Answer: 6 feet x 3 feet
Step-by-step explanation:
Let the height be given by= x
The length is= 6x -2 (1) from both sides= 6x-2
The width is= 3x-2(1) from both sides= 3x-2
The total volume= length * width * height
4=(6x-2)*(3x-2)*x
Solving we get,
x=1 and other factor is not the valid option.
So the outer dimensions should be 6 feet x 3 feet
This little pool is 10 feet in diameter and 3 feet tall. Use the formula for volume to find the total water needed to fill the pool.
V=π r ^2 h
The total water needed to fill the pool is 75π cubic feet.
Given: The pool is 10 feet in diameter and 3 feet tall. To find: The total water needed to fill the pool using V = πr²h formula.
Calculations: Radius (r) = 5 feet, Height (h) = 3 feet. Substitute values into formula: V = π(5)^2(3) = 75π cubic feet.
Answer: The total water needed to fill the pool is 75π cubic feet.
What is the angle measure 52∘48′51′′ equivalent to in decimal degrees? Enter your answer, rounded to the nearest thousandth of a degree, in the box.
Answer:
52.814 degrees
Step-by-step explanation:
we know that
[tex]1^o=60'\\1'=60''[/tex]
we have
[tex]52^o48'51''[/tex]
[tex]52^o48'51''=52^o+48'+51''[/tex]
Convert 51'' to minutes
[tex]51''=\frac{51}{60}= 0.85'[/tex]
[tex]52^o48'51''=52^o+48'+0.85'=52^o+48.85'[/tex]
Convert 48.85' to degrees
[tex]48.85'=\frac{48.85}{60}= 0.814^o[/tex]
[tex]52^o+48.85'=52^o+0.814^o=52.814^0[/tex]
Final answer:
The angle measure 52°48'51'' is equivalent to 52.814 degrees in decimal form when you convert the minutes and seconds to a decimal and add them to the degree part.
Explanation:
The angle measure 52°48'51'' equivalent to in decimal degrees is calculated by converting minutes and seconds to a decimal form. One degree equals 60 minutes, and one minute equals 60 seconds. To convert, divide the number of minutes by 60 and the number of seconds by 3600, then add those amounts to the degrees to get the decimal degree.
Starting with the minutes: 48 minutes / 60 = 0.8 degrees.
Now converting the seconds: 51 seconds / 3600 = approx. 0.014167 degrees.
So, adding these together: 52 + 0.8 + 0.014167 = 52.814167 degrees, which rounded to the nearest thousandth of a degree is 52.814.
Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward along the z-axis a distance of 5 units. What are the coordinates of your position? (x, y, z)
Answer:
(4,0,-5)
Step-by-step explanation:
Since we move 4 points along +ve x-axis so, x coordinate is 4
We did not move any point along y-axis so y coordinate is 0
we moved 5 points along -ve z-axis so z coordinate is -5
so our position is (x,y,z) = (4,0,-5)
Select one of the factors of the quadratic expression.
x2 + 5x - 14
A)
(x + 14)
B)
(x + 2)
C)
(x + 7)
D)
(x - 3)
Answer:
The answer to your question is letter C (x + 7)
Step-by-step explanation:
Expression
x² + 5x - 14
Factor the expression
- Find two number that multiplied give -14 and that added give 5
- Find the prime factors of -14
-14 2
- 7 7
-1
-From the prime factors, we notice that these numbers are + 7 and -2
- x² + 7x - 2x - 14
- Factor the expression
(x + 7)(x - 2)
The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures are 40 and 20°C, respectively, has been determined to be 40 W/m2. What is the thermal conductivity of the wood?
Answer:
[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]
Step-by-step explanation:
Previous concepts
The Fourier's law, states that the "rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows".
And we have the following formula given:
[tex] q_x = -k A \frac{dT}{dx}[/tex]
For this case we have the following data given:
[tex] L= 50 mm * \frac{1m}{1000 mm}=0.05m[/tex]
[tex] T_i = 40 C[/tex] represent the inner surface temperature
[tex] T_o = 20 C[/tex] represent the outer surface temperature
[tex] \frac{q_x}{A} = 40 W/m^2 [/tex] represent the heat flux
So then we are interested on the value of k.
Solution to the problem
if we solve for the value of k from the formula:
[tex] q_x = -k A \frac{dT}{dx}[/tex]
We got:
[tex] k = - \frac{q_x}{A \frac{dT}{dx}}[/tex]
We can rewrite this expression like this:
[tex] k = - \frac{q_x}{A \frac{T_o -T_i}{L}}[/tex]
And if we replace the values given we got:
[tex] k = - \frac{40 W/m^2}{\frac{20-40 C}{0.05 m}}= 0.1 \frac{W}{m C}[/tex]
Using Fourier's law of heat conduction, the thermal conductivity of the wood slab is calculated to be 0.1 W/m·K given a heat flux of 40 W/m², a temperature difference of 20°C, and a thickness of 50 mm.
Explanation:The student is asking about the thermal conductivity of a wood slab, given its thickness, the temperature difference across it, and the heat flux. To find the thermal conductivity (k), we can use Fourier's law of heat conduction which states:
Q/t = k × A × (T2 − T1) / d
where:
Q/t is the rate of heat transfer (40 W/m²),k is the thermal conductivity,A is the cross-sectional area (not needed here as we have heat flux per unit area),(T2 − T1) is the temperature difference across the material (40°C − 20°C = 20°C),d is the thickness of the material (50 mm = 0.05 m).Rearranging the formula to solve for k gives:
k = Q/t × d / (T2 − T1)
Plugging in the values:
k = 40 W/m² × 0.05 m / 20°C
k = 0.1 W/m·K
So, the thermal conductivity of the wood is 0.1 W/m·K.
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The ages of three siblings Jason John and Jackson totals 21 years. Jason is one year older than John. Jackson is three times as old as John. How old is John?
Answer:Jason is 5 years old.
John is 4 years old.
Jackson is 12 years old.
Step-by-step explanation:
Let x represent the age of Jason.
Let y represent the age of John.
Let z represent the age of Jackson.
The ages of three siblings Jason John and Jackson totals 21 years. It means that
x + y + z = 21 - - - - - - - - - - -1
Jason is one year older than John. It means that
x = y + 1
Jackson is three times as old as John. It means that
z = 3y
Substituting x = y + 1 and z = 3y into equation 1, it becomes
y + 1 + y + 3y = 21
5y = 21 - 1 = 20
y = 20/5 = 4
x = y + 1 = 4 + 1
x = 5
z = 3y = 3 × 4
z = 12
Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be . The actual difference is .
Answer:
Mike estimated the difference to be 72.
The actual difference is 72.74.
Step-by-step explanation:
Mike estimated 79 as 79.44 and 7 as 6.7, therefore Mike estimated the difference, this way:
79 - 7 = 72
Actual difference of the numbers is:
79.44 - 6.7 = 72.74
Mike estimated the difference to be 72.
The actual difference is 72.74.
In a large class of introductory Statistics students, the professor has each person toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. How much variability would you expect among these proportions?
Answer:
Variability expected among these Proportions is given by Standard deviation = 0.125
Step-by-step explanation:
The probability of tossing heads is the same for a fair coin as the probability of tossing tails.
The probability of tossing heads is then 1 chance out of 2
P = 1/2 = 0.5
The standard deviation of the sample distribution of the sample proportion = √Pq/n
Standard deviation = √p(1-p)/n
= √0.5(1-0.5)/16
Standard deviation = 0.125
The variability among the proportions of heads obtained in the coin tosses is due to the random nature of the experiment. The law of large numbers explains that as the number of tosses increases, the observed relative frequencies of heads will approach the theoretical probability of 0.5.
Explanation:The amount of variability that can be expected among the proportions of heads obtained by the students tossing a coin 16 times can be determined by understanding the concept of probability.
In a single coin toss, the probability of getting a head is 0.5. However, when the coin is tossed more times, the observed proportions of heads will vary from the theoretical probability of 0.5.
The variability among these proportions is attributed to the random nature of the coin tosses and is due to the fact that the short-term results of an experiment do not necessarily match the theoretical probability. The law of large numbers states that as the number of repetitions of an experiment is increased, the observed relative frequencies of heads will tend to become closer to the theoretical probability of 0.5.
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Which of the following describe the function
g(x) = log2 (x - 2) – 3.
Choose ALL that apply.
The domain is the set of all real number greater than 2.
The x-intercept = ( 10,0) and there is no y-intercept
Avertical asymptote at x = 2.
There is no x-intercept and the y-intercept = (0,10 ).
The domain is the set of all real numbers less than 2
The graph of g(x) is symmetric to its inverse exponential function over the line y = 0
The graph of g(x) is symmetric to its inverse exponential function I’ve ether like y = x
A vertical asymptote at x = 10
Answer:
From the plot and from inspection of the equation the following are true
a.) The domain is the set of all real numbers greater than 2
b.) The x-intercept = (10,0) and there is no y-intercept
c.) A vertical asymptote is at x = 2
f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x
Step-by-step explanation:
The plot of the graph is attached.
From the plot and from inspection of the equation the following are true
a.) The domain is the set of all real numbers greater than 2
b.) The x-intercept = (10,0) and there is no y-intercept
c.) A vertical asymptote is at x = 2
f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x
The annual tuition at a specific college was $20,500 in 2000, and $45,4120
in 2018. Let x be the year since 2000, and y be the tuition. Write an
equation that can be used to find the tuition y for x years after 2000. Use
your equation to estimate the tuition at this college in 2020.
Final answer:
The estimated tuition at this college in 2020 is $51,137.
Explanation:
To find the equation to determine the tuition y for x years after 2000, we need to use the given information: the annual tuition in 2000 was $20,500 and it increased to $45,120 in 2018.
Let's calculate the rate of increase per year:
The change in tuition over the number of years is:
(Tuition in 2018 - Tuition in 2000) / (Year in 2018 - Year in 2000) = (45,120 - 20,500) / (2018 - 2000)
Now, we can use this rate of increase to find the tuition in any given year x:
Tuition in a specific year = Tuition in 2000 + (Rate of increase per year) * x
To estimate the tuition in 2020, we substitute x = 20 into the equation:
Tuition in 2020 = 20,500 + ((45,120 - 20,500) / (2018 - 2000)) * 20 = $51,137
PLEASE HELP!!! PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.
Find CD.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
CD =
Answer:
[tex]CD = 7.8[/tex]
Step-by-step explanation:
Given:
Δ DBC is a right angled triangle.
[tex]\angle B = 90\°\\\\\angle C = 59\°[/tex]
BC = 4
We need to find the value of CD
Solution:
Now we know that:
[tex]cos\ \theta = \frac{adjacent \ side}{hypotenuse}[/tex]
So we can say that;
[tex]Cos \angle C =\frac{BC}{CD}[/tex]
Substituting the given values we get;
[tex]Cos\ 59 = \frac{4}{CD}\\\\\\CD = \frac{4}{Cos\ 59} = 7.766[/tex]
Rounding to nearest tenth we get;
[tex]CD = 7.8[/tex]
Hence the Value of CD is 7.8.
Consider the triangle graphed below. Classify it by its angles.
Answer:
The answer to your question is right
Step-by-step explanation:
Acute is a triangle in which three internal angles are acute (less than 90°). The other angles measure 90°, so this option is incorrect.
Obtuse is a triangle that has one angle greater than 90°. This option is incorrect because of the angles of this triangle measure 30, 60, 90.
Equiangular is a triangle in which angles measures the same. This option is wrong because the angles have different values.
A Right triangle is a triangle that has an angle that measures 90°. This option is right.
The statement "The square of any rational number is rational" can be rewritten formally as "For all rational numbers x, x 2 is rational" or as "For all x, if x is rational then x 2 is rational." Rewrite each of the following statements in the two forms "∀ x, " and "∀x, if , then " or in the two forms "∀ x and y, " and "∀x and y, if , then ."
a. The reciprocal of any nonzero fraction is a fraction.
b. The derivative of any polynomial function is a polynomial function.
c. The sum of the angles of any triangle is 180◦.
d. The negative of any irrational number is irrational.
e. The sum of any two even integers is even.
f. The product of any two fractions is a fraction.
Answer:
a.
For all non zero fraction 1(1/x), 1/x is a fraction
For all 1/(1/x), if 1/(1/x) is non zero, 1/x is a fraction
b.
For all polynomial function f(x) = x³ + x² + x - 1, the derivative (dy/dx) is a polynomial function
For all f(x) x³ + x² + x - 1, if f(x) is polynomial, f'(x) is a polynomial function
c.
For all angles x,y,z of a triangle, the sum, x + y + z = 180
For all x,y,z, if x,y and z are the angles of a triangle, x+y+z = 180
d.
For all irrational numbers x, -x is irrational
For all x, if x is irrational then -x irrational.
e.
For two integers, x and y, the sum x+y is an integer
For x,y if x and y are integers, then x + y is an integer
f.
For two fractions, x/y and a/b the product ax/by is a fraction
For x/y and a/b, if x/y and a/b are fractions then ax/by is a fraction
Final answer:
The statements have been rewritten in both universal quantification and conditional forms to describe relationships in mathematics, such as the property of being a fraction, polynomial function, or summing up to 180 degrees for triangles.
Explanation:
To rephrase the given statements in mathematical terms:
For all nonzero fractions x, if x is a fraction, then 1/x is a fraction.For all polynomial functions f(x), if f(x) is a polynomial function, then f'(x) is a polynomial function.For all triangles, if a figure is a triangle, then the sum of its angles is 180 degrees.For all irrational numbers x, if x is irrational, then -x is irrational.For all even integers m and n, if m and n are even, then m + n is even.For all fractions a and b, if a and b are fractions, then a * b is a fraction.Worth 50 points and I will mark brainliest.
Use the linear combination method to solve the system of equations. Justify each step of your solution. Please explain the steps you used so I could learn.
-3x-7y= -28
2x+3y=7
Answer:
x= -13 , y=11
Step-by-step explanation:
Using elimination method, make the x variable equal to eliminate the variable
-3x - y = -28
2x+ 3y=7
2(-3x-y =28)
3(2x+3y=7)
-6x - 2y =56
6x +9y=21
Apply addition
7y = 77
y=77/7 = 11
Use the value of y=11 in
2x+ 3y=7
2x +3(11) =7
2x +33 =7
2x=7-33
2x= -26
x= -26/2 = -13
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Anna is standing on the roof of a 35-foot building and is located at point A.
There is a 60-foot rope hanging from a point on the roof. When the rope is stretched out, it reaches to point C. She wants to know how far she is from point
B.
If Anna can show that triangles ABD ABD and ACD ACD are congruent, she can find the distance from A to B
Which additional segment lengths could be used to prove that △ADB≅△ADC by using the SAS Congruence Postulate?
THERE IS MORE THAN ONE ANSWER
CD=7 ft.
BD=6 ft.
CD=12 ft.
BD=5 ft.
CD=8 ft.
BD=8 ft.
9514 1404 393
Answer:
CD = 8 ft.
BD = 8 ft.
Step-by-step explanation:
To make use of the SAS postulate, Anna needs to identify two sides on either side of congruent angles.
The only marked angle is the right angle. We know that AD is congruent to itself, so Anna also needs to use the segments CD and BD, which are on the other side of the right angle in the right triangles.
The two choices in which BD and CD have the same length are
CD=8 ft.BD=8 ft.R(x) = -13.85x2 + 1,660x
C(x) = 55,400 – 279x
Answer:
What am I suppose to do?
Step-by-step explanation:
(Geometry Question) A sledding run is 300 yards long with a vertical drop of 27.6 yards. Find the angle of depression of the run.
Please show all work on how you got your answer
Answer:
5.28°
Step-by-step explanation:
Draw the triangle formed by the sledding run. The hypotenuse is 300. The height is 27.6. The angle of depression is opposite of the height.
Using sine:
sin θ = 27.6 / 300
sin θ = 0.092
θ = 5.28°
Which expression is equivalent to RootIndex 4 StartRoot x Superscript 10 Baseline EndRoot? x squared (RootIndex 4 StartRoot x squared EndRoot) x2.2 x cubed (RootIndex 4 StartRoot x EndRoot) x5
Answer:
The option x squared ( root index 4 start root x squared end root) is correct
Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]
Step-by-step explanation:
Given expression is [tex]\sqrt[4]{x^{10}}[/tex]
To find the equivalent expression to the given expression :
[tex]\sqrt[4]{x^{10}}[/tex]
[tex]=\sqrt[4]{x^{8+2}}[/tex]
[tex]=\sqrt[4]{x^8.x^2}[/tex] ( using the property [tex]a^m.a^n=a^{m+n}[/tex] )
[tex]=\sqrt[4]{x^{2\times 4}.x^2}[/tex]
[tex]=\sqrt[4]{(x^2)^4x^2}[/tex] ( using the peoperty [tex]a^{mn}=(a^m)^n[/tex] )
[tex]=\sqrt[4]{(x^2)^4}\times \sqrt[4]{x^2}[/tex] ( using the property [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex] )
[tex]=x^2\sqrt[4]{x^2}[/tex]
Therefore [tex]\sqrt[4]{x^{10}}=x^2\sqrt[4]{x^2}[/tex]
Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]
The option "x squared (RootIndex 4 StartRoot x squared EndRoot)" is correct
That is [tex]x^2\sqrt[4]{x^2}[/tex] is correct
Answer:
the correct answer is A
Step-by-step explanation:
hope this helped
Martha has 8 cubic feet ofputting soil in the three flowerpots she wants to put the same amount of soil in each pot how many cubic feet of soil she put in each flower pot
Answer:
[tex]2\frac{2}{3}\text{ ft}^3\approx 2.67\text{ ft}^3[/tex]
Step-by-step explanation:
We have been given that Martha has 8 cubic feet of putting soil in the 3 flowerpots. She wants to put the same amount of soil in each pot.
To find the amount of soil in each pot, we need to divide total soil (8 cubic feet) by number of pots (3) as shown below:
[tex]\text{Amount of soil in each pot}=\frac{8\text{ ft}^3}{3}[/tex]
[tex]\text{Amount of soil in each pot}=2\frac{2}{3}\text{ ft}^3[/tex]
[tex]\text{Amount of soil in each pot}=2.6666\text{ ft}^3[/tex]
[tex]\text{Amount of soil in each pot}\approx 2.67\text{ ft}^3[/tex]
Therefore, Martha needs to put approximately 2.67 cubic feet of soil in each flower pot.
To determine the amount of soil Martha puts in each flowerpot, divide the total cubic feet of soil (8) by the number of flowerpots (3), which results in approximately 2.67 cubic feet of soil per pot.
Explanation:The question pertains to the division of cubic feet of soil into equal amounts across three flowerpots. To find out how many cubic feet of soil Martha should put in each flower pot, we simply divide the total amount of soil by the number of flowerpots. In this case, Martha has 8 cubic feet of soil to distribute evenly into 3 pots.
The calculation would be as follows:
Determine the total volume of soil available: 8 cubic feet.Count the number of flowerpots: 3.Divide the total volume of soil by the number of pots to get the amount of soil per pot: 8 cubic feet ÷ 3 pots = 2.67 cubic feet per pot.Therefore, Martha can put approximately 2.67 cubic feet of soil in each flower pot.
Perform the indicated operation. (2x + y)(3x2 + y)
WILL CHOOSE FIRST W/ RIGHT ANSWER BRAINLIEST!!!!!!!!
Answer:
Step-by-step explanation:
(2x+y)(3x²+y)=2x(3x²+y)+y(3x²+y)=6x³+2xy+3x²y+y²=6x³+3x²y+2xy+y²
Write the slope-intercept form (y=mx+b) of the equation of the line given the slope and y-intercept.
Use the formula for computing future value using compound interest to determine the value of an account at the end of 6 years if a principal amount of $6,000 is deposited in an account at an annual interest rate of 6% and the interest is compounded quarterly.
Answer: the value of the account at the end of 6 years is is $8577
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 6000
r = 6% = 6/100 = 0.06
n = 4 because it was compounded 4 times in a year.
t = 6 years
Therefore,.
A = 6000(1+0.06/4)^4 × 6
A = 6000(1+0.015)^24
A = 6000(1.015)^24
A = $8577
Andre has been practicing his math facts. He can now complete 135 multiplication facts in 90 seconds. If Andre is answering questions at a constant rate, how many facts can he answer per second?
Andre can complete 1.5 facts in one second.
Step-by-step explanation:
Given,
Number of multiplication facts completed in 90 seconds = 135
Therefore;
90 seconds = 135 facts
Dividing both sides by 90 to fins the facts per second
[tex]\frac{90}{90}\ seconds=\frac{135}{90}\ facts\\\\1\ second = 1.5\ facts[/tex]
Andre can complete 1.5 facts in one second.
Keywords: unit rate, division
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Andre can answer 1.5 multiplication facts per second by dividing the total number of facts he completed (135) by the time it took (90 seconds).
Explanation:Andre has been answering multiplication facts at a consistent pace. To find out how many facts he can answer per second, we need to divide the total number of facts he answered by the total number of seconds it took him to answer them.
Andre answered 135 multiplication facts in 90 seconds.
To calculate the rate per second, the formula is:
Division of total facts by total seconds: 135 facts ÷ 90 seconds = 1.5 facts per second.Therefore, Andre can answer 1.5 facts per second.
In this year’s
7
th
7th
grade class, there are 4 boys for every 5 girls. How many girls are in the class if there are 20 boys in the class?
Answer:
The answer to your question is 25 girls
Step-by-step explanation:
Data
4 boys for every 5 girls
20 boys ? number of girls
To solve this problem use proportions
Number of boys : Number of girls :: New number of boys : New number of
girls
Substitution
4 : 5 :: 20 : x
Solve for x
x = (5 x 20) / 4
Simplification
x = 100 / 4
Result
x = 25
There are 25 girls
_____ are systematic tendencies to use information about others in ways that result in inaccurate perceptions.
Answer:
biases
Step-by-step explanation
i toke the test
Bias is the systematic tendency to use information about others.
What are systematic tendencies?The propensity to give facts that can be quickly recalled from memory as much weight as possible while making a decision.
You may reap the rewards of group judgments while avoiding frequent challenges to effective judgment in groups by managing group judgment processes well. Fundamental judgment ideas may be learned, but like with other abilities, practice is required. A professional judgment framework is a useful example of a sound decision-making procedure and enables you to identify potential areas for error. A shared framework enables the use of a common language and understanding. It normally pays off to put in some work up front, especially in the initial few stages of the judging process.
Therefore, A few properties of systematic bias are Heuristics are quite effective; typically speaking, benefits outweigh costs; yet, they may lead to biased judgment.
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A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of x?
Answer:
A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of π?
The expression which represents the value of π is option C from the attachment that is π = 43.96/14
Step-by-step explanation:
Given:
Circumference of the circle = 43.96 feet
Diameter f the circle = 14 feet
So,
We know that :
Circumference of the circle = [tex]2(\pi )r[/tex] or [tex](\pi)d[/tex]
Re-arranging the formula:
⇒ [tex](\pi)d = Circumference\ (C)[/tex]
⇒ [tex](\pi )d =C[/tex]
⇒ [tex]\frac{\pi\times d}{d}=\frac{C}{d}[/tex]
⇒ [tex]\pi =\frac{C}{d}[/tex]
Plugging the numeric values:
⇒ [tex]\pi =\frac{43.96}{14}[/tex]
So the expression for π is 43.96/ 14,and option C is the correct choice.
The required expression for value of x is [tex]\frac{43.96}{14}[/tex].
Given that,
The circumference of the circle was about 43.96 feet,
And the diameter of the circle was 14 feet
We have to determine,
Which expression best represents the value of x.
According to the question,
Circumference of the circle = 43.96 feet
Diameter f the circle = 14 feet
Then,
Circumference of the circle = [tex]\pi \times d[/tex]
Let, [tex]\pi = x[/tex]
Circumference of the circle [tex]= x d[/tex]
Circumference of the circle = 43.96 feet
Therefore,
[tex]= 43.96 = x\times 14\\\\= x = \frac{43.96}{14} \\\\[/tex]
Hence, The required expression for value of x is [tex]\frac{43.96}{14}[/tex].
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Use a ruler to measure the side length of the rectangle in centimeters mark 8 cm with a point and connect the points to show the square units then count the squares you're true to find the total area
Answer:
The total area of the rectangle is found by counting the total number of 1 cm squares inside the rectangle.
Note: This question is missing some details.
A more complete question is this: Use a ruler to measure the side lengths of the rectangle in centimeters. Mark each centimeter with a point and connect the points to show the square units. Then, count the squares you drew to find the total area.
Step-by-step explanation:
This method is used to determine area of a rectangle by counting the square unit inside the given rectangle.
For example, if the measurement of the sides of the rectangle is 8 cm and 5 cm respectively. To find the area;
Step 1: Mark out 1 cm points on each side of the rectangle.
Step 2: Connect each of the points.
Step 3: Count the number 1 cm squares within the triangle. The total number of squares gives the area of the triangle.
In this example, the number of 1 cm squares will be found to be 40. So the area of the rectangle is 40 cm squares or 40 cm².
Jody, a statistics major, grows tomatoes in her spare time. She measures the diameters of each tomato. Assume the Normal model is appropriate. One tomato was in the 50th percentile. What was its z-score?
Answer:
Zscore = 0.5
Step-by-step explanation:
If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).
By that, we mean that the mean (μ) = 0 and variance ([tex]\sigma^{2}[/tex]) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.
Thus:
==> Z score = [tex]\frac{x-\mu}{\sigma}[/tex] = [tex]\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5[/tex]
The infant measures 21.5 in (54.6 cm) at birth. If the infant is following a normal pattern of growth, what would be an expected height for the infant at the age of 6 months?
Answer:
27.5 in (69.85 cm)
Step-by-step explanation:
The normal growth rate for an infant after birth is 1 in per month.
After six month, the infant will be 27.5 in which is equivalent to 69.85 cm.
2 math questions. Please show your work if you can, I struggle with this, Thanks !!
20pts
Step-by-step explanation:
To find the solution, Tanisha can graph each side of the equation as its own function:
y₁ = log₃(5x)
y₂ = log₅(2x + 8)
The solution is where the two curves cross. From the graph, that happens at x ≈ 0.957.
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