = 294 cm²
The length of each side be
6a² = 294
simplifying the above equation, we get
a² = 294/6
a² = 49
a = √49
a = 7 cm
Surface area of the new solid
= surface area of the two identical cubes - 2(area of the surface where both are joined)
Surface area of the new solid = 2(294) - 2(7²) = 490 cm²
Therefore, the surface area of the new solid be 490 cm².
The complete question is;
Two identical rectangular prisms and two identical cubes are joined. Answer the questions to find the new solid’s surface area. The numbers are 9 and 4.
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you are given the following information about a population:• There are two alleles: C and c.• C codes for green hair and c codes for white hair.• C is dominant over c.• The frequency of the c allele is 0.3.• The population is comprised of 100 individuals.Assuming the population is in Hardy-Weinberg equilibrium, how many individuals have green hair?
In this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.
What is the quadratic equation?
A quadratic equation in one variable is a mathematical sentence of degree 2 that can be written in the following standard form. a+ bx + c = 0, where a, b, and c are real numbers and a 0.
The Hardy-Weinberg equilibrium is an idealized model of a population that assumes that the frequency of alleles remains constant from generation to generation in the absence of external forces.
According to this model, the frequency of a particular genotype can be calculated using the following formula:
p² + 2pq + q² = 1
where p is the frequency of the dominant allele (C) and q is the frequency of the recessive allele (c). In this case, p = 1 - q = 1 - 0.3 = 0.7, and q = 0.3.
The frequency of individuals with the genotype CC (green hair) is given by p², or 0.7² = 0.49.
The frequency of individuals with the genotype Cc (green hair) is given by 2pq, or 2 * 0.7 * 0.3 = 0.42.
Hence, in this population of 100 individuals, approximately 49 individuals will have green hair due to the dominant allele CC and approximately 42 individuals will have green hair due to the dominant allele Cc. The total number of individuals with green hair is 49 + 42 = 91.
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EASY POINTS!
There are two submarines, Submarine 1 and Submarine 2, that are diving under the sea.
The proportional equation y = -22x represents the relationship between the depth
below sea level (in feet) of Submarine 1 to the time (in minutes). Meanwhile, the graph
shown here represents the relationship between the depth below sea level (in feet) and
the time (in minutes) of Submarine 2:
Determine which submarine will reach a depth of -1,056 feet below sea level in the
fastest time. How long will it take the faster submarine to reach a depth of -1,056 feet
below sea level?
Submarine 2 will reach a depth of -1,056 feet below sea level in the fastest time.
It will take the faster submarine 44 minutes to reach a depth of -1,056 feet below sea level.
How to determine which submarine will reach a depth of -1,056 feet below sea level in the fastest time?Since the proportional equation for Submarine 1 is y = -22x.
In order to determine which submarine will reach a depth of -1,056 feet below sea level in the fastest time, we need to find the proportional equation for Submarine 2 using the graph.
From the graph:
proportionality constant = depth/time
proportionality constant = -120/5 = -24
y = -24x
Since the proportionality constant of Submarine 2 (-24) is greater than that of Submarine 1 (-22). Thus, Submarine 2 will reach a depth of -1,056 feet below sea level in the fastest time.
The faster submarine is Submarine 2:
y = -24x
y = -1,056 feet
-1,056 = -24x
x= 1,056/24
x = 44 minutes
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wen and five friends equally share 1/3 of a pan of snack bars. which expression shows how much of the pan each person gets?
The solution is, 1/3 ÷ 6, expression shows how much of the pan each person gets.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
wen and five friends equally share 1/3 of a pan of snack bars.
so, we get,
the expression is 1/3 ÷ 6
This is because there are 6 friends in all and you are splitting 1/3 of the pan snack bars to each of them.
So, what your splitting/cutting/dividing would be the dividend (1/3) and then the friends would be the divisor (6)
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9. What is the money factor for a lease with an interest rate of 8%.
a. 0.00375
b. 0.00333
C. 2.26000
d. 22.60000
Answer:
Step-by-step explanation:
I think its A
6 times of the age of a daughter is the age of her mother. If the difference of their ages be 35years find the age of the mother.
Answer:
the age of her mother is 35 yrs old
Step-by-step explanation:
Let the age of daughter be x and mother be 6x
Now,
By question
6x -x=35
or, 5x =35
or,x=35/5
or x =5
Lastly,
age of daughter=x=5
age of mother =6x
=6*5
=35
finish this sentence to make it true: the maximum number of times you can overload a method in a class definition...
overload it by doing it again and again.
A model rocket is launched with an initial upward velocity of 50m / s The rocket's height (meters) after seconds is given by the following h = 50t - 5t ^ 2
The complete question
A model rocket is launched with an initial upward velocity of 50m/s. The rocket's height h (in meters) after t seconds is given by the following. h=50t-5t².
Find all values of t for which the rockets height is 20 meters.
The values of t for which the rockets height is 20 meter are, (10 + 2√21) / 2 and (10 - 2√21) / 2
What is velocity ?Velocity is a vector quantity that represents the rate of change of an object's position. It is defined as the derivative of the position vector with respect to time and has units of meters per second (m/s). Velocity includes both speed and direction, and is an important concept in physics and engineering.
We can find the values of t for which the rocket's height is 20 meters by setting h equal to 20 and solving for t.
h = 50t - 5t² = 20
Expanding the equation, we have:
50t - 5t² = 20
Adding 5t² to both sides:
50t = 20 + 5t²
Dividing by 5 both the sides,
10t = 4 + t²
t² - 10t + 4 = 0
t = (10 + 2√21) / 2
and t = (10 - 2√21) / 2
So the values of t for which the rocket's height is 20 meters are
(10 + 2√21) / 2 and (10 - 2√21) / 2
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Paul's car is 12 feet long. He is making a model of his car that is the actual size. What is the length of the model?
The length of the model is 2 feet
What is the length of the model?The model is the actual size. This means that for every 6 feet measured on the actual car, the model will span 1 foot.
Note that the model length is in the numerator and the actual length is in the denominator.
Thus, if the car is 12 feet long and L represents the length of the model, then write the ratio as .
Set the two ratios equal to each other to obtain the proportion below.
The length of the model is given as 2 feet
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Could someone please help me solve this problem, please show evidence of the answer, process
Answer:
[tex]\tan \theta=-\dfrac{\sqrt{5}}{2}[/tex]
[tex]\cos \theta=\dfrac{2}{3}[/tex]
[tex]\sin \theta=-\dfrac{\sqrt{5}}{3}[/tex]
Step-by-step explanation:
To find the exact values of the trigonometric functions of θ, we can use the following trigonometric identities:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Trigonometric Identities}\\\\$\sec x=\dfrac{1}{\cos x}$\\\\\\$\tan x=\dfrac{\sin x}{\cos x}$\\\\\\$\sin^2x+\cos^2x=1$\\\end{minipage}}[/tex]
In quadrant IV, cosine of the angle is positive, whereas sine of the angle is negative.
Given that sec θ = 3/2, and secant is the reciprocal of cosine:
[tex]\sec \theta=\dfrac{3}{2}[/tex]
[tex]\dfrac{1}{\cos \theta}=\dfrac{3}{2}[/tex]
[tex]\boxed{\cos \theta=\dfrac{2}{3}}[/tex]
To find sin θ, we can substitute the found value of cos θ into the Pythagorean identity:
[tex]\sin^2 \theta+\cos^2 \theta=1[/tex]
[tex]\sin^2 \theta+\left(\dfrac{2}{3}\right)^2=1[/tex]
[tex]\sin^2 \theta=1-\left(\dfrac{2}{3}\right)^2[/tex]
[tex]\sin \theta=\sqrt{1-\left(\dfrac{2}{3}\right)^2}[/tex]
[tex]\sin \theta=\dfrac{\sqrt{5}}{3}[/tex]
As sine of the angle is negative in quadrant IV:
[tex]\boxed{\sin \theta=-\dfrac{\sqrt{5}}{3}}[/tex]
Finally, substitute the values of sin θ and cos θ into the tan θ identity to find tan θ:
[tex]\tan \theta=\dfrac{\sin \theta}{\cos \theta}[/tex]
[tex]\tan \theta=\dfrac{-\frac{\sqrt{5}}{3}}{\frac{2}{3}}[/tex]
[tex]\boxed{\tan \theta=-\dfrac{\sqrt{5}}{2}}[/tex]
Therefore, the exact values of the trigonometric functions for θ are:
[tex]\tan \theta=-\dfrac{\sqrt{5}}{2}[/tex]
[tex]\cos \theta=\dfrac{2}{3}[/tex]
[tex]\sin \theta=-\dfrac{\sqrt{5}}{3}[/tex]
The table shows the distance that Rachel jogged last weekend. How much farther did Rachel jog on Sunday than on Saturday?
The number of miles further that Rachel was able to jog on Sunday more than Saturday was 10 miles.
How to find the distance ?On Saturday, the table shows that Rachel jogged a total of 15 miles. On Sunday, Rachel was able to jog 25 miles.
This means that Rachel was able to jog more miles on Sunday than she was able to jog on Saturday. The difference in the miles was :
= Miles jogged on Sunday - Miles jogged on Saturday
= 25 - 15
= 10 miles
In conclusion Rachel jogged 10 miles more on Sunday than Saturday.
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Mr B aged 52 years, has earned rupees 75,00,000 out of his business. His ex- wife gifted him cash in account worth rupees 6 lakh. He spent a total of rupees 15 lakh during a family trip. He won a lottery of 19 lakh rupees. Out of happiness he gifted his wife cash of rupees 450000. He bought a life insurance policy and paid a premium of 50000 annually. He paid tuition fee for his daughter for rupees 50000. He invested rupees 80000 in PPF. One of his existing life insurance policy got matured and he received a total of rupees 32 lakh. Seeing his health conditions the doctor adviced him a medical test of rupees 6000 following he bought a health insurance for rupees 27000. Calculate his taxable income and tax liability
The taxable income of the family is 1,15,37,000, the tax liability is given as 34,61,100.
How to solve for the taxable incomeMr. B's taxable income calculation:
Income from Business: 75,00,000
Gift received: 6,00,000
Lottery winnings: 19,00,000
Maturity amount of life insurance: 32,00,000
Total Income: 1,32,00,000
Expenditures:
Family trip: 15,00,000
Gift to wife: 4,50,000
Life insurance premium: 50,000
Tuition fee: 50,000
PPF investment: 80,000
Medical test fee: 6,000
Health insurance premium: 27,000
Total Expenditures: 16,63,000
Taxable Income: 1,15,37,000 (Total Income - Total Expenditures)
Tax liability calculation:
Taxable Income Tax Rate Up to (in Rupees)
2.5 Lakhs NIL
2.5 Lakhs to 5 Lakhs 5% (12,500)
5 Lakhs to 7.5 Lakhs 10% (25,000)
7.5 Lakhs to 10 Lakhs 15% (37,500)
10 Lakhs to 12.5 Lakhs 20% (50,000)
12.5 Lakhs to 15 Lakhs 25% (62,500)
Above 15 Lakhs 30%
In this case, Mr. B's taxable income is 1,15,37,000, which falls in the tax bracket of above 15 Lakhs, so his tax liability would be 30% of 1,15,37,000 = 34,61,100.
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A rectangular
farm has an area of square miles. If
its length is miles, what is its width?
Input your answer as a fraction.
Please and thank you <3
Answer:
start by using the formula for the area of a rectangle:
Area = length × width
We know that the area of the farm is given as square miles, so we can write:
lw =
Solving for w, we can divide both sides by l:
w =
Therefore, the width of the rectangular farm is miles.
To simplify the expression, we can multiply the numerator and denominator by 2:
w =
So the width can also be expressed as the fraction __.
You are playing a solitaire game in which you are dealt three cards without replacement from a simplified deck of 10 cards (marked 1 through 10). You win if one of your cards is a 10 or if all of your cards are odd. How many winning hands are there?
The total number of winning hands are 276.
What is the probability?Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.
Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.
In the given question,
If the first card drawn is a 10, then there are
[tex]P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands[/tex]
There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,
[tex]9*8= 72 hands[/tex]
If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for
second card, it gives us
[tex]9*8= 72 hands[/tex]
And there are 5 odd cards, and it gives us:
[tex]P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands[/tex]
So, we have that in total we have
72+72+72+60=276 winning hands.
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What is the perimeter? Step by step.
Answer: 36
Step-by-step explanation:
to find the length, find the hypotenuse of a triangle formed by the x-axis and the distance the parallelogram is from the x-axis.
hypotenuse= [tex]a^{2}+b^{2} =c^{2}[/tex]
the distance from -6 to -3 is 3 units
the distance from 0 to 4 is 4 units
[tex]3^{2} +4^{2} =9+16=25[/tex]
then [tex]\sqrt{25} =5[/tex]
therefore the length of the parallelogram is 5 units
repeat on other side
the distance from -3 and 9 is 12 units
the distance from 0 and 5 is 5 units
[tex]12^{2} +5^{2} =144+25=169[/tex]
then [tex]\sqrt{169} =13[/tex]
therefore the width of the parallelogram is 13 units
now to find the perimeter add all side lengths of the given shape
since parallelograms have equal lengths and widths add 13+13+5+5
therefore the perimeter of the parallelogram is 36
If I have a car that can move at a speed of 6 km/h
and the distance from Talas to Bishkek is 2 km,
how long will the car drive? (in minutes)
Answer: 20 minutes
Step-by-step explanation:
What is the compound interest on a $10,000 investment that earns 6% compounded monthly for 5 years?
Answer:
$13,488.50
Step-by-step explanation:
annual rate 6%
so every month = 6/12 = 0.5%
compounding monthly so every month the money grows at (1+0.5%)
for 5 years, it's 60 months
10,000 * (1+0.5%)^60 = $13,488.50
It is normal for some newborn babies to lose weight in their first week of life. At one week old, Jenny's weight is 6.8 pounds. That is 3.7% lighter than she was at birth. What was the baby's birth weight?
Round your answer to the nearest tenth.
Based on the information, it can be inferred that the baby weighed 7.06 pounds at birth.
How to calculate how much the baby weighed at birth?To calculate how much the baby weighed at birth we must take into account the information we have available
Current Weight: 6.8 lbs.
% lost: 3.7%
According to the above, we must calculate what percentage the current weight is equal to:
100% - 3.7% = 96.3%
Now we must make a rule of three to find the weight of the baby at birth:
96.3 - 6.8
100 - ?
100% * 6.8 pounds / 96.3% = 7.06 pounds
According to the above, the baby was born thinking 7.06 pounds, that is, she lost 0.26 pounds.
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Lainey is sliding down a water slide that is 336 feet long at a rate of 48 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?
A.
-288 seconds
B.
288 seconds
C.
7 seconds
It will it take Lainey 7 seconds to travel from the top to the bottom of the slide. Option C
How to calculate the speed from the top to the bottom of the slide
Using the formula for calculating speed
The formula for Speed is given as [Speed = Distance ÷ Time].
To calculate the time, the speed formula can be molded as:
Time = Distance ÷ Speed].
Given Distance = 336 feet
Given speed = 48 feet per second
Time = Distance ÷ Speed
= 336 ÷ 48 = 7 seconds
Hence, the time it will take Lainey to travel from the top to the bottom of the slide is 7 seconds
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help its due tmr please
On evaluating, the function f(x) and g(x) the values of f(g(3)) = - 11 and f(g(x)) = -35x + 22.
Evaluating functions:A relation between a collection of inputs and outputs is known as a function. A function is an association between inputs in which each input is connected to approximately one output. To find f(a) for a given function f(x) we simply substitute 'a' instead of 'x' in the given function f(x).
Here we have
f(x) = 7x - 5 and g(x) = - 5x + 4
10. f(g(3))
To find g(3) take x = 3 in g(x)
=> g(3) = - 5(3) + 4 = - 15 + 4 = 11
=> g(3) = - 11
To find f(g(3)) take x = g(x) = - 11 in f(x)
f(g(3)) = 7(-11) - 5 = - 77 - 5 = - 82
∴ The value of f(g(3)) = - 11
11. f(g(x)
To find f(g(x)) take x = g(x)
=> f(g(x) = 7(-5x + 4) - 5
=> f(g(x)) = -35x + 28 - 5
=> f(g(x)) = -35x + 22
∴ f(g(x)) = -35x + 22
Therefore,
On evaluating, the function f(x) and g(x) the values of f(g(3)) = - 11 and f(g(x)) = -35x + 22.
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which student is correct
Leonard gave the correct value of approximate average rate of change of function.
What is a function?
In mathematics, a function is an expression, rule, or law that specifies the relationship between an independent variable x and a dependent variable y.
The average rate of change of function means the typical rate at which one quantity is changing in respect to another. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
The formula for average rate of change of function in the interval [a,b] is
[tex]\frac{f(b) - f(a)}{b-a}[/tex].
We are asked to find the rate of change when x = -3 to 6
From graph
when x = -3 , y = -2
when x = 6, y = 2
So average rate of change of function = [tex]\frac{f(6) - f(-3)}{6-(-3)} = \frac{2 - (-2)}{9} = \frac{4}{9}[/tex]
Therefore Leonard gave the correct value of approximate average rate of change of function.
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(- 6, 8) and (- 8, 2)
Answer:
Step-by-step explanation:
m= 3
The amount of water that a spherical tank can hold varies directly as the cube of its radius. If a tank with radius 7.5 ft holds 1767 ft3 of water, how much water can a tank with radius 16 ft hold?
The amount of water a tank can hold is 17155.86 cubuic ft.
Volume definition:Every three-dimensional object occupies some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.
Now in the given quetion, it is stated that ,
The amount of water that a spherical tank can hold varies directly as the cube of its radius.
Therefore,
[tex]V_1\alpha R^3\\\\\\V_1= aR^3\\\\a=\frac{1767}{7.5^3}[/tex]
Now , for the tank with radius 16 ft.
[tex]V_2\alpha R^3\\\\\\V_2= aR^3\\\\V_2=\frac{1767}{7.5^3}*16^3\\\\V_2=17155.86 ft^3[/tex]
Hence, the amount of water a tank can hold is 17155.86 cubuic ft.
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joel will fence a rectangular yard measuring 20 yds .how many yards of fencing will he need what will be the area of the fenced yard
Answer: he will need an area of 6*4 fencing
Step-by-step explanation: if 6+4 is 10 times that by 2 and you have 20
I hope this helped