In linear equation ,The mean number that the test positive for the HIV virus is 2.1 .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let x be the number of blood samples test positive for the HIV virus in a sample of 70 blood test.
Here X ~ Binom( n = 70, p = 0.03)
Using binomial distribution property , the mean of X is
μ = ηp
= 70 * 0.03 = 2.1
The mean number that the test positive for the HIV virus is 2.1 .
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Solve the equation 3(n + 3) = -4n+ 30.
Answer:
n= 3
Step-by-step explanation:
3(n+3)= -4n+30
3n+9= -4n +30 expand
7n+9 = 30 +4n to both sides
7n = 21 -9 from both sides
n= 3 divide by 7 on both sides
Find the missing number so that the equation has no solutions.
-4x - 15 = X-7
Answer:4 and 3
Step-by-step explanation:
Can someone help me solve this please? Karen Gaines invested $14,000 in a money market account with an interest rate of 1.75% compounded semiannually. Six years later, Karen withdrew the full amount to put toward the down payment on a new house. How much did Karen withdraw from the account?
Answer:
Given that,
Karen Gaines invested $14,000 in a money market account with an interest rate of 1.75% compounded semiannually.
Six years later, Karen withdrew the full amount to put toward the down payment on a new house.
To find the amount withdraw.
we know that, formula for finding amount of compound interest as,
[tex]A=P(1+\frac{r}{100})^n[/tex]where P is the principal, nis the number of years, r is the rate of interest per annum.
Given that, interest rate of 1.75% compounded semiannually, therefore number of years is 6x2=12 years.
Substitute the values we get,
[tex]A=14000\times(1+\frac{1.75}{100})^{12}[/tex][tex]=14000(1.0175)^{12^{}}[/tex][tex]=14000(1.2314)[/tex][tex]=17240.15[/tex]Karen withdraws $17,240.15 from the account.
The Quadrilateral ABCD has the vertices A (-5,4), B (0,6), C (1,3), and D (-4,1) how do I determine whether it classifys as a parallogram. Help me please
The given vertices when plotted gives a parallelogram.
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
To solve this problem, we simply need to plot the vertices and check if the opposite sides are equal to each other.
Kindly find the attached image of the parallelogram below.
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Complete the point-slope equation of the line through (-4,8)(−4,8)left parenthesis, minus, 4, comma, 8, right parenthesis and (4,4)(4,4)left parenthesis, 4, comma, 4, right parenthesis.
The point slope equation of the line that passes through the points (-4,8) and (4,4) is x + 2y = 12 .
The point slope form of the line passing through the points (x₁,y₁) having slope as m is given by the formula .
y-y₁ = m(x-x₁)
In the question ,
it is given that
the required line passes through the points (-4,8) and (4,4) ,
So , the slope(m) is = (4-8)/(4-(-4)
= -4/8
= -1/2
the equation of the line passing through (4,4) and slope as -1/2 in the point slope form is
(y-4) = -1/2(x-4)
y - 4 = (-x + 4)/2
2y-8 = -x + 4
x + 2y = 12
Therefore , The point slope equation of the line that passes through the points (-4,8) and (4,4) is x + 2y = 12 .
The given question is incomplete , the complete question is
Write the point slope equation of the line that passes through the points (-4,8) and (4,4) .
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Answer:
y - 4 = -1/2 (x-4)
Step-by-step explanation:
thats the answer on khan
the monthly income of residents of daisy city is normally distributed with a mean of $3398 and a standard deviation of $571. the highest tax bracket applies to 3.67% of residents. what is the income a person must make to be in the highest income bracket?
The income a person must make to be in the highest income bracket $4420.09 using standard deviation
What is standard deviation?
The standard deviation is a statistician's way of gauging how much a group of numbers can vary or be dispersed. The values tend to be close to the set's mean when the standard deviation is low, while the values are dispersed over a larger range when the standard deviation is high.
As per the question,
mean = u = $3398
standard deviation = σ = $571
Using standard normal
P(Z > z) = 3.67%
1 - P(Z < z) = 0.0367
P(Z < z) = 1 - 0.0367
P(Z < 1.79) = 0.9633
z = 1.79
Using z-score formula,
x = z * σ + u
x = 1.79 * 571 + 3398
= 4420.09
Hence the total income is $4420.09 using standard deviation.
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a biologist studying florida bass observed a quadratic relationship between the lengths and weights of fish in a large sample. the biologist took the base 101010 logarithm for the values of both variables, and they noticed a linear relationship in the transformed data. here's the least-squares regression equation for the transformed data, where weight is in kilograms and length is in centimeters. \widehat{\log(\text{weight})}
Answer:
We're given a least-squares regression equation that we can use to predict weight (in kilograms) from a given length (in centimeters). The question asks to predict the weight of a fish that is 70cm long, so let's plug in 70 for "length" and solve for the predicted weight: logweight = 3.08 (log length) -5.07
(logweight) 3.08 (log 70) - 5.07
(logweight) ≈ 3.08 (1.84) - 5.07
log weight ≈ 0.613
Next, we use the fact that these are base 10 logarithms and the definition of a logarithm to solve for the predicted weight:
log₁₀ (weight) ≈ 0.613
Taking logarithms on both sides
weight ≈ 10₀.₆₁₃
weight ≈ 4.1
According to this model, the predicted weight for a 70 cm long Florida bass is about 4.1kg.
Which equation best represents the relationship between x and y in the
graph?
The equation y + 2x = 3 best represents the relationship between x and y in the graph.
We are provided with the graph shown in question. We were supposed to find the equation of the line shown in the graph. From this graph we can clearly see that the line is passing through ( 1.5 , 0 ) and ( 0 , 3 ).
The equation of line passing through two points is given below:
[tex](y - y_{1}) = (\frac{y_{2}-y_{1} }{x_{2}-x_{1} }) (x - x_{1} )[/tex]
As the line is passing through points ( 1.5 , 0 ) and ( 0 , 3 ) , so we can write the above equation as
( y - 0 ) = ( ( 3 - 0 )/( 0 - 1.5 ) ) ( x - 1.5 )
y = -2 ( x - 1.5 )
y = -2x + 3
y + 2x = 3
The required equation of line is y + 2x = 3 i.e., this equation best represents the relationship between x and y in the graph.
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Imagine that 1 in 5 individuals is allergic to peanuts. A peanut allergy test gives a positive result 10% of the time. If someone has a peanut allergy, the test will give a positive result 40% of the time. What is the probability that you have a peanut allergy if the test result is positive?.
The probability that you have a peanut allergy given a positive test result is 50%.
To find the probability that you have a peanut allergy given a positive test result, we can use Bayes' theorem.
Let's define the following events:
A: You have a peanut allergy.
B: The test result is positive.
We are given the following probabilities:
P(A) = 1/5 = 0.2 (1 in 5 individuals is allergic to peanuts).
P(B|A) = 0.4 (if you have a peanut allergy, the test will give a positive result 40% of the time).
P(B|not A) = 0.1 (if you don't have a peanut allergy, the test will give a positive result 10% of the time).
We want to find P(A|B), which is the probability that you have a peanut allergy given a positive test result.
Bayes' theorem states:
P(A|B) = (P(B|A) × P(A)) / P(B)
Now, let's calculate P(B):
P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)
P(not A) is the probability of not having a peanut allergy, which is equal to 1 - P(A):
P(not A) = 1 - P(A) = 1 - 0.2 = 0.8
Now, we can calculate P(B):
P(B) = (0.4 × 0.2) + (0.1 × 0.8) = 0.08 + 0.08
= 0.16
Now, let's calculate P(A|B) using Bayes' theorem:
P(A|B) = (P(B|A) × P(A)) / P(B)
P(A|B) = (0.4 × 0.2) / 0.16
P(A|B) = 0.08 / 0.16
P(A|B) = 0.5
Therefore, the probability that you have a peanut allergy given a positive test result is 50%.
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A side of the triangle below has been
extended to form an exterior angle of 64°.
Find the value of x.
16⁰
Answer:
X =
64°
xº
The measure of the interior angle x is 48°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.
We know that sum of all the interior angles of a triangle is 180°.
The measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Given, An exterior angle that measures 64° and two opposite interior angle measuring 16° and x°.
∴ x° + 16° = 64°.
x = (64 - 16)°.
x = 48°.
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A person walked 2.5 miles in 45 minutes, then jogged 1.5 more miles in 20 minutes. What was
the person's average speed in miles per minute?
The person's average speed is 15.65 miles per minute.
What is average?The definition of the average is the mean value, which is the ratio of the sum of the values in a given set to the total number of values in the set. The mean is typically meant when the word "average" is used in a mathematical context, especially when no other context is provided. Divide the total by the quantity of numbers after averaging the numbers. (The value(s) total divided by the value(s) total).
Given Data
A person walked 2.5 miles in 45 minutes, then jogged 1.5 more miles in 20 minutes.
Speed = [tex]\frac{Distance}{Time}[/tex]
Speed while walking = 18
Speed while jogging = 13.3
Average = [tex]\frac{18 +13.3}{2}[/tex]
Average = [tex]\frac{31.3}{2}[/tex]
Average = 15.65
The person's average speed is 15.65 miles per minute.
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please help, please omg
Answer:
Step-by-step explanation:
I believe the equation would be 3(f-5)=60.
The answer to that equation would be:
3(f-5)-60
3f-5=60 Open parentheses
3f=60+5 Take 5 to the other side
3f=65 Add 60 and 5
f=65/3 Divide the sum of 60 and 5 with 3
f=21.6 Answer
the base-ten representation for 19!19! is 121121, 6t56t5,100100,40m40m, 832832, h00h00, where tt, mm, and hh denote digits that are not given. what is t m ht m h?
the base-ten representation for 19! = 121,6T5,100,40M,832,000 then
H+M+T =12
19! has three 5s so it will end with three 0s.
Hence H = 0
19! = 121,6T5,100,40M,832,000 = 121,6T5,100,40M,832 * 1000
19! has many 2s. So M832 will be divisible by 16 (last 4 digits).
So M000 + 832 is divisible by 16. 832 is completely divisible by 16. Since 16*5 = 80, 8000 must be divisible by 16.
M = 8
19! = 121,6T5,100,408,832,000
Since 19! is divisible by 9, sum of all digits must be divisible by 9.
1+2+1+6+T+5+1+4+8+8+3+2 = T + 41
To make this divisible by 9, T must be 4.
H+M+T = 0 + 8 + 4 = 12
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Please help! Attachment is above
I can’t figure out 6 and 10
The solution of m for question 6 and the value of z for question 10 does not exist.
According to the question,
We have the following information,
6) 1/3 + 2m/3 = 2m/3-2/3
Now, moving the terms with the same variables in one side:
2m/3-2m/3+1/3 = -2/3
Now, when 2m/3 is subtracted from 2m/3 then we have no variable left.
So, the solution of this equation does not exist.
10) 2.5(2z+5) = 5(z+2.5)
Now, multiplying the numbers outside the bracket into bracket:
5z+12.5 = 5z+12.5
Moving the terms with the same variables on one side:
5z-5z+12.5 = 12.5
Now, when 5z is subtracted from5z then we have no variable left.
So, the solution of this equation does not exist.
Hence, the solutions of the equation 6 and equation 10 does not exist.
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WHAT IS THIS ANSWER I NEED HELP PLSSS :(
Answer:
6.9
Step-by-step explanation:
6 4/5 in decimal form is 6.8.
6.9 is higher than 6.8 but lower than 7.
C = -5
-2c -2c
————-
2c
Evaluate the expression
.............................................
Note the graph of an athletes performance after finishing a triathlon the X axis measures time in hours and the Y axis measures distance in kilometers first she swam, then biked, and then She finished the race with a run the data states she ran four times as fast as she swam and she biked twice as fast as she ran based on the graph choose the statement below that is false
From the graph, the athlete spent 2 hours biking (from hour 1 to hour 3)
And, the athlete spent 3 hours running (from hour 3 to hour 6)
Then, the athlete spent equal amounts of time biking and running is false
Triangle ABC has side lengths of AB = 16 and BC = 30 and hypotenuse AC = 34. Find the sin, cos, and tan for A.
In the given right-angled triangle, the sine, cosine, and tan of the angle A are: sin A =0.88, cos A = 0.4705, tan A= 1.875
We have a right angles triangle ABC with AC as the hypotenuse and AB and AC as the other two sides.
Given, hypotenuse AC=34, side BC = 30, side AB = 16
∴From the formulae for evaluating sin, cos, and tan of an angle
sin A[tex]=\frac{opposite}{hypotenuse}= \frac{BC}{AC}=\frac{30}{34}=\frac{15}{17}=0.88[/tex] (1)
cos A[tex]= \frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{8}{17}=0.4705[/tex] (2)
tan A[tex]=\frac{OppositeSide}{AdjacentSide}=\frac{30}{16}=\frac{15}{8}=1.875[/tex] (3)
Thus sin A= 0.88, cos A= 0.4705, tan A= 1.875
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19. Choose all expressions that are equal
to 15.02.
12.96 + 2.06
0.56 +14.64
2.62 +12.4
1.22 +1.8+12
1+0.5 +13.8
Sum expressions are true and some are false.
What does a math expression mean?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical functions. An expression's format is as follows: Expression: (Math Operator, Number/Variable, Math Operator)a) Calculate the sum or difference = 15. 02
Check equivalency = True
Answer: True
b)Calculate the sum or difference = 15.02
Check equivalency = False
Answer: False
c)
Calculate the sum or difference = 15.02
Check equivalency =True
Answer: True
d)
Calculate the sum or difference = 3.02+12
Calculate the sum or difference = 15.02
Check equivalency: True
Answer: True
e)
Calculate the sum or difference = 1.5 + 13.8
Calculate the sum or difference = 15.3
Check equivalency: False
Answer: False
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Write a rule of reflection
???????
Answer:
(x, y) to (-y,-x)
Step-by-step explanation:
You have to find the reflection which is the opposite so the opposite of x is -x the opposite of y is -y!
The graph shows a linear relationship between x and y. What is the rate of change of y with respect to x for this function?
A) 2
B) -2
C) -1/2
D) 1/2
Answer:
A
Step-by-step explanation:
the slope of the line is a measure of the rate of change.
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (2, 5) ← 2 points on the line
m = [tex]\frac{5-(-3)}{2-(-2)}[/tex] = [tex]\frac{5+3}{2+2}[/tex] = [tex]\frac{8}{4}[/tex] = 2
the rate of change of y with respect to x is 2
Answer:
A) 2
Step-by-step explanation:
Rise over run,
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1}}[/tex]
-2 will be [tex]x_{1}[/tex] and -3 will be [tex]y_{1}[/tex]
2 will be [tex]x_{2}[/tex] and 5 will be [tex]y_{2}[/tex]
It doesn't matter which order you place the points, for [tex]x_{1}[/tex], or [tex]x_{2}[/tex] but [tex]x_{1}[/tex] and and [tex]y_{1}[/tex] must be one point while [tex]x_{2}[/tex] and [tex]y_{2}[/tex] must be one point.
Then, we replace the values to find:
[tex]\frac{5-(-3)}{2-(-2)}[/tex]
We then simplify this expression to [tex]\frac{8}{4} = 2[/tex]
Therefore, our slope for this function is 2
The pentagons ABCDE and JKL MN are similar.
Find the length x of JK.
C
3
B
N
D
4
E
3
A
7
2.1
1.4
K
M
X
2.8
N
2.1
J
Answer:
3.5
Step-by-step explanation:
find the ratio between any two corresponding sides. for example : 1.4/2 = 0.7
this should be the same number for all sides
thus 5 * 0.7 = 3.5
Answer:
23456892245u
Step-by-step explanation:
Allah sh all will am am well ram chirac flow
PLEASE HELP WITH WORK SHEET PUT NUMBERS BY THE ANSWER PLEASE AND THANK YOU
Answer:
Step-by-step explanation:
The points (6, −2) and (h, −3) fall on a line with a slope of 1. What is the valu
h =
============================================================
Explanation:
m = 1 is the given slope
(x1,y1) = (6,-2) and (x2,y2) = (h,-3) are the two points on a line of slope 1.
Let's use the slope formula to find h
[tex](x_1,y_1) = (6,-2) \text{ and } (x_2,y_2) = (h,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\1 = \frac{-3 - (-2)}{h - 6}\\\\1 = \frac{-3 + 2}{h - 6}\\\\1 = \frac{-1}{h-6}\\\\1(h-6) = -1\\\\h-6 = -1\\\\h = -1+6\\\\h = 5[/tex]
------------------
The point (h,-3) updates to (5,-3).
The slope of the line through (6,-2) and (5,-3) is 1.
Use the slope formula to confirm this.
[tex](x_1,y_1) = (6,-2) \text{ and } (x_2,y_2) = (5,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - (-2)}{5 - 6}\\\\m = \frac{-3 + 2}{5 - 6}\\\\m = \frac{-1}{-1}\\\\m = 1\\\\[/tex]
The answer is confirmed.
Multiply. Write your answer as a fraction in simplest form. −2(−1 1/4)=
The simplest form is [tex]\frac{11}{2}[/tex] .
What is a fraction?fraction, In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given that,
−2(−1 1/4)
Multiplying the numerator with numerator and denominator with denominator. According to integer multiplication of two negative terms is always positive.
= [tex]\frac{22}{4}[/tex]
The simplest form = [tex]\frac{11}{2}[/tex]
Hence, The simplest form is [tex]\frac{11}{2}[/tex] .
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I'm not sure how to answer this.
Which expression is equivalent to 6(x – 4)Zoe, Latoya, Christina, and Rhoda each used a different method to verify that Negative 2 (3 x minus 12) = negative 6 x + 24
Answer:
Rhoda
Step-by-step explanation:
sub same values of x into both expressions. The expressions are equivalent if the values of the expressions are equal
-10=5/7(-7)+b
Solve for B
Answer: b = -5
Step-by-step explanation:
-10 = 5/7 (-7) +b
-10 = -5 + b
-5 = b
Bananas are priced at $0.39 per pound. If Harvey buys 7 pounds of bananas, whatwill he expect to pay?
Answer:
He is expected to pay $2.73
Explanation:
We can solve this, by adding 0.39 7 times:
[tex]2\text{ }pounds\text{ }of\text{ }bananas:0.39+0.39=0.78[/tex][tex]3\text{ }pounds\text{ }of\text{ }bananas:0.78+0.39=1.17[/tex][tex]4\text{ }pounds\text{ }of\text{ }bananas:1.17+0.39=1.56[/tex][tex]5\text{ }pounds\text{ }of\text{ }bananas:1.56+0.39=1.95[/tex][tex]6\text{ }pounds\text{ }of\text{ }bananas:1.95+0.39=2.34[/tex][tex]7\text{ }pounds\text{ }of\text{ }bananas:2.34+0.39=2.73[/tex]Thus, 7 pound of bananas cost $2.73