NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!
Answers
Answer:
y = 178.3 ftStep-by-step explanation:
Since the above figure is a right angled triangle we can use trigonometric ratios to find y
To find y we use tan
tan∅ = opposite/ adjacent
From the question
the opposite is y
the adjacent is 350 ft
Substitute the values into the above formula
That's
[tex] \tan(27) = \frac{y}{350} [/tex]
y = 350 tan 27
y = 178.3339
We have the final answer as
y = 178.3 ft to the nearest tenthHope this helps you
Related Questions
To the nearest tenth, what is the area of the figure shown in the image? Segment BF is a line of symmetry of the pentagon ABCDE. Use 3.14 for pi. A. 30.3 in.^2 B. 33.0 in.^2 C. 39.3 in.^2 D. 48.3 in.^2 Please include ALL work! <3
Answers
Answer:
C, 39.3 in²
Step-by-step explanation:
Lets first find the area of the rectangle part of the house.
To find the area of a rectangle its base × height.
So its 6×4=24 in².
Now lets find the area of the top triangle.
Area for a triangle is (base × height)/2.
The height is 3 inches, because its 7-4. While the base is 6 inches.
(6×3)/2=9 in².
To find the area of the half circle the formula, (piR²)/2.
The radius of the circle is 2 because its half of the diamter which is 4.
(pi2²)/2=6.283 in².
Now we just need to add up the area of every part,
24+9+6.283=39.283in²
If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is
Answers
Answer:
The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.
Step-by-step explanation:
A coefficient of correlation of 0.8 means that dependent variable changes in 0.8 when independent variable changes in a unit. Hence, the percentage of such variation ([tex]\%R[/tex]) is:
[tex]\%R = \frac{\Delta y}{\Delta x}\times 100\,\%[/tex]
Where:
[tex]\Delta x[/tex] - Change in independent variable, dimensionless.
[tex]\Delta y[/tex] - Change in dependent variable, dimensionless.
If [tex]\Delta x = 1.0[/tex] and [tex]\Delta y = 0.8[/tex], then:
[tex]\%R = 80\,\%[/tex]
The percentage of variation in the dependent variable explained by the variation in the independent variable is 80 %.
I will mark u brainleiest if u help me and 5 stars
Answers
Answer:
[tex]\boxed{50}[/tex]
Step-by-step explanation:
Because the initial temperature is 40 degrees and it increases by 10, add the two values together to get the final temperature.
40 + 10 = 50
Therefore, the final answer is 50 degrees.
Answer:
50
Step-by-step explanation:
If it starts at 40 degrees and increases 10 degrees, it is going to be 50 degrees. Increases means adding, so it is asking you to add 10 to 40 which is 50. If it asks decreases in the future you will have to subtract.
the area of triangle ABC is 31 1/4 square centimeters. What is the measure of b?
Answers
Answer:
102 cm
Step-by-step explanation:
Is -5/6 Real, Rational, Irrational, Integer, Whole, or real number?
Answers
Answer:
Rational
Step-by-step explanation:
Rational number consists of
Whole NumbersNatural NumbersIntegersNegative NumbersFractionsDecimals-5/6 is a Fraction and we can also simply it to a Decimal.
Hope this helps ;) ❤❤❤
Find the measure of the remote exterior angle. mZx = (4n – 18)º
m2y = (n+9)°
m2z = (151 – 5n)º
y
Х
Z
Answers
Answer:
71°
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle
m<x + m<y = m<z
4n - 18 + n + 9 = 151 - 5n
5n - 9 = 151 - 5n add like terms
10n = 160
n = 16
Since m<z = 151 - 5n we replace n with 16 and 151 - 5×16 = 71
Answer:
A. 71
Step-by-step explanation:
x + y = z
4n - 18 + n + 9 = 151 - 5n
5n - 9 = 151 - 5n
10n = 160
n = 16
Z = 151 - 5(16) = 71
The dance team is selling headbands to raise
money for dance team jackets. They need
to sell 1,260 headbands. The headbands must
be divided equally among the three coaches.
Each coach is in charge of 10 dancers. If all
the headbands must be sold, how many
headbands will each dancer on the team
need to sell?
Answers
Answer:
42 headbands per dancer
Step-by-step explanation:
Selling 1260 headband
Divide by the three coaches
1260/3
420 per coach
Divide by each dancer under a coach
420/10 = 42
Each dancer must sell 42 headbands
what is the magnitude of the vector?
Answers
Answer:
[tex]\boxed{\sqrt{65}}[/tex]
Step-by-step explanation:
Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]
Therefore, just plug in your x and y-values and solve.
[tex]\sqrt{4^{2}+7{^{2}}[/tex]
[tex]\sqrt{16 + 49}[/tex]
[tex]\sqrt{65}[/tex]
Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.
Will mark Brainliest! Which point is a vertex of the hyperbola?
A. (1,−15)
B. (1,−2)
C. (1,3)
D. (1,11)
Answers
Answer:
So (1,3) is a vertex (out of two) of the hyperbola.
Step-by-step explanation:
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
So (1,3) is a vertex (out of two) of the hyperbola.
So (1,3) is a vertex (out of two) of the hyperbola.
What is hyperbola?a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
According to the question
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
Hence , (1,3) is a vertex (out of two) of the hyperbola.
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find the greatest common factor of 108d^2 and 216d
Answers
Answer:
Below
Step-by-step explanation:
If d is a positive number then the greatest common factor is 108d.
To get it isolate d and d^2 from the numbers.
108 divides 216. (216 = 2×108)
Then the greatest common factor of 216 and 108 is 108.
For d^2 and d we will follow the same strategy
d divides d^2 (d^2 = d*d)
Then the greatest common factor of them is d.
So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer
Answer:
[tex]\boxed{108d}[/tex]
Step-by-step explanation:
Part 1: Find GCF of variables
The equation gives d ² and d as variables. The GCF rules for variables are:
The variables must have the same base.If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.The GCF for the variables is d.
Part 2: Find GCF of bases (Method #1)
The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.
Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!
Prime Factorization of 108
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.
Prime Factorization of 216
216 ⇒ 108 & 2
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.
After completing the prime factorization trees, check for the common factors in between the two values.
The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.
Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].
Part 3: Find GCF of bases (Method #2)
This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.
[tex]\frac{216}{108}=2[/tex]
Therefore, the coefficient of the GCF will be 108.
Then, follow the process described for variables to determine that the GCF of the variables is d.
Therefore, the GCF is [tex]\boxed{108d}[/tex].
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 5.1 inches, and standard deviation of 1.1 inches. If 49 items are chosen at random, what is the probability that their mean length is greater than 4.8 inches? How do you answer this with the answer rounded 4 decimal places?
Answers
Answer:
0.9719
Step-by-step explanation:
Find the mean and standard deviation of the sampling distribution.
μ = 5.1
σ = 1.1 / √49 = 0.157
Find the z score.
z = (x − μ) / σ
z = (4.8 − 5.1) / 0.157
z = -1.909
Use a calculator to find the probability.
P(Z > -1.909)
= 1 − P(Z < -1.909)
= 1 − 0.0281
= 0.9719
The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
What is Standard deviation?In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.
What is Mean?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
Given,
Mean = 5.1 inches
Standard deviation = 1.1 inches
Sample size = 49
New mean = 4.8
Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])
Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]
Z score = -1.909
Then the probability
P(Z>-1.909)
=1-P(Z>-1.909)
=1-0.0281
=0.9719
Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719
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In the figure below.. Please help!!!
Answers
====================================================
Explanation:
Both AB and XY are the first two letters of ABC and XYZ respectively. So we have one fraction of AB/XY = 2/7.
AC and XZ are the first and last letters of ABC and XYZ respectively. We can form another fraction AC/XZ. I'm dividing in the same order of small over large to keep things consistent. As you can probably guess, the order of the letters ABC and XYZ are important so we see how the angles match up and how the proportional sides match up.
Because the triangles are similar, the two fractions formed earlier are equal to one another.
The equation we need to solve is AB/XY = AC/XZ
-----
AB/XY = AC/XZ
2/7 = 3/N ... plug in given values
2N = 7*3 .... cross multiply
2N = 21
N = 21/2 .... divide both sides by 2
N = 10.5
ZX is 10.5 units long.
Is 1.45 times 10 to the -7 power a scientific notation
Answers
Answer:
Yes.
It is 1.45 x 10^-7 or 0.000000145
Hope it helps!
Answer:
It is 1.45 x 10^-7 or 0.000000145
Step-by-step explanation:
PLEASE ANSWER ASAP!!!!
Divide. Equation and answer choices in picture
any unrelated answer will be reported
Answers
Answer:
B =
[tex]4x - 1 - \frac{4}{2x - 3} [/tex]
Step-by-step explanation:
In this type of questions the answers are required in the
[tex]quotient \: + \frac{remainder}{divisor} [/tex]
form.
First of all, the equations in question must be arranged properly
[tex](8 {x}^{2} - 14x - 1) \div 2x - 3[/tex]
Then you divide.
[tex]2x - 3 \sqrt{8 {x}^{2} - 14x - 1 } [/tex]
Answer
[tex]4x - 1 - \frac{4}{2x - 3} [/tex]
there was a total of 400 oranges and mangoes at a fruit stall.3/8 of these fruits were mangoes.each orange was priced at 40 cents,and each mango was priced at 60 cents.how much would mr.mead make if he sold 2/3 of the mangoes and 4/5 of the oranges?
Answers
Answer:
First find the number of Mango and oranges. 400 divided by 8 = 50. We use 8 because it is the whole part of the percentage. Since, there is 3/8 mangoes, multiply 50* 3= 150 mangoes and 50*5= 250 oranges.
2/3 of 150=100 mangoes. You would find this by dividing 150/3=50 then multiply by 2.
4/5 of 250= 200 oranges. You would find this by dividing 250/5=50 then multiply by 4.
$.40*100= $40.00 mangoes
$.60*200= $120.00 oranges
Mr. Mead would make $160.00
Step-by-step explanation:
How do you solve an expansion?
Answers
[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]
Answer:
[tex]\large \boxed{560x^3}[/tex]
Step-by-step explanation:
[tex](x+2)^7[/tex]
Expand brackets.
[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]
[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]
[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]
[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]
The fifth term is 560x³.
Which equation is represented by the graph shown in the image? A. y + 2= x B. y + 1= x C. y - 1= x D. y - 2= x Please show ALL work! <3
Answers
Answer:
A. y + 2= x
Step-by-step explanation:
Which equation is represented by the graph shown in the image?
A. y + 2= x
B. y + 1= x
C. y - 1= x
D. y - 2= x
Please show ALL work! <3
The graph shown has a slope of +1 and a y intercept of -2.
All given answer choices have a slope of +1, so that's not the problem.
We need one that has a y-intercept of -2, or the equation should be
y = x-2, or equivalently y+2 = x
which corresponds to answer choice A.
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
Answers
Complete Question
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. , The mean, , is nothing. (Round to the nearest tenth as needed.)
p = 0.6 n = 18
Answer:
The mean [tex]\mu = 10.5[/tex]
The standard deviation [tex]\sigma = 2.08[/tex]
The variance [tex]var = 4.32[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is [tex]p = 0.6[/tex]
The sample size is [tex]n = 18[/tex]
Generally given that the distribution is binomial, then the probability of failure is mathematically represented as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.6[/tex]
[tex]q =0.4[/tex]
Generally the mean is mathematically evaluated as
[tex]\mu = np[/tex]
substituting values
[tex]\mu = 18 * 0.6[/tex]
[tex]\mu = 10.5[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{npq}[/tex]
substituting values
[tex]\sigma = \sqrt{18 * 0.6 * 0.4}[/tex]
[tex]\sigma = 2.08[/tex]
The variance is evaluated as
[tex]var = \sigma^2[/tex]
substituting value
[tex]var = 2.08^2[/tex]
[tex]var = 4.32[/tex]
If 5x + 2 =12x- 5, then x = ?
Answers
Answer:
x = 1
Step-by-step explanation:
First, move all the variables to one side by subtracting 5x on both sides:
5x + 2 = 12x - 5
2 = 7x - 5
Add 5 to both sides:
7 = 7x
1 = x
Answer:
x=1
Step-by-step explanation:
5x + 2 =12x- 5
Subtract 5x from each side
5x-5x + 2 =12x-5x- 5
2 = 7x-5
Add 5 to each side
2+5 = 7x-5+5
7 = 7x
Divide each side by 7
7/7 = 7x/7
1 =x
for each of the following express the first quantity as a percentage of the second quantity 1 year ' 4 month
Answers
Answer:
300%
Step-by-step explanation:
1 year = 12 months
percent = part/whole * 100%
percent = 12/4 * 100% = 300%
Answer:
please can u follow me I've started following you
You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (Enter your answer as a fraction.) (b) What is the probability of getting a sum of 10? (Enter your answer as a fraction.) (c) What is the probability of getting a sum of 6 or 10? (Enter your answer as a fraction.) Are these outcomes mutually exclusive? Yes No
Answers
Answer:
5/36 ; 1/12 ; 2/9 ; yes
Step-by-step explanation:
Given the following :
Roll of two fair dice : green and red
Probability = (number of required outcomes / number of total possible outcomes)
(a) What is the probability of getting a sum of 6?
Number of required outcomes = 5
P(sum of 6) = 5/36
b.) What is the probability of getting a sum of 10?
Number of required outcomes = 3
P(sum of 10) = 3 / 36 = 1/12
c.) What is the probability of getting a sum of 6 or 10?
P(getting a sum of 6) + P(getting a sum of 10)
(5/36) + (1/12) = (5 + 3) / 36
= 8/36 = 2/9
The events are mutually exclusive because each event cannot occur at the same time.
An ‘in shuffle’ is a perfect shuffle on a standard deck of 52 playing cards that splits the deck in half, then interleaves cards starting with the top half.
Required:
a. What is the position of the first card after the 7th shuffle?
b. How many times must one perform the shuffle so that the top card becomes the bottom card?
c. When do the first and last cards in the deck touch?
Answers
Answer:
a) position 22
b) 26
c) shuffle 25
Step-by-step explanation:
Assuming the shuffling occurs so that the bottom card of the top half of the deck (card 26) becomes the bottom card (card 52), while the top card of the bottom half (card 27) becomes the top card (card 1), the sequence of card 1 positions with successive shuffles is ...
{2, 4, 8, 16, 32, 11, 22, 44, 35, 17, 34, 15, 30, 7, 14, 28, 3, 6, 12, 24, 48, 43, 33, 13, 26, 52, 51, 49, 45, 37, 21, 42, 31, 9, 18, 36, 19, 38, 23, 46, 39, 25, 50, 47, 41, 29, 5, 10, 20, 40, 27, 1}
That is, after the first shuffle, card 1 is at position 2; after the second shuffle, it is at position 4; and so on.
(a) Hence the position of card 1 after the 7th shuffle is 22.
__
(b) The top card is in position 52 after 26 shuffles.
__
(c) The top card is in position 26 after 25 shuffles; the bottom card is in position 27 after 25 shuffles. That is when they first touch. (They touch again after 51 shuffles.)
Find the midpoint of the segment connecting (−1.8, 1.9) and (1.2, 2.7).
Answers
Answer:
(-0.3, 2.3)
Step-by-step explanation:
(-1.8+1.2)/2 = -0.3
(1.9+2.7)/2 = 2.3
Answer:
( - 0.3 , 2.3 )Step-by-step explanation:
Let the points be A and B
A ( - 1.8 , 1.9 ) ⇒( x₁ , y₁ )
B ( 1.2 , 2.7 )⇒ ( x₂ , y₂ )
Now, let's find the midpoint:
[tex] \mathsf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2} )}[/tex]
Plug the values
[tex] \mathsf{ = (\frac{ - 1.8 + 1.2}{2} \: , \frac{1.9 + 2.7}{2} )}[/tex]
Calculate
[tex] \mathsf{ = ( \frac{ - 0.6}{2} \: , \frac{4.6}{2} )}[/tex]
[tex] \mathsf{ = (- 0.3 \:, 2.3)}[/tex]
Hope I helped!
Best regards!
The sequence below represents Marisa’s fine at the library for each day that she has an overdue book: $0.50, $0.65, $0.80, $0.95, $1.10, ... Which equation represents Marisa’s library fine as a function of a book that is n days overdue? f(n) = 0.15n f(n) = 0.50n f(n) = 0.15n + 0.35 f(n) = 0.50n + 0.15
Answers
Answer:
f(n) = 0.15n + 0.35Step-by-step explanation:
The sequence of the problem above is an arithmetic sequence
For an nth term in an arithmetic sequence
F(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
To find the equation first find the common difference
0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15
The first term is 0.5
Substitute the values into the above formula
That's
f(n) = 0.5 + (n - 1)0.15
f(n) = 0.5 + 0.15n - 0.15
The final answer is
f(n) = 0.15n + 0.35Hope this helps you
Answer:
The correct option is: f(n) = 0.15n + 0.35Step-by-step explanation:
Took the math test on edge
PLEASE HELP WILL GIVE BRAINLIEST AND THX Which ratios have a unit rate of 3? Choose all that apply. 15/2 cups: 2 1/2 cups 1 cup: 1/4 cups 2/3 cups: 1 cup 3 3/4 cups: 2 cups 2 cups: 2/3 cups 2 1/2 cups: 5/6 cups
Answers
Answer:
15/2 cups: 2 1/2 cups
2 cups: 2/3 cups
2 1/2 cups: 5/6 cups
Step-by-step explanation:
Take and divide each by the smaller number
15/2 cups: 2 1/2 cups
First put in improper fraction form
15/2 : 5/2
Divide each by 5/2
15/2 ÷ 5/2 : 5/2 ÷5/2
15/2 * 2/5 : 1
3 :1 yes
1 cup: 1/4 cups
Divide each by 1/4 ( which is the same as multiplying by 4)
1*4 : 1/4 *1
4 : 1 no
2/3 cups: 1 cup
Divide each by 2/3 ( which is the same as multiplying by 3/2)
2/3 * 3/2 : 1 * 3/2
1 : 3/2 no
3 3/4 cups: 2 cups
Change to improper fraction
( 4*3+3)/4 : 2
15/4 : 2
Divide each side by 2
15/8 : 2/2
15/8 : 1 no
2 cups: 2/3 cups
Divide each side by 2/3 ( which is the same as multiplying by 3/2)
2 * 3/2 : 2/3 *3/2
3 : 1 yes
2 1/2 cups: 5/6 cups
Change to an improper fraction
( 2*2+1)/2 : 5/6
5/2 : 5/6
Divide each side by 5/6( which is the same as multiplying by 6/5)
5/2 * 6/5 : 5/6 * 6/5
3 : 1 yes
The 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3
What is the ratio?It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.
For checking: 15/2 cups: 2 1/2 cups
= (15/2)/(5/2) [2(1/2) = 5/2]
= 3
For checking: 1 cup: 1/4 cups
= 1/(1/4)
= 4
For checking: 2/3 cups: 1 cup
=(2/3)/1
= 2/3
For checking: 3 3/4 cups: 2 cups
= (15/4)(2)
= 15/8
For checking: 2 cups: 2/3 cups
= (2)/(2/3)
= 3
For checking: 2 1/2 cups: 5/6 cups
= (5/2)/(5/6)
= 3
Thus, the 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3
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What is the sign of -1.69+(-1.69)
Answers
Answer: Negative sign
Adding two negative values results in another negative value.
-1.69 + (-1.69) = -3.38
It's like starting $1.69 in debt and then adding 1.69 dollars of more debt. You'll slide further into debt being $3.38 in debt total.
The sign is negative as the value of -1.69 + (-1.69) is -3.38.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-1.69 + (-1.69)
= -1.69 - 1.69
= -3.38
This means,
The sign is negative.
Thus,
The value of -1.69 + (-1.69) is -3.38.
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If x and y are two positive real numbers such that x 2 +4y 2 =17 and xy =2, then find the value of x- 2y. a. 3 b. 4 c. 8 d. 9
Answers
Answer: The value of x- 2y is a. [tex]\pm 3[/tex].
Step-by-step explanation:
Given: x and y are two positive real numbers such that [tex]x^2+4y^2=17[/tex] and [tex]xy= 2[/tex] .
Consider [tex](x-2y)^2=x^2-2(x)(2y)+(2y)^2\ \ \ [(a+b)^2=(a^2-2ab+b^2)][/tex]
[tex]=x^2-4xy+4y^2[/tex]
[tex]=x^2+4y^2-4(xy)[/tex]
Put [tex]x^2+4y^2=17[/tex] and [tex]xy= 2[/tex] , we get
[tex](x-2y)^2=17-4(2)=17-8=9[/tex]
[tex]\Rightarrow\ (x-2y)^2=9[/tex]
Taking square root on both sides , we get'
[tex]x-2y= \pm3[/tex]
Hence, the value of x- 2y is a. [tex]\pm 3[/tex].
Two math classes took the same quiz. The scores of 10 randomly selected students from each class are listed below. • Sample of Class A: 75, 80, 60, 90, 85, 80, 70, 90, 70, 65 • Sample of Class B: 95, 90, 85, 90, 100, 75, 90, 85, 90, 85 Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in Class A compared to all the students in Class B? Explain your reasoning to justify your answer.
Answers
Answer:
Step-by-step explanation:
First you have to find the medians which is when you put the numbers in number order and find the one in the middle.
Class A: 60,65,70,70,75,80,80,85,90,90
=77.5
Class B: 75,85,85,85,90,90,90,90,95,100
=90
That the class B is more advanced, and they probably studied.
A baseball player has a batting average (probability of getting on base per time at bat) of 0.215. Based on this: What is the probability that they will get on base more than 6 of the next 15 at bats
Answers
Answer:
[tex]\mathbf{P(x>6) = 0.0265}[/tex]
Step-by-step explanation:
Given that:
A baseball player has a batting average (probability of getting on base per time at bat) of 0.215
i.e
let x to be the random variable,
consider [tex]x_1 = \left \{ {{1} \atop {0}} \right.[/tex] to be if the baseball player has a batting average or otherwise.
Then
p(x₁ = 1) = 0.125
What is the probability that they will get on base more than 6 of the next 15 at bats
So
[tex]\mathtt{x_i \sim Binomial (n,p)}[/tex]
where; n = 15 and p = 0.125
P(x>6) = P(x ≥ 7)
[tex]P(x>6) = \sum \limits ^{15}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]
[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]
[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=0} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]
[tex]P(x>6) = 1 -0.9735[/tex]
[tex]\mathbf{P(x>6) = 0.0265}[/tex]
A company will need to replace 35% of their computers this year. If they replaced 140 computers this year, how many computers do they have in total?
Answers
Hi
35/100= 140/ X
X = 100*140 /35
X= 14000/35
X= 400
There are 400 computer in the compagny.
