There are 12 people having lunch.Each person wants 1/3 of a sub sandwich.How many whole sub sandwiches are needed ?use models to show answer.
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Hey can you please help me posted picture of question
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The length of the major axis of the ellipse below is 14, and the length of the red line segment is 3. how long is the blue line segment?
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The length of the blue line segment is 11 units.
What is relation between sum of the distance of a point from the focus of ellipse and the length of major axis?For any point P on an ellipse, the sum of the distances from P to the two foci is equal to the length of the major axis of the ellipse. This is known as the "distance property" of an ellipse.
To see why this is true, consider an ellipse with foci F₁ and F₂ and major axis length 2a. Let P be any point on the ellipse, and let D₁ and D₂ be the distances from P to F₁ and F₂, respectively. Then, by definition of an ellipse, we know that:
D₁+ D₂ = 2a
Given that,
Two line segments
Red segments of length = 3 unit
So from the definition we know that,
The sum of segments = the length of major axis
The length of major axis = 2a
2a = D₁+ D₂
14= 3 + D₂
D₂ = 11
Therefore, the length of the blue line segment is 11 units.
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What is the volume of a rectangular prism with the dimensions: L = 1 in, W = 3/4 in, and H = 1/2in. V = LWH.
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V = LWH
V = (1 in.)(3/4 in.)(1/2 in.) = 3/8 in.^3 = 0.375 in.^3
if the leg of a right triangle are 3 ft and the 4ft the length of the hypotenuse is
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The Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.
Plug in the leg lengths and solve.
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
5 = c
Answer:
The length of the hypotenuse is 5 ft.
How can I derive the first equation to get the second equation?
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[tex]\bf s^2=R^2+r^2-2Rrcos(\theta )\implies 2s^1=0+0-2Rr\left[ \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{ds}} \right] \\\\\\ 2s=2Rrsin(\theta )\cfrac{d\theta }{ds}\implies 2s=\cfrac{2Rrsin(\theta )d\theta }{ds}\implies \cfrac{2s\cdot ds}{2Rr}=sin(\theta )d\theta \\\\\\ \cfrac{s\cdot ds}{Rr}=sin(\theta )d\theta[/tex]
To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.
Explanation:To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps:
Start with the equilibrium equation for the problem.Substitute the expression for T₂ in terms of T₁ into the equation.This will eliminate one unknown and result in a new equation with only one unknown left.9(T - 1) = 6(T + 2) - T
T = ?
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9T-9=6T+12-T
9T-9=5T+12
4T-9=12
4T=21
T=5.25
but the equation is wrong
i think that answer is T=5.25
what has to be added to the sum of 2/3 & 3/2 to get 3? give answer as whole number or fraction <question 10 in the image>
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(2/3+3/2)+x=3
Solving for x:
(2*2+3*3)/6+x=3
(4+9)/6+x=3
13/6+x=3
13/6+x-13/6=3-13/6
x=(6*3-13)/6
x=(18-13)/6
x=5/6
Answer: 5/6 has to be added to the sum of 2/3 and 3/2 to get 3
a + 5=5a +5
[tex]a + 5 = 5a + 5 = [/tex]
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a = 5a
Now subtract both sides by a:
4a = 0
a = 0
20 points! plz help me
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- 3 - 3
2a + a = 177
3a = 177
---- ---- = 59
3 3
59 is a.
Distributive Property: 2(5c-7)=1
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a(b + c) = ab + ac
Steps:
so, 2(5c - 7) = 1
1.) 2(5c) - 2(7) = 1
10c - 14 = 1
2.) Add 14 to both sides:
10c - 14 + 14 = 1 + 14
3.) Simplify:
10c = 15
4.) Then, divide both sides by 10:
10c/10 = 15/10
5.) Simplify:
c = 3/2
is the answer.
Hope this helped you solve this question!!!
~Shane
Good Luck! Hope this helps! <3
Q #6 in the figure A B || C D Find the measure ГGEB
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Answer: Second option 50°
the answer is b hoped i helped
Suppose the entering freshmen at a certain college have a mean combined application test score of 1225, with a standard deviation of 120. in the first semester, these students attained a mean gpa of 2.64, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a first-semester gpa of 2.9?suppose the entering freshmen at a certain college have a mean combined application test score of 1225, with a standard deviation of 120. in the first semester, these students attained a mean gpa of 2.64, with a standard deviation of 0.58. a scatterplot showed the association to be reasonable linear, and the correlation between application test score and gpa was 0.44. what combined test score would you predict for a freshmen who attained a first-semester gpa of 2.9?
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Using the correlation coefficient, mean test scores, and mean GPA, we can predict that a freshman with a GPA of 2.9 would have an approximate combined test score of 1260.71.
Since we know the mean combined application test score is 1225, the standard deviation is 120, the mean GPA is 2.64, and the standard deviation for GPA is 0.58, we can use this information to predict scores.
First, we will use the correlation coefficient (r), which in this case is 0.44, to calculate the slope (b) of the best-fit line. The slope (b) is calculated by dividing the product of the standard deviations by the mean test score, and then multiplying by the correlation coefficient.
b = r * (Sy / Sx)
b = 0.44 * (0.58 / 120)
b = 0.44 * 0.0048333
b ≈ 0.0021
Next, we need to find the intercept (a) of the best-fit line, which can be calculated using the means of the two variables (mean test score and mean GPA).
a = mean of GPA - b * mean of test scores
a = 2.64 - 0.0021 * 1225
a ≈ 0.10
With the slope (b) and the intercept (a), we can now predict the combined test score for a student with a GPA of 2.9.
Predicted Test Score = a + b * GPA
Predicted Test Score = 0.10 + 0.0021 * 2.9
Predicted Test Score ≈ 1260.71
Thus, for a freshman with a first-semester GPA of 2.9, the predicted combined test score would be approximately 1260.71.
I need yo help B, on dis question
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We have then:
[tex]5 / sine (68) = 5 / sine (x) [/tex]
From here, we clear the value of x.
We have then:
[tex]sine (x) = (5/5) * (sine (68)) [/tex]
Rewriting we have:
[tex]sine (x) = (1) * (sine (68)) sine (x) = sine (68) x = arcsine (sine (68)) x = 68[/tex]
Answer:
The angle R is given by:
x = 68 degrees
option B
Answer:
b
Step-by-step explanation:
perimeter and circumference 9-1
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The number of cartoons watched on saturday mornings by students in mrs. kelly's first grade class is shown below. number of cartoons watched x 0 1 2 3 4 5 probability p(x) 0.15 0.20 0.30 0.10 0.20 0.05 what is the mean of the data?
a.1.37
b.2.15
c.1.89
d.1.18
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[tex]\mu =\sum \left(x\cdot p\left(x\right)\right)[/tex]
[tex]\mu =0\left(0.15\right)+1\left(0.20\right)+2\left(0.30\right)+3\left(0.10\right)+4\left(0.20\right)+5\left(0.05\right)[/tex]
[tex]\mu =2.15[/tex]
The mean is 2.15.
At one store, Julia saved $10 with a coupon for 40% off her total purchase. At another store, the $29 she spent on books is 58% of her total bill. How much did Julia spend in all at the two stores?
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0.40*(original price of "a") = $10
(original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
a = $25.00 -10.00 = $15.00
At the other store,
$29 = 0.58b
$29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate
Then Julia's total spending is
a + b = $15.00 +50.00 = $65.00
Julia spent $65 in all at the two stores.
PLZ HELP ASAP TANGENTS OF CIRCLES WORD PROBLEMS
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70 + 90 + 90 + O = 360
O = 110 degrees.
Sally bought a car for 35000 in 2017. If the car loses 5.5% semiannually, what will the value of the value of the car be at the end of 2025
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A=P(1+r/100)^n
where:
A=future value
P=principle
r=rate
n=number of terms
hence for the data given;
p=35000
R=5.5
n=(2025-2017)*2=16
Thus
A=35000(1+5.5/100)^16
A=$82, 434. 20
Find the length of each hypotenuse such that KMN = LMN
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1) KM must be congruent with LM→KM=LM→
x+2y=3x-y→x+2y-x-2y=3x-y-x-2y→0=2x-3y→2x-3y=0 (1)
2) KN must be congruent with LN→KN=LN→
5x+3y=8x-7→5x+3y-5x-3y+7=8x-7-5x-3y+7→7=3x-3y→3x-3y=7 (1)
We have a system of two equations and two unkowns:
(1) 2x-3y=0
(2) 3x-3y=7
Subtracting equation (1) from equation (2)
(3x-3y)-(2x-3y)=7-0
3x-3y-2x+3y=7
x=7
Replacing x=7 in equation (1)
(1) 2x-3y=0→2(7)-3y=0→14-3y=0→
14-3y+3y=0+3y→14=3y→14/3=3y/3→14/3=y→y=14/3
The length of the hypotenuse is:
KN=5x+3y=5(7)+3(14/3)=35+14→KN=49
or
LN=8x-7=8(7)-7=56-7→LN=49
Answer: Option C. 49
Hey can you please help me posted picture of question
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The option B gives only such a probability which can represent a simple event. The rest of the options belong to the compound events as they are sum or product of probabilities.
So, the correct answer is option B
The access code for a car's security system consists of four digits. the first digit cannot be zero or one and the last digit must be even. how many different codes are available?
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Select three ratios that are equivalent to 11:1
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B. 22 : 2. 22 : 2 is equivalent to 11 : 1.
C. 55 : 5. 55 : 5 is equivalent to 11 : 1.
E. 110 : 10. 110 : 10 is equivalent to 11 : 1.
In order to determine the ratios that are equivalent to the given ratio, we would evaluate by dividing each of them by their respective common multiple (numerator or denominator):
For 22 : 2, we would divide all through by 11;
22 : 2 = 11 : 1
For 55 : 5, we would divide all through by 5;
55 : 5 = 11 : 1
For 110 : 10, we would divide all through by 10;
110 : 10 = 11 : 1
Complete Question:
Select three ratios that are equivalent to 11 : 1.
Choose 3 answers:
1 :11
22 : 2
55 : 5
9 : 99
110 : 10
find the circumference of a circle with an area of 254.47 square inches
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A circle with an area of 254.47 square inches is given.
We have to determine the circumference of the circle.
Since, Area of circle = [tex] \Pi r^{2} [/tex] where r is the radius of the circle.
[tex] \Pi r^{2}=254.47 [/tex]
[tex] \frac{22}{7} \times r^{2}=254.47 [/tex]
[tex] r^{2}=\frac{254.47 \times 7}{22} [/tex]
[tex] r^{2}=80.97 [/tex]
[tex] r=\sqrt{80.97} [/tex]
r = 8.99
Therefore, r = 9 inches (approximately)
Circumference of a circle = [tex] 2\Pi r [/tex]
= [tex] 2 \times \frac{22}{7} \times 9 [/tex]
= 56.57 inches
= 56.6 inches (approximately).
Therefore, the circumference of the circle is 56.6 inches.
Pete has the option of borrowing $380 for one week at an APR of 600% or borrowing the $380 for one week with a fee of $45. Which is the "better" deal?
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Since Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.
There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.
[tex] \frac{600}{365} = 1.643[/tex]
The daily interest rate of the loan will be 1.643%.
The following equation is used to find the total interest payment:
[tex]A = P(1+ \frac{r}{365})^{t} - P[/tex]
A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.
Plug in your values into the equation.
[tex]P = 380, r = 1.643, t = 7[/tex]
[tex]380(1+ \frac{1.643}{365})^{7} - 380 = 12.136[/tex]
Rounded to the nearest hundredths value, the total interest paid will be $12.14.
Compare the total amounts paid for both loans.
$12.14 < $45
The better deal is the loan with the 600% APR.
The better deal is the loan with the 600% APR.
What is interest rate?An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum).
Given that, Pete is borrowing the money for one week, the APR must be divided into a daily interest rate before we can figure out how much he'll pay for the loan.
There are 365 days in a year. Divide the APR by 365 to find the daily interest rate.
600/365 = 1.643
The daily interest rate of the loan will be 1.643%.
The following equation is used to find the total interest payment:
[tex]A = P(1+\frac{r}{365} )^{t} -P[/tex]
A represents the total amount paid in interest. P represents the amount borrowed for the loan. r represents the daily interest rate. t represents the amount of days the loan will last.
Plug in your values into the equation.
P = 380 r = 1.643 and t = 7
380(1+1.643/365)^7 - 380 = 12.136
Rounded to the nearest hundredths value, the total interest paid will be $12.14.
Compare the total amounts paid for both loans.
$12.14 < $45
Hence, The better deal is the loan with the 600% APR.
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Suppose that a test is standardized (normally distributed) with a mean of 75 and a standard deviation of 11. what is the probability that an individual will have a test score greater than 80
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A suitable calculator can help you figure this.
how much interest is earned on 2,700 in one year if it is invested at 3%?
a. $8.10
b.$81.00
c.$810.00
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Suppose a1=2,an+1=12(an+2an). assuming an has a limit, find limn→∞an= . hint: let a=limn→∞. then, since an+1=12(an+2an), we have a=12(a+2a). now solve for
a.
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[tex]a_{n+1}=\dfrac{a_n+\frac2{a_n}}2[/tex]
Assume that [tex]\displaystyle\lim_{n\to\infty}a_n=L[/tex]. Then taking the limit of both sides, we have
[tex]L=\dfrac{L+\frac2L}2\implies L=\pm\sqrt2[/tex]
But in order for the sequence to converge, only one of these values must be true. Since [tex]a(1)=2>0[/tex], each successive number will also be positive, so the limit must be [tex]L=\sqrt2[/tex].
The limit of the sequence defined by an+1=1/2*(an+2an), as n approaches infinity, is 0. This is determined by setting a = limn→∞an and solving for 'a' in the equation a=1/2*(a+2a).
Explanation:This question is about calculating the limit of a sequence, where the sequence, denoted as {an}, is defined recursively with a given formula, an+1=1/2*(an+2an).
To calculate the limit as n approaches infinity (limn→∞an), we first suppose a is this limit. This means as n grows very large, the values of an and an+1 converge to 'a'. Hence we can write the recursive formula of the sequence in terms of 'a': a=1/2*(a+2a).
By simplifying the equation, we get: a = 1/2 * (3a). This implies that 2a = 3a, and thus 'a' must be 0.
Therefore, the limit of the sequence as n tends to infinity is 0.
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hey can you please help me posted picture of question
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G(x) is obtained by subtracting 3 from F(x). This means G(x) is obtained by vertical translation of F(x). Since 3 is subtracted from F(x), the vertical translation is downwards.
So, we can say: G(x) is obtained by moving F(x) 3 units vertically down.
Therefore, the correct answer is option D
Name all numbers between 67 and 113 that are a multiple of 4, 9 and 12.
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I believe that there are 2 number that are in between the given numbers and are multiples of 4, 9, and 12. The numbers are...
72 and 108.
You can find these numbers by counting by the given one digit numbers
For example...
9, 18, 27, 36, 45, 54, 63, 72
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30..., 68, 70, 72
You can do the same for 108 as well
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72..., 104, 108
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30..., 100, 102, 104, 106, 108
I hope this helps!
In the equation 6x − 2 = −4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain
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Spencer: 6x - 2 = -4x + 2 /+4x6x - 2 + 4x = -4x + 2 + 4x10x - 2 = 2
Jeremiah:6x - 2 = -4x + 2 /-6x6x - 2 - 6x = -4x + 2 - 6x-2 = -10x + 2
They both are correct. But in Jeremiah's version of solving the equation, we would have to multiply equation by -1, which we don't have to do in the Spencer's version.
Source: Brainly.com
Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.