Answer:
Step-by-step explanation:
Let the length of first piece be L .
Length of second piece = 56 - L
radius of circle made from first piece
R = L / 2π
Area of circle = π R²
= L² / 4π
side of square made fro second piece
= (56 - L) / 4
area of square = ( 56-L)² / 16
Total area
A = L² / 4π + ( 56-L)² / 16
For smallest possible combined area
dA / dL = 0
dA / dL = 2L / 4π - 2( 56-L)/16 =0
2L / 4π = 2( 56-L)/16
.159 L = 7 - .125 L
.284 L = 7
L = 24.65 inch
other part = 56 - 24.65
= 31.35 inch .
The Coffee Counter charges $8 per pound for Kenyan French Roast coffee and $7 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for $7.30 per pound?
Answer:
Kenyan French Roast coffee x=6
Sumatran coffee y=14
Step-by-step explanation:
x+y=20 blend coffee
8x+7y=7.3(20) selling price
x+y=20 ⇒ x=20-y
substitute in the equation:
8x+7y=7.3(20)
8(20-y)+7y=7.3(20) for 20 pound blend
160-8y+7y=146
-y=146-160
y=14 pond
x+y=20
x=20-14=6
check : 14*7+6(8)=146/7.3=20 pound
The price of the Kenyan French Roast coffee is $6 and the price of Sumatran coffee is $14.
Two equations can be derived from the question:
8x + 7y = 20(7.3)
8x + 7y = 146 equation 1
x + y = 20 equation 2
Where: x
x = Kenyan French Roast coffee
y = Sumatran coffee.
To determine the value of y, multiply equation 2 by 8
8x + 8y = 160 equation 3
Subtract equation 1 from 3
y = 14
Substitute for y in equation 2
x + 14 = 20
x = 20 - 14
x = 6
To learn more about simultaneous equations, please check: brainly.com/question/23589883
A pianist plans to play 5=pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second etc. to create a good flow. How many different recital programs are possible?
Answer:
2432902008176640000 programs are possible using 20 distinct (different) songs.
Step-by-step explanation:
There are 20 choices for the first song, 19 choices for the second, ...1 song for the last for a total of
N = 20*19*18*...*3*2*1 = 20!= 2432902008176640000 programs
The number 20! is the number of permutations for 20 distinct objects put in order.
20! is pronounced as 20 factorial.
Example: factorial of 5 is 5*4*3*2*1 = 120
Answer:
20*19*18*17*16=1 860 480 different programs
Step-by-step explanation:
So there are 20 pieces total and each of them can be first.
Each of residual 19 can be the second
Each of residual of 18 can be the third
Each of residual 17 can be the fourth
Each of residual 16 can be the fifth
Total amont of possible different programs ( the order of the pieces matters)
is : 20*19*18*17*16=1 860 480 different programs
800x87979 cuanto es?
800x87979 es 70, 383, 200
Espero que esto te ayude
Answer:
Step-by-step explanation:
800*87979 = 70,383,200
Solve for x: ex = 5.2
Answer:
x = ln (5.2)
Step-by-step explanation:
e^x = 5.2
Take the natural log of each side
ln ( e^x) = ln( 5.2)
x = ln (5.2)
Answer:
x ≈ 1.91, if e refers to 2.718281828...
x = 5.2/e, if e is simply another variable
Step-by-step explanation:
We are given:
ex = 5.2
Now, if e is referring to the irrational value of e that is about 2.718281828..., then when we divide both sides by e to solve for x, we get:
ex = 5.2
x = 5.2 / 2.718281828... ≈ 1.91
However, if e is simply another varialbe, then we just have:
ex = 5.2
x = 5.2/e
~ an aesthetics lover
Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB
Answer:
AB = 2 sqrt(35) (or 11.83 to two decimal places)
Step-by-step explanation:
Refer to diagram.
ABO'P is a rectangle (all angles 90)
=>
PO' = AB
AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)
using Pythagoras theorem.
If g(x)=f(1/3x) which statement is true
Answer:
the graph of g(x) is horizontally stretched by a factor of 3
Step-by-step explanation:
Use the line of best fit to determine the x-value when the y- value is 190
Answer:
A. 9
Step-by-step explanation:
Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.
Thus,
A.9 is the correct answer.
Hope this helps :)
Answer:
A. 9
Step-by-step explanation:
A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.
A record store owner assesses customers entering the store as high school age, college age,
or older, and finds that among all customers 30%, 50%, and 20% respectively, fall into these
categories. The owner also found that purchases were made by 20% of high school age
customers, by 60% of college age customers, and by 80% of older customers.
(a) Find the probability that a randomly chosen customer will make a purchase?
(b) If a customer makes a purchase, what is the probability that this customer is of college
age?
Step-by-step explanation:
(a) P = (0.3)(0.2) + (0.5)(0.6) + (0.2)(0.8)
P = 0.52
(b) (0.5)(0.6) = 0.3
P = 0.3 / 0.52
P = 0.58
If a customer makes a purchase, then the probability that this customer is of college will be 0.58
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given that purchases were made by 20% of high school age customers, by 60% of college age customers, and by 80% of older customers.
(a) the probability that a randomly chosen customer make a purchase will be;
P = (0.3)(0.2) + (0.5)(0.6) + (0.2)(0.8)
P = 0.52
(b) if a customer makes a purchase, then the probability that this customer is of college will be;
(0.5)(0.6) = 0.3
P = 0.3 / 0.52
P = 0.58
Learn more about probability here;
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A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies:
Grade A B C D E
Frequency 18 20 28 23 11
Compute the value of the test statistics. Do the data provide enough evidence to support the professor’s claim?
Answer:
clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.
Step-by-step explanation:
lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.
first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.
in particular lets take grade A proportional to grade B which implies that 18:20
clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.
helpppppppppppppppppppppppppppppp
Answer:
0
Step-by-step explanation:
Hope this helps
Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 7 inches shorter than the length of the mat and the hypotenuse is 1 inches longer than the length of the mat, what is the length of the mat?
Answer: length = 12
Step-by-step explanation:
Use Pythagorean Theorem: length² + height² = hypotenuse²
length = L
height = L - 7
hypotenuse = L + 1
L² + (L - 7)² = (L + 1)²
L² + L² - 14L + 49 = L² + 2L + 1
2L² - 14L + 49 = L² + 2L + 1
L² - 14L + 49 = 2L + 1
L² - 16L + 49 = 1
L² - 16L + 48 = 0
(L - 4)(L - 12) = 0
L - 4 = 0 L - 12 = 0
L = 4 L = 12
Input L = 4 and L = 12 to find the height:
Height = L - 7 height = L - 7
= 4 - 7 = 12 - 7
= -3 = 5
↓
negative height is not valid
So, the only valid solution is L = 12
helppppppppppp i give you brailienst
Answer:
5%
Step-by-step explanation:
Well let’s make a fraction 2/40.
So we have to simplify it to 1/20.
And we do 1 / 20.
So 1 / 20 is .05.
To make this a percent we put the seminal place 2 places to the right.
So the percent is 5%.
Can someone please help me!
Part B
In the right triangle shown below, are any altitudes shown? Does this lead to any generalizations about right triangles?
Explain your answer.
Answer:
In the right triangle, either leg could be considered as the heigh
Step-by-step explanation:
In the right triangle, if you have the length of the two legs, the triangle is already defined, the two legs are the base and the height (no matters the way you choose the order, either AB could be defined as the base or as the height, and if you decide to call AB the base then you necessarily need to take AC as the height.
As can be seen, the area of the triangle and its hypothenuse will be the same.
A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the lighthouse.
Answer: 34.64 m
Step-by-step explanation:
Given: A boat is 60 m from the base of a lighthouse.
The angle of depression between the lighthouse and the boat is 37°.
By using trigonometric ratios :
[tex]\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}[/tex]
here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m
[tex]\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64[/tex]
Hence, the lighthouse is 34.64 m tall.
Translate into a variable expression the product of p and the sum of p and 12
They're making me write something here so I can post the answer:
p(p + 12)
The probability density of a random variable X is given in the figure below.
From this density, the probability that X is between 0.68 and 1.44 is:
Find the probability that X is between 0.68 and 1.44.
Answer:
0.38
Step-by-step explanation:
The area under the probability density curve is equal to 1.
The width of the rectangle is 2, so the height of the rectangle must be ½.
The probability that X is between 0.68 and 1.44 is therefore:
P = ½ (1.44 − 0.68)
P = 0.38
Using the uniform distribution, it is found that there is a 0.38 = 38% probability that X is between 0.68 and 1.44.
-----------------------
Uniform probability distribution:
Has two bounds, a and b. The probability of finding a value between c and d is:[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
In this problem:
The bounds are 0 and 2, thus [tex]a = 0, b = 2[/tex].The probability that X is between 0.68 and 1.44 is:
[tex]P(0.68 \leq X \leq 1.44) = \frac{1.44 - 0.68}{2 - 0} = 0.38[/tex]
0.38 = 38% probability that X is between 0.68 and 1.44.
A similar problem is given at https://brainly.com/question/13547683
will give brainly and thanks
Answer:
x = 39
Step-by-step explanation:
The two angles will be equal when the lines are parallel
4x-24 = 3x+15
Subtract 3x from each side
4x-24-3x = 3x+15-3x
x-24 = 15
Add 24 to each side
x-24+24 = 15+24
x = 39
Answer:
x=39
Step-by-step explanation:
Since these are alternate interior angles they should be set equal to each other so
4x-24=3x+15
Now simplify to get...
x=39
Which of the following rational functions is graphed below?
Answer:
Option (D)
Step-by-step explanation:
The given graph represents a rational function having,
1). Vertical asymptote → x = 2
2). Horizontal asymptote → y = 0
Parent function representing the rational function will be in the form of,
F(x) = [tex]\frac{1}{x^{2} }[/tex]
Since, vertical asymptote of the function is x = 2, denominator of the function will be in the form of (x - 2)².
Since, horizontal asymptote of the function is y = 0, highest exponent term in the numerator will be 0.
Therefore, numerator of the fraction will be x⁰.
The rational function given in the graph will be,
F(x) = [tex]\frac{x^{0}}{(x-2)^2}[/tex]
F(x) = [tex]\frac{1}{(x-2)^2}[/tex]
Option (D) will be the answer.
A man is standing 20 feet away from the base of a tree and looking at the top of a tree wondering it’s height. If the man’s eyes are located 6 feet off the ground and the angle of elevation is 67°, how tall is the tree? Round to the nearest tenth of a foot.
Answer: 53.1ft
Step-by-step explanation:
We can draw a triangle rectangle.
Where the distance between the man and the tree is one cathetus, (the vertex is on the man's eyes)
The tree itself is the other cathetus, and the line that connects the man's eyes and the tip of the tree is the hypotenuse.
We know that:
The angle at the vertex of the man's eyes is 67°
And the adjacent cathetus, the distance between the man and the tree, is 20ft.
Then using the relation:
Tan(A) = (opposite cathetus)/(adjacent cathetus)
We can find the height of the treee:
Tan(67°) = X/20ft
Tan(67°)*20ft = X = 47.1ft
But remember that this is measured from the mans eye's, and the man's eyes are 6ft away from the ground.
Then the height of the tree is 47.1ft + 6ft = 53.1ft
The graph for the equation y=-2x+1 is shown below.
ch
-3
-2 -2
х
-2
-3
If another equation is graphed so that the system has no solution, which equation could that be?
O y=-2(x-3)
Hark this and return
Save and Exit
Next
Submit
Answer:
Step-by-step explanation:
Given the equation y=-2x+1 and given another equation y=mx+b in order for us to have no solution we must guarantee that both lines do not intersect. Recall that m is the slope of the second equation and b the y-intercept. To guarantee that both lines don't intersect, they must be parallel. To have this result, we must have that they have the same slope but different y intercept. That is take m = -2 and b any value different to +1. For example, the b = 6. So
y = -2x+6 = -2(x-3) is another equation that gives no solution to the system.
Answer:
B. y = -1/2 (4x + 2)
Step-by-step explanation:
hope this is the answer that you are looking for :)
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?
Answer:
A sample size of 2080 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Based on previous evidence, you believe the population proportion is approximately 60%.
This means that [tex]\pi = 0.6[/tex]
How large of a sample size is required?
We need a sample of n.
n is found when [tex]M = 0.025[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]
[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]
[tex]n = 2079.3[/tex]
Rounding up
A sample size of 2080 is needed.
What is the correct option? How to do this one
Answer:
Option C is the answer.
Step-by-step explanation:
here, given that;
angle XYZ=82°
we know, according to the inscribed angle theorem,
angle XYZ=1/2 of arc XZ.
or, arc XZ = 2×82°
Therefore, the value of arc XYZ is 164°.
hope it helps..
Find the GCF of 207c^3 and 108c^2
Answer: 9c²
Step-by-step explanation:
To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.
207c³ 108c²
∧ ∧ ∧ ∧
9·23 c·c·c 9·12 c·c
∧ ∧ ∧
3·3 3·3 3·4
∧
2·2
207c³: 3·3·23 c·c·c
108c²: 2·2·3·3·3·4 c·c
GCF = 3·3 c·c
= 9c²
The GCF of 207c^3 and 108c² is 9c²
Given the expressions [tex]207c^3 \ and \ 108c^2[/tex]
We are to find the GCF of both terms
First, we need to get the factors as shown::
207c³ = 9 * 23 * c² * c
108c² = 9 * 12 * c²
From the factors, we can see that 9 and c² are common to both terms:
The GCF of 207c^3 and 108c² is 9c²
Learn more here: https://brainly.com/question/21612147
#if a sum become rs 6480 in 3 years and rs 7776 in 4 years interest being compounded annually, find the sum and rate of interest.
solve it
it's urgent
Answer:
The rate of interest is 20% and the sum is $3,750
Step-by-step explanation:
In order to calculate the sum and rate of interest we would have to make the following calculation:
rate of interest= (sum in 4 years-sum in 3 years)*100/sum in 3 years*1
According to the given data we have the following:
sum in 4 years=$7,776
sum in 3 years=$6,480
Therefore, sum in 4 years-sum in 3 years=$7,776-$6,480=$1,296
Therefore, rate of interest=$1,296*100/$6,480*1
rate of interest=20%
To calculate the sum we would have to make the following calculation:
FV=PV(1+20%)∧3
$6,480=PV(1,20)∧3
PV=$3,750
Sum is $3,750
What is the radius of a circle that has a circumference of 3.14 meters?
Answer:
Hey there!
Circumference of a circle=0.5[tex]\pi[/tex]r
3.14=0.5[tex]\pi[/tex]r
1=0.5r
r=2
Hope this helps :)
Answer:
1/2 meter
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c= pi* 2r
We know that the circumference of the circle is 3.14 meters. Therefore, we can substitute 3.14 in for c.
3.14= pi* 2r
We want to find out what r, or the radius is. To do this, we must get r by itself.
First, divide both sides of the equation by pi, or 3.14. We divide because 2r is being multiplied by pi, and division is the inverse of multiplication.
3.14= pi* 2r
3.14/3.14=3.14* 2r/3.14
3.14/3.14=2r
1=2r
Next, divide both sides by 2. We divide because 2 and r are being multiplied, and the inverse of division is multiplication.
1/2=2r/2
1/2=r
0.5=r
The radius of the circle is 1/2 or 0.5 meters.
What is 4sqrt7^3 in exponential form?
Answer:
[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]
Step-by-step explanation:
[tex]4 (\sqrt{7} )^3[/tex]
Square root can be written as a power.
[tex]4(7^{\frac{1}{2} })^3[/tex]
Multiply the exponents.
[tex]4(7^{\frac{3}{2} })[/tex]
Answer:
A (7^3/4)
Step-by-step explanation:
ed 2020
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
Answer:
B'(0,-2)
Step-by-step explanation:
the coordinates of B (-5,0)
the translation is(x+5,y-2)
B' : (-5+5,0-2)
B'(0,-2)
What value of x is I the solution set of 3(x-4)>5x+2
Answer:
-7 > x
Step-by-step explanation:
3(x-4)>5x+2
Distribute
3x-12>5x+2
Subtract 3x from each side
3x-12-3x>5x-3x+2
-12 > 2x+2
Subtract 2 from each side
-12-2>2x+2-2
-14 > 2x
Divide by 2
-14/2 > 2x/2
-7 > x
Answer:
[tex]\boxed{x<-7}[/tex]
Step-by-step explanation:
3(x-4)>5x+2
Expand brackets.
3x - 12 > 5x+2
Subtract 3x and 2 on both sides.
-12 - 2 > 5x - 3x
-14 > 2x
Divide both sides by 2.
-7 > x
Switch sides.
x < -7
A student's course grade is based on one midterm that counts as 10% of his final grade, one class project that counts as 5% of his final grade, a set of homework assignments that counts as 45% of his final grade, and a final exam that counts as 40% of his final grade. His midterm score is 60, his project score is 80, his homework score is 75, and his final exam score is 78. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answer:
His overall final score is a 73, which means that that student recieved a letter grade of a C.
Step-by-step explanation:
First, we are finding the mean of the scores to average everything out.
So, start by adding up all the scores given: 60+80+75+78=293.
Then, divide that sum by the number of scores given: 293/5=73.25, or rounded to a whole number is a 73.
In most schools, a 73 is a C, so this students letter grade for this course is a C.
Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30
Answer:
x = 30
Step-by-step explanation:
1/2(x+6) = 18
Expand brackets or use distributive law.
1/2(x) + 1/2(6) = 18
1/2x + 6/2 = 18
1/2x + 3 = 18
Subtract 3 on both sides.
1/2x + 3 - 3 = 18 - 3
1/2x = 15
Multiply both sides by 2.
(2)1/2x = (2)15
x = 30
Answer:
30
Step-by-step explanation: