The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the
test is positive.) Experimentation has shown that the probability of a positive test is 0.79, given that a person has
tuberculosis. The probability is 0.08 that the test registers positive, given that the person does not have tuberculosis.
Assume that in the general population, the probability that a person has tuberkulosis is 0.05. What is the probability that a
person chosen at random will fall in the following categories. (Enter your answers to four decimal places.)
(a) have tuberculosis and have a positive test
(b) not have tuberculosis
(c) not have tuberculosis and have a positive test

The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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Answer: KL = KN LM=NO=9 Side-Side-Side

Step-by-step explanation:

The required answers to the question is given below.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved. "≅" is the congruence symbol.

Use the following figure to understand the answer.

The Proof is

1. KM=KO=5 (GIven)

2. MN=3 (Given)

3. KN=KM+MN=8 (because the lengths are equal to the sum of their parts.)

4. KL=8 (Given)

5. KL=KN (from 3,4 substitution)

6. NO=ML=9 (Given)

7. ΔKLM=ΔKNO the congruence criterion used is SSS congruence.

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By substitution; x = 4 and y = -31

An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.

y=-6x-7 --- 1

7x+y=-3 --- 2

Substituting y as 6x - 7 in equation 2

7x + (-6x - 7) = -3

7x - 6x - 7 = -3

x - 7 = -3

x = -3 + 7

x = 4

Substitute x as 4 in equation 1

y = -6x - 7

y = -6(4) - 7

y = -24 - 7

y = -31

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Answer:

im pretty sure this is right  its a 6/30 chance he would pick blue

Step-by-step explanation:

The actual consumer spending at a price of $27 per unit is $268.26.

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

Answer:

What do we have to do in this? Find x? Let me know I'll explain it in the comment section

The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.

The ratio refers to the relative size of one quantity compared to another.

The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction.  We can also express the ratio in its standard form (:).

Given   Sum of     Equivalent

Ratio     Ratios          Ratios

5/36        36         13.89% or 0.1389

2:9           11          18.18% or 0.1818

3 to 18     21          14.28% or 0.14.28

1:3            4           25% or 0.25

Thus, we can conclude that 1:3 is the largest ratio amont the others.

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Using the unit circle, it is found that the terminal point of the angle 5pi/4 is given by:

A. \(\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)\)

For an angle \(\theta\) the unit circle is a circle with radius 1 containing the following set of points: \((\cos{\theta}, \sin{\theta})\).

The angle 5pi/4 is in the third quadrant, as it is greater than pi and less than 1.5pi, in which both the sine and the cosine are negative. Hence, considering the reference angle, we have that:

\((\cos{(\left(\frac{5\pi}{4}\right)}, \sin{(\left(\frac{5\pi}{4}\right)}) = (-\cos{(\left(\frac{\pi}{4}\right)}, -\sin{(\left(\frac{\pi}{4}\right)}) = \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)\)

Hence option A is correct.

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Answer:

i think x is equal to 5 if that's what your looking for

Step-by-step explanation:

3x + 7= 22

    -7    -7

    3x = 15

    3       3

      x = 5

The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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Answer:  9984

Step-by-step explanation:

In think you just multiply right cause you dis not give any direct message!?!

hope this helped you in any kind of way!?

Answer:

the answer is 9984

Step-by-step explanation:

312

× 32

_______

+624

+936

______

=9984

Answer:

7^2/(4+3)=7^2/7=7

(6+2^2)*10=(6+4)*10=10*10=100

Step-by-step explanation:

7²÷(4+3)

First you solve the bracket first;

7²÷(7)

And then you multiply 7 by 7 because of 7²

So it is going to be;

49÷7

=7

(6+2²)×10

Solve bracket first;

(6+2×2)

(6+4)×10

10×10

=100

Your average rate of change of elevation is 10 ft/min.

The rate of change defines how a given quantity changes per unit change in another quantity.

We can write the average rate of change as -

r{avg.} = {Δy/Δt} = {y₂ - y₁/x₂ - x₁}

We can write the instantaneous rate of change as -

r{ins.} = dy/dt

Given is that on a mountain hike, you see a sign posting that you are at an elevation of 130 ft. You arrive at another sign 30 minutes later that says you are at an elevation of 430 ft.

We can write the average rate of change as -

r{avg.} = {Δy/Δt} = {y₂ - y₁/x₂ - x₁}

r{avg.} = (430 - 130)/(30 - 0)

r{avg.} = (430 - 130)/(30)

r{avg.} = 300/30

r{avg.} = 10 ft/min

Therefore, your average rate of change of elevation is 10 ft/min.

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After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

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The proportion of all CEOs of medium and large companies who have MBAs is between 27.9% and 33.5%.

The formula we use is the Wilson Score Interval, which is a modified version of the Binomial Proportion Confidence Interval.

In this formula, we will use the following variables:

n = 344 (the total number of CEOs surveyed)

X = 97 (the number of MBAs)

z = 1.96 (the z-value corresponding to a 95% confidence level)

We then calculate the confidence interval as follows:

Lower Bound = (X + (z^2/2))/(n + z^2) - (z * SQRT((X * (1-X))/(n + z^2) + (z^2/4)) / (n + z^2)

Upper Bound = (X + (z^2/2))/(n + z^2) + (z * SQRT((X * (1-X))/(n + z^2) + (z^2/4)) / (n + z^2)

Plugging in the values for n, X, and z, we get the following confidence interval:

Lower Bound = 0.279

Upper Bound = 0.335

Therefore, we can be 95% confident that the proportion of all CEOs of medium and large companies who have MBAs is between 27.9% and 33.5%.

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Answer:

False

Step-by-step explanation:

The dependent variable changes, the size of the order will change depending on how many employes want a shirt.

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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The reading that separates the rejected thermometers from the others is given as follows:

1.175 ºC.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 0, \sigma = 1\)

The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.

Hence:

1.175 = X/1

X = 1.175 ºC.

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Answer:

2

Step-by-step explanation:

5 + 2(x – 3) = 3(x - 1)

5+2x-6=3x-3

-1+2x=3x-3

-1+3=3x-2x

2=x

Answer: 3.2x = 48

Step-by-step explanation: So that means x = 15.

Answer:

18 pupils

Step-by-step explanation:

11 like cola

32 like other stuff

11+32=43 - 50-43=7

therefore 11+7=18

18 students like cola the best

The area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 is 11.8334.

The graph of the question is given below:

We have to evaluate the integral needed to determine the area A of the region between the two curves x = y^3–4y^2+3y and x+y=y^2 i.e. x = y^2-y.

Now the area A of the given region is:

A = \(\int^1_{y=0}\left[g(y)-f(y)\right]dy+\int^4_{y=1}\left[g(y)-f(y)\right]dy\)

A = \(\int^1_{y=0}\left[(y^3-4y^2+3y)-(y^2-y)\right]dy+\int^4_{y=1}\left[(y^2-y)-(y^3-4y^2+3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-4y^2+3y-y^2+y)\right]dy+\int^4_{y=1}\left[y^2-y-y^3+4y^2-3y)\right]dy\)

A = \(\int^1_{y=0}\left[y^3-5y^2+4y\right]dy+\int^4_{y=1}\left[5y^2-y^3-4y)\right]dy\)

Further simplification

A = \(\left[\frac{y^4}{4}-\frac{5y^3}{3}-\frac{4y^2}{2}\right]^1_{y=0}+\left[\frac{5y^3}{3}-\frac{y^4}{4}-\frac{4y^2}{2}\right]^4_{y=1}\)

A = \(\left[(\frac{1}{4}-\frac{5}{3}-2)\right-(0-0+0)]+\left[(\frac{320}{3}-64-32)\right-(\frac{5}{3}-\frac{1}{4}-2)]\)

A = (3-20+24)/12 + 320/3 - 96 - (20-3-24)/12

A = 7/12 + 32/3 + 7/12

A = (7+128+7)/12

A = 142/12

A = 11.8334

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Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

If Santiago has been approved for a mortgage up to $195,000 and the conventional loan requires a 20% down payment, then his down payment will be:

Down payment = 20% * $195,000

Down payment = $39,000

Therefore, if Santiago buys a house for the maximum amount he has been approved for, he will need to make a down payment of $39,000.

To calculate how much house Santiago can afford, we need to subtract the down payment from the total amount he has been approved for:

Maximum home price = Total mortgage amount - Down payment

Maximum home price = $195,000 - $39,000

Maximum home price = $156,000

Therefore, Santiago can afford a home up to a maximum price of $156,000.

To summarize:

Santiago's down payment will be $39,000.

Santiago can spend up to $156,000 on a house.

I'm sorry to disturb but can you please mark me BRAINLEIST if this ans is helpfull

The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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Answer:

14.4

Step-by-step explanation:

6^2+12^2=x^2

64+144+x^2

208=x^2

square root of 208= 14.4

x=14.4

Answer:0.011

Step-by-step explanation:

The probability for exact 4 chickens being infected out of the 7 is ⁷C₄(0.15)⁴(0.85)³. The correct option is (A).

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Given that,

The probability of the infected chicken is 15%.

Which can be written as,

P(infected) = 15%

                  = 15/100

                  = 0.15

Then, the probability of not getting infected chicken is,

P(not infected) = 1 - 0.15

                        = 0.85

The total number of chicken for test = 7.

Now, in order to find the probability of the exact 4 infected chickens, binomial distribution can be used as.

The general expression for binomial distribution is ⁿCₓpˣqⁿ⁻ˣ.

For the given case p = P(infected) and q = P(not infected), n = 7 and x = 4.

Thus, the probability is given as,

P(Exact 4 are infected) = ⁷C₄(0.15)⁴(0.85)³

Hence, the  probability that exactly 4 of the 7 chickens sampled have the virus is  ⁷C₄(0.15)⁴(0.85)³.

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The complete question is given as, "Salim has flock of 300 chickens, 15% of which are infected with virus: He plans on taking an SRS of 7 chickens to test for the virus_ Which of the following would find the probability that exactly 4 of the 7 chickens sampled have the virus? Choose answer: 1(0.15) '(0.85)? (0.15)*(0.85)4 300 ` (0.15)'(0.85)3 (0.15)3(0.85)4 (0.15)4(0.85)".

Answer:

19 6/8 or 19 3/4

I’m not sure if you want the smallest possible fraction or not. If you don’t know just put the second one. K.