Probability of the person has the diseases and the test result is positive = 1/90 = 0.011
What is probability?Probability refers to the possibility of occurring a certain event. It is expressed by the ratio of the number of favorable outcome to the total possible outcome.
How can we calculate probability?Given, percentage of people who have disease and test result positive =90
percentage of people who has not disease but test result positive =3.1
Suppose 6.0 percent of population are infected
Now, probability of a randomly selected person who has diseases and test positive
= 1/90
= 0.011
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What is the degree of 5x³+3x²-4x+1?
03
04
05
06
Answer:
03
Step-by-step explanation:
it is 03. in a polynomial the hightest power of varibale shows the degree of it.
Solve for the value of x
A. 20
B. 10
C. 45
D. 3
Answer:
10
Step-by-step explanation:
[tex]x + 5 = 15 \\ x + 5 - 5 = 15 - 5 \\ x = 10 [/tex]
Salma made $378 for 18 hours of work.
At the same rate, how many hours would she have to work to make $147?
hours
Answer:
7 hours
every hour she makes $21
Step-by-step explanation:
378÷18=21
147÷21=7
7 hours
378÷18=21$/h in ONE hour Salma makes 21$ so you have to do 147÷21=7h
Marcus invested $5000 in a bank at an interest rate of 2.5% compounded annually. (a) Find the total amount he had at the end of second year. At the end of second year, Marcus withdrew all the money in the bank and invested it into another bank which offered simple interest rate of 8% per annum. (b) Find the minimum number of years he had to leave the money in the bank in order for it to be more than $10 000.
1. The total amount (future value) Marcus had at the end of the second year of investing $5,000 at 2.5% compounded annually was $5,253.13.
2. The minimum number of years Marcus must leave the $5,253.13 to be more than $10,000 is 11.3 years.
What is the future value?The future value is the compounded present value at an interest rate.
The future value can be derived from an online finance calculator as follows:
With the future value so determined, we can then compute the minimum time in years required for it to reach more than $10,000 at the simple interest rate.
Initial investment = $5,000
Interest rate = 2.5% compounded annually
Investment period = 2 years
Future Value at Compound Interest:N (# of periods) = 2
I/Y (Interest per year) = 2.5%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
FV = $5,253.13
Total Interest = $253.13
Simple Interest Investment:Principal = $5,253.13
Interest rate = 8% per annum
Future amount = $10,000
Time to reach the future amount = (Future Value/Principal - 1) ÷ Interest rate
= ($10,000/$5,253.13 - 1) ÷ 0.08
= 11.3 years
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The speed of sound, S, in meters per second, is a linear function of the temperature of the air through which
the sound travels. Air temperature, T, is measured in degrees Celsius and S=0.6T+331.4. Which of the
following is the best interpretation of the number 331.4 in the context?
a) The speed of sound in meters
per second at 0.6 degrees Celsius
c) The speed of sound in meters
per second at 0 degrees Celsius
b) The increase in speed of sound at 331.4 degrees
per degree of temperature
d) none of the above
Answer:
C
Step-by-step explanation:
S = .6T + 331.4
When S = 331.4:
331.4 = .6T + 331.4 <=====you should be able to see this is true when T= 0
Solve each equation by completing the square
z-5=z^2-25
after completing the equation, the equation is __ and the solution is ____
WHOEVER ANSWERS CORRECTLY AND FIRST WILL BE MARKED AS BRAINLIEST
The equation becomes z + 5 = 1 and the value of the z in the given equation by completing the square is z = -4.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
z - 5 = z² - 25
z - 5 = z² - 5²
By property that A² - B² = (A + B)(A - B)
z - 5 = (z - 5)(z + 5)
z + 5 = 1
z = - 1 / 5 = - 4
Hence "By completing the square, the equation is changed to z + 5 = 1, and the value of z in the given equation is changed to z = -4".
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Answer:
The equation after completing the square is (z - 1/2)² = (9/2)²;The solution is z = {-4; 5}-----------------------------------------------------------
Given equation:
z - 5 = z² - 25Solve it as follows:
z - 5 = z² - 25 Givenz² - 25 - z + 5 = 0 Bring all terms to one sidez² - z - 20 = 0 Simplifyz² - 2*z*1/2 + (1/2)² = 20 + (1/2)² Complete the square on left(z - 1/2)² = 20 1/4 (z - 1/2)² = 81/4 Square on the right(z - 1/2)² = (9/2)² Square root both sidesz - 1/2 = 9/2 and z - 1/2 = - 9/2z = 1/2 + 9/2 and z = 1/2 - 9/2z = 10/2 and z = - 8/2z = 5 and z = - 4 AnswerQuestion 7
GEOMETRY The perimeter of a square is four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the
square is 4 centimeters. Write an equation in point-slope form to find the perimeter y of a square with side length x.
Answer:
y= 4x + 0
Step-by-step explanation:
The perimeter y of a square with side length x can be described by the equation y = 4x + 0.
The perimeter of a square is equal to four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. We can use this information to write an equation in point-slope form to describe the relationship between the side length of a square and its perimeter.
Point-slope form is a way of writing the equation of a line when we know the slope of the line and the coordinates of a point on the line. In this case, the slope of the line is 4, since the perimeter of a square is four times the length of one side. The coordinates of a point on the line are (1, 4), since the side length of a square is 1 centimeter and the perimeter of the square is 4 centimeters.
We can use this information to write the equation of the line in point-slope form. The equation of a line in point-slope form is given by the following equation:
y - y1 = m(x - x1)
where y is the y-coordinate of a point on the line, y1 is the y-coordinate of a known point on the line, m is the slope of the line, and x is the x-coordinate of a point on the line.
In this case, we can substitute the values we know into the equation above to get:
y - 4 = 4(x - 1)
This simplifies to:
y = 4x + 0
Therefore, the equation in point-slope form that describes the relationship between the side length x of a square and its perimeter y is y = 4x + 0.
This equation tells us that for any square, the perimeter is four times the side length plus zero. For example, if the side length of a square is 5 centimeters, then the perimeter is 4 x 5 + 0 = 20 centimeters. If the side length of a square is 10 centimeters, then the perimeter is 4 x 10 + 0 = 40 centimeters.
In summary, the perimeter y of a square with side length x can be described by the equation y = 4x + 0.
please helppp
my brain is not working
Answer:
Below
Step-by-step explanation:
27 = 3^3 and 9 = 3^2
3^3 * (3^2)^3x
3^3 * 3^6x
3^(3+6x) so k = 3+6x
When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. How tall wa the buh after the two week
When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is [tex]\\26 \frac{2}{5}[/tex].
What is improper fractions?
An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.
12 times 120% + 12
12*120%+12
[tex]$$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$[/tex]
Follow the PEMDAS order of operations
Multiply and divide (left to right) [tex]$12 \times \frac{6}{5}: \frac{72}{5}$[/tex]
[tex]=\frac{72}{5}+12$$[/tex]
Add and subtract (left to right) [tex]$\frac{72}{5}+12: \frac{132}{5}$[/tex]
[tex]=\frac{132}{5}$$[/tex]
Convert improper fractions to mixed numbers: [tex]$\frac{132}{5}=26 \frac{2}{5}$[/tex]
[tex]=26 \frac{2}{5}$$[/tex]
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when jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters. the collection of nickels and quarters totaled $2.60. how many quarters did jim find?
When jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters , the collection of nickels and quarters totaled $2.60 then he find eight quarters.
Given that:
Let N be the number of nickels.
Q be the number of quarters.
The value of one nickels N is 0.05N
The value of quarters Q = 0.25Q
Sum of total quarters is $ 2.60
Total number of coins
N + Q = 20 , N = 20 - Q
0.05 N + 0.25 Q = 2.60
substitute n = 20 - Q , we get
0.05 (20 - Q) + 0.25 Q = 2.60
1 - 0.05 Q + 0.25 Q = 2.60
1 + 0.2Q = 2.60
0.2 Q = 1.6
Q = 1.6 / 0.2
Q = 8
Therefore , Jim finds 8 quarters
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what equation passes (-4,-1) and is parallel to y=2x+14?
Answer:
y = 2x + 7.
Step-by-step explanation:
An equation that passes through the point (-4,-1) and is parallel to the line y = 2x + 14 is of the form y = 2x + b, where b is the y-intercept of the line. Since the line passes through the point (-4,-1), we can use this point to solve for b:
-1 = 2 * (-4) + b
-1 = -8 + b
b = 7
Therefore, an equation that passes through (-4,-1) and is parallel to y = 2x + 14 is y = 2x + 7.
Answer:
y = 2x + 7
Step-by-step explanation:
parallel = same slope
y-(-1) = 2(x-(-4)
y+1 = 2(x+4)
y+1 = 2x + 8
y = 2x + 8 - 1
y = 2x + 7
A ring-shaped region is shown below. Its inner radius is 15 yd. The width of the ring is 3 yd. Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Answer:
612.3 in.²
Step-by-step explanation:
Inner circle diameter = 34 in.
Inner circle radius = r = 17 in.
Outer circle diameter = 34 in. + 5 in. + 5 in. = 44 in.
Outer circle radius = R = 22 in.
The are of the ring is the area of the outer circle minus the area of the inner circle.
A = πR² - πr²
A = π(R² - r²)
A = 3.14[(22 in.)² - (17 in.)²]
A = 612.3 in.²
Suppose you walk at the rate of 210 ft/min. You need to walk 10,000 ft.
How many more minutes will it take you to finish if you have already walked 550 ft?
Answer:
Step-by-step explanation:
210x550=115500
115,500 divide 10,000=11.55?
Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and the other person starts going up in the elevator at a rate of 7 ft/sec. What rate is the distance between the two people changing 15 seconds later?.
The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.
Here, we note the following
Let the person walking away from the elevator be X
Let the other person going up in the elevator be Y
Therefore after 15 seconds, their positions will be;
For X, 2 ft/sec × 15 s = 30 ft away from the elevator
For Y, 7 ft/sec × 15 s = 105 ft up in the elevator
At that instant, the distance between them is given as
d² = x² + y²
d=√ 30² +105² = 11925 ft²
d = √11925 ft² = 109.202 ft
The rate of change of the distance between the two people, X and Y is given as
[tex]\frac{dd^2}{dt} =\frac{dx^2}{dt} +\frac{dy^2}{dt} \\Therefore,2d\frac{dd}{ydt} =2x\frac{dx}{dt} +2y\frac{dy}{dt} \\[/tex]
(or)
[tex]d\frac{dd}{dt} =x\frac{dx}{dt} +y\frac{dy}{dt} \\[/tex]
Since dx/dt is given as 2ft/sec and dy/dt is 7ft/sec
Then [tex]d\frac{dd}{dt} =30*2+105*7=975\\\frac{dd}{dt} =\frac{795}{105*202} =7.28ft/sec[/tex]
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What is the area of the rectangle shown on the coordinate plane?
Enter your answer in the box. Do not round at any step.
The area of the rectangle shown on the coordinate plane is 12 square units.
What is the area of the rectangle shown on the coordinate plane?
To calculate the area of a rectangle, multiply the length by the width of the rectangle.
To find the area of the rectangle shown on the coordinate plane, first, we need to calculate the distance between the points that conforms two of the sides of the rectangle (base and height).
We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:
1 - (-4, 1)
2 - (-1,-2)
3 - (-3,-4)
4 - (-6, -1)
Then, calculating the length of the sides,
Consider rectangle ABCD with vertices A(-4, 1), B(-1, -2), C(-3, -4) and D(-6, -1). The area of the rectangle is
A = length * Width
Find the length and the width:
AB = √(-1 - (-4))² + (-2 - 1)² = √9 + 9 = √18
BC = √(-3 - (-1))² + (-4 - (-2))² = √4 + 4 = √8
Then the area of the rectangle ABCD is
A = √18 * √8
A = 12 unit²
Hence, the area of the rectangle shown on the coordinate plane is 12 square units.
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the radius of a spherical ball is increasing at a rate of . at what rate is the surface area of the ball increasing when the radius is cm?
Although part of your question is missing, you might be referring to this full question: The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm? The surface area of a sphere with radius r is given by 4πr².
The rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.
Given A = 4πr²
So, we have:
dA/dt = d/dt (4πr²)
= 4π * d/dt * (r²)
= 4π * 2r * dr/dt
= 8πr * dr/dt
Now, we have that dr/dt = 2 cm/min. So, when the radius of the ball is 8 cm, we have that:
dA/dt = 8πr * dr/dt
= 8π * 8 * 2
= 128π
Since we are measuring area, our unit is cm²/min, not cm/min.
Thus, the rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.
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Which division problem can be described using this model?
Answer:
12/3=4
Step-by-step explanation:
You have 12 blocks in total, and 3 sections each. It is asking you how many blocks per section.
12 blocks in total/ 3 sections each = 4 blocks per section
Recall that two angle are complementary if the um of their meaure i 90 degree°. Find the meaure of two complementary angle if one angle i 20 degree° more than forty four time the other angle
The measure of one angle is 1.56° and another angle is 88.64°.
Complementary angles are two angles whose combined angle is 90 degrees.
Let's consider the smaller angle as A and the larger angle as B.
Given that the two angles are complementary, then their sum is A+B = 90°.
The angle B is 20° more than and 44 times angle A. Then B = 44A+20°. Substituting this equation in the A+B = 90° equation, we get,
A+44A+20° = 90°
45A = 90°-20°
A = 70°/45
A = 1.56°
Substitute A = 1.56°in B = 44A+20°, we get,
B = 44(1.56°)+20°
B = 88.64°
The answers are 1.56° and 88.64°. The sum of these two angles gives 90.2°. By rounding off, we will get 90°.
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What is 6 x 2 / 4 / 3?
/=divide
Answer:1
Step-by-step explanation: 6x2= 12. 12/4=3. 3/3 is 1.
Answer:
1
Step-by-step explanation:
We can see only multiply and divide here so we go from left to right
6x2/4/3
= 12/4/3
= 3/3
= 1
2
x² + 14x − 24 = 4x
The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
x² + 14x − 24 = 4x
Simplify the equation, then we have
x² + 14x − 24 = 4x
x² + 10x − 24 = 0
Factorize the equation, then we have
x² + 10x − 24 = 0
x² + 12x − 2x − 24 = 0
x(x − 12) − 2(x − 12) = 0
(x − 2)(x − 12) = 0
x = 2, 12
The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.
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Algebra 2 Questions that i need help with
The graph has a horizontal intercept at (1, 0)
The line x = 0 (the y-axis) is a vertical asymptote; as x→0+,y→∞
The graph is decreasing if 0 < b < 1.
The domain of the function is x > 0, or (0, ∞)
The range of the function is all real numbers, or (−∞,∞)
What is function?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The set of all positive real numbers serves as the function's domain. Assume that base 10 is written when no base is specified for the log. The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally. The graph would be moved upward if k>0.
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given that a = b/(1+b) , express b in terms of a.
[tex]a = \frac{b}{1 + b} [/tex]
Answer:
b = - [tex]\frac{a}{a-1}[/tex]
Step-by-step explanation:
a = [tex]\frac{b}{1+b}[/tex] ( multiply both sides by 1 + b to clear the fraction )
a(1 + b) = b ← distribute parenthesis on left side
a + ab = b ( subtract b from both sides )
a + ab - b = 0 ( subtract a from both sides )
ab - b = - a ← factor out b from each term on left side
b(a - 1) = - a ( divide both sides by a - 1 )
b = - [tex]\frac{a}{a-1}[/tex]
PLEASE HELP BRO I NEED IT !!!!
The value of x = 25
The measure of the angle ∠R = 101°
What is a Parallelogram?
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
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be TPRS
Now , the measure of ∠T = ( 4x + 1 )°
The measure of ∠S = ( 3x + 4 )°
Now , from the properties of a parallelogram ,
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
So ,
The value of ∠T = ∠R
And , value of ∠T + ∠S = 180°
Substituting the values in the equation , we get
∠T + ∠S = 180°
( 4x + 1 ) + ( 3x + 4 ) = 180
On simplifying the equation , we get
7x + 5 = 180
Subtracting 5 on both sides of the equation , we get
7x = 175
Divide by 7 on both sides , we get
x = 25
So , the value of x = 25
Now , the measure of ∠T = ( 4x + 1 )° = ∠R
So , the measure of ∠R = ( 4 x 25 + 1 )°
The measure of ∠R = 101°
Hence , The value of x = 25
The measure of the angle ∠R = 101°
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an equation for a tangent to the graph of y=arcsin(x/2) at the origin is
y=x/2 is equation for a tangent to the graph of y=arcsin(x/2) at the origin.
In order to fing the equation of tangent of any graph we need 2 things
i . A point on the graph
ii . Slope a line on that point
Given y=[tex]sin^-^1(\frac{x}{2} )[/tex]
put x=0
y = [tex]sin^-^1[/tex] (0)
=> y =0
so the graph passes through point (0,0)
now we have to find slope of the graph
slope = [tex]y^'[/tex] = [tex]\frac{d(y)}{dx}[/tex]
=> [tex]\frac{1}{\sqrt{4-x^2} }[/tex]
slope of line at point (0,0) is 1/2
so equation of line is y-0=1/2(x-0)
so the equation of tangent to the given graph is y=x/2
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Water is dripping from an inverted cone with a diameter of 12 cm 12cm and a height of 12 cm 12cm at a rate of 1 cm 3 / sec 1cm3/sec. At what rate is the water level decreasing when the radius of the water's surface is r
The rate is the water level decreasing when the radius of the water's surface is r = 2cm is 0.08 cm/sec or dh/dt = - 0.08 cm/sec.
We have given that,
Water is dripping from an inverted cone.
height , h = 12 cm
diameter , d = 12 cm
so, radius, r = 6 cm
rate , dV/dt = - 1 cm³/sec
At any point, the portion of the cone that is filled will have the ratio of radius/height = 6/12 = 1/2. Put another way, h = 2r.
we have to calculate the rate is the water level decreasing , dh/dt when radius of the water's surface is r = 2 cm .
Volume of cone , V = 1/3 π (r)²h = 1/3π (h/2)²h
plugging all known values,
V = 1/3 ( h³/4)π
differentiating with respect to h we get,
dV/dh = 1/3(3h²)π/4 , h = 12
= 1/12(3× 4r²)π ( from r = 2 cm)
= 4π cm²
but we have required, dh/dt = dV/dt × dh/dV
= - 1 cm³/sec × 1/4π cm²
= - 1/4π cm/sec
= - 0.0792 ~ 0.08 cm/sec
Hence, the required value is - 0.08 cm/sec.
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Complete question:
Water is dripping from an inverted cone with a diameter of 12 cm and a height of 12 cm at a rate of 1 cm3 /sec. At what rate is the water level decreasing when the radius of the water's surface is r = 2 cm?"
both must be true for a person to ride: (1) at least 5 years old, (2) taller than 36 inches. which expression evaluates to true if a person can ride?
Both conditions must be met in order to ride: being at least five years old and being at least 36 inches tall. expression evaluates to true if a person can ride - (Age >= 5) && (Height > 36)
In order for a person to ride, two conditions must be true: they must be at least 5 years old and taller than 36 inches. In order to evaluate whether a person can ride, we can use the expression (Age >= 5) && (Height > 36). This expression evaluates to true if both conditions are true; if either one is false, then the expression will evaluate to false. For example, if a person is 4 years old and 40 inches tall, then the expression will evaluate to false because the first condition is false. On the other hand, if a person is 5 years old and 40 inches tall, then the expression will evaluate to true because both conditions are true.
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Shade 2 circles. Shade 7/4 more
Answer:
The answer is 3 3/4
Step-by-step explanation:
2 7/4 = 15/4 = 3 3/4
I need help with this problem
Answer:
x = 6
Step-by-step explanation:
We have a 30°-60°-90° right triangle here, so the length of the hypotenuse (12) is twice the length of the shorter leg (6). So x = 6.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation with the correct solution. 20 POINTS!!!
Could someone help me with this it would be appreciated
Answer:
0.65
Step-by-step explanation:
The probability that we would get tails is 0.35
so the probability we will get heads is
1 – 0.35 = 0.65
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