The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease. Round to three decimal places as needed.

Yes - Have the disease No - Do not have the disease
Positive 142 6
Negative 7 145

Answer:

The integers are 7 and 14.

Step-by-step explanation:

y = 2x

1/y + 1/x = 3/14

1/(2x) + 1/x 3/14

1/(2x) + 2/(2x) = 3/14

3/(2x) = 3/14

1/2x = 1/14

2x = 14

x = 7

y = 2x = 2(7) = 14

Answer: The integers are 7 and 14.

The required two integers are 7 and 14

This is a question on word problems leading to the simultaneous equation:

Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1

Also, if the sum of the reciprocals of the two positive integers is 3/14, then:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2

Substitute equation 1 into 2

[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]

Find the LCM of 2y and y

[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]

Substitute y = 7 into equation 1:

Recall that x = 2y

[tex]x = 2(7)\\x = 14[/tex]

Hence the required two integers are 7 and 14.

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Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=50-1=49[/tex]

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]

The 95% confidence interval for the mean is (5.73, 6.95).

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

Answer:  If the sum of the measures of two angles is not 90°, then they  are not complementary angles.

Step-by-step explanation:

Contrapositive of p → q    is    ~q → ~p  where p is the hypothesis and q is the conclusion.

Hypothesis (p) = Two angles are complementary

                  ~p = Two angles are not complementary

Conclusion (q) = The sum of their measures is 90°

                  ~q = The sum of their measures is not 90°

~ p → ~q = If the sum of the measures of two angles is not 90°,

                then they are not complementary angles.

If the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees

These are statements that negates the given statement:

Given the statement; If two angles are complementary, then the sum of their measures is 90

Hypothesis (p) = Two angles are complementary  

                 ~p = Two angles are not complementary

Conclusion (q) = The sum of their measures is 90°  

                 ~q = The sum of their measures is not 90°

Hence the  statement that is the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees

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Answer:

1. y² - 3x - 18

2. 4x² - 33x + 35

3. 12x² - 11x + 2

Step-by-step explanation:

All we do with these questions are expanding the factored binomials. Use FOIL:

1. y² + 3y - 6y - 18

y² - 3y - 18

2. 4x² - 28x - 5x + 35

4x² - 33x + 35

3. 12x² - 3x - 8x + 2

12x² - 11x + 2

Answer:

1) (y-6) (y+3)

=> [tex]y^2+3y-6y-18[/tex]

=> [tex]y^2-3y-18[/tex]

2) (4x-5) (x-7)

=> [tex]4x^2-28x-5x+35[/tex]

=> [tex]4x^2-33x+35[/tex]

3) (3x - 2) ( 4x - 1)

=> [tex]12x^2-3x-8x+3[/tex]

=> [tex]12x^2-11x+3[/tex]

Start by making a table for the ordered pairs with the x-values

in the left column and the y-values in the right column.

            --x--|--y--

             -2  |  -5

              1   |  -3

                  |

                  |

Now remember that the slope is equal to the rate of change

or the change in y over the change in x.

We can see that the y-values go from -5 to -3 so the change in y is 2.

The x-values go from -2 to 1 so the change in x is 3.

So the change in y over the change in x is 2/3.

This means that the slope is also equal to 2/3.

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose you are forming a committee from a group of 15 biology student, 12 math students, and 9 physics students. How many possibilities are there if your committee needs to have at most 2 biology students, exactly 3 math students, and exactly 2 physics students?

To tackle this question, we will use the concept of combination since it deals with selection. Generally, selecting 'r' objects out of 'n' pools of object can be done using the formula;

nCr = n!/(n-r)!r!

If we are to form a committee of at most 2 biology students, exactly 3 math students and exactly 2 physics students from a group of 15 biology student, 12 math students, and 9 physics students, this can be done in the following ways;

For Physics students:

Selecting exactly 2 physics students from a group of 9 students will be:

9C2 = [tex]\frac{9!}{(9-2)!2!}\\[/tex]

= [tex]\frac{9!}{(7)!2!}\\[/tex]

[tex]= \frac{9*8*7!!}{(7)!2!}\\= 9*4\\= 36ways[/tex]

for Mathematics students:

Selecting exactly 3 math students from a group of 12 students will be:

[tex]12C3 = \frac{12!}{12-3)!3!}\\= \frac{12!}{9!3!}\\= \frac{12*11*10*9!}{9!*6}\\= 220 ways[/tex]

For Biology Students:

Selecting at most 2 biology students from a group of 15biology student will be:

15C1 * 15C2 (at most 2 students)

= [tex]\frac{15!}{14!1!} * \frac{15!}{13!2!}\\\\[/tex]

= 15*105

= 1,575 ways

The total number of possibilities will be = 36*220*1,575 = 12,474,000 possibilities

Answer:

The sine and cosine are equal for 45 degrees.

Choose the triangle that has a 45-deg angle.

Answer:

Answer is the second choice

Step-by-step explanation:

jut did it on edge

Answer:

  $904,510.28

Step-by-step explanation:

If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.

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

where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.

Filling in your values, we have ...

  P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)

  P = $904,510.28

You need to have $904,510.28 in your account when you begin withdrawals.

Answer:

You need to have $904,510.28 in your account when you begin

Answer:

A

Step-by-step explanation:

f(x) = x² + 3x + 5

Substitute x value with (a+ h)

f(a+h) = (a+h)² + 3(a+h) + 5

         = a² +2ah +h² + 3a + 3h + 5

Answer:

Step-by-step explanation:Josh

By comparing the given numbers, Jhon had most money.

As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.

The rules of the ordering and the comparing of the integers are given below:

Given that, John had $800 Tasha has $500 Kyle had $300.

Here, 300<500<800

Therefore, by comparing the given numbers, Jhon had most money.

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Answer:

y = 2x - 6

Explanation:

* note

the equation provided is written in standard form.

· standard form → Ax + By = C

· slope-intercept form → y = mx + b

To convert the given equation to slope-intercept form, start by subtracting '2x' from both sides of the equation. This will move 'y' to the left side of the equation.

2x - y = 6

2x - 2x - y = 6 - 2x

-y = -2x + 6

Next, multiply both sides of the equation by negative one.

-y = -2x + 6

(-y × -1) = (-2x × -1) + (6 × -1)

y = 2x - 6

Therefore, the given equation should be y = 2x - 6 when converted to slope-intercept form.

The equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.

Given is an equation of a line we need to convert it into slope-intercept form,

To convert the equation 2x - y = 6 to slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate the "y" variable on one side of the equation.

Starting with the given equation:

2x - y = 6

Move the 2x term to the right side by adding "y" to both sides:

2x = y + 6

Rearrange the equation by swapping the sides:

y + 6 = 2x

Move the constant term (6) to the right side by subtracting 6 from both sides:

y = 2x - 6

Hence the equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.

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Answer:

C. side CW ≅ side BM,

Step-by-step explanation:

When two triangles are said to be congruent, it means they have the same shape and size. This implies that their corresponding sides and corresponding angles are equal.

Therefore, given that triangles CPW and BHM are congruent, their corresponding sides should be equal.

Thus, the statement side CW ≅ side BM, must be true.

Other statements given are not true.

Answer:

487 ÷ 14

Hope that helps.

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.32

For the alternative hypothesis,

p ≠ 0.32

This is a two tailed test

Considering the population proportion, probability of success, p = 0.32

q = probability of failure = 1 - p

q = 1 - 0.32 = 0.68

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 261

n = number of samples = 750

P = 261/750 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.32)/√(0.32 × 0.68)/750 = 1.8

Recall, population proportion, p = 0.32

The difference between sample proportion and population proportion(P - p) is 0.35 - 0.32 = 0.03

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.32 - 0.03 = 0.29

the p for the right tail is 0.32 + 0.03 = 0.35

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the z score in the right tail 1 - 0.9641 = 0.0359

We would double this area to include the area in the right tail of z = 0.44 Thus

p = 0.0359 × 2 = 0.07

Since alpha, 0.05 < the p value, 0.07 then we would fail to reject the null hypothesis. Therefore, this is not sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level.

Answer:

True

Step-by-step explanation:

The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.

Answer:

Always the same

Step-by-step explanation:

The temperature at the beginning of a change of state is always the same as the temperature at the end.

This is because phase change is an isothermal process. it means that all the energy absorbed during the phase change process is utilized in the breaking of the bonds in the compound as it changes from one state of matter to another.

As a result, no increase in the temperature of the material will be detected by the thermometer.

━━━━━━━☆☆━━━━━━━

▹ Answer

V ≈ 160.22

▹ Step-by-Step Explanation

V = πr²[tex]\frac{h}{3}[/tex]

V = π3²[tex]\frac{17}{3}[/tex]

V ≈ 160.22

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer: A

Step-by-step explanation: A diameter is 2 times a circumference, and so a diameter is a line crossing through the center of a circle, since we know that, a circumference is just half of that, just half the center in the middle of a circle to the edge of a point on a circle.

Step-by-step explanation:

The equation of this circle is:

(x-3)^2 +(y+5)^2 = 16

The equatiin of a circle in general is:

(x-a)^2 +(y-b)^2 = r^2

a and b are the coordinates of the center and r is the radius

● in the given equation: (x-3)^2 + (y+5)^2 = 16

-3 and 5 are the coordinates if the center so start by ploting the center in the point (-3,5)

16 is the radius multiplied by itself

16 is 4×4 so the radius is 4

Take a four unit radius from the center and strat drawing your circle using a compass

Answer:

1.2m

Step-by-step explanation:

You must first find out how much the daffodil grew over the 8 days:

0.05 x 8 = 0.4

Then you must add how much it grew to the original height:

0.4 + 0.8 = 1.2

Hope this helps you out! : )

the length of the daffodil on the 8th day is 1.2m.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

A daffodil grows 0.05m every day.

the initial length of the daffodil is 0.8m.

You must first find out how much the daffodil grew over the 8 days:

0.05 x 8 = 0.4

Then you must add how much it grew to the original height:

0.4 + 0.8 = 1.2

hence,  the length of the daffodil on the 8th day is 1.2m.

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Answer:

Just x

Step-by-step explanation:

√x times √x equals √x²

√x² = x

Answer:

option D 9x³

Step-by-step explanation:

the monomial 9x³ comes from (3x)³, which gives, 3×3×3×x×x×x= 9x³

9 is 3 times 3 and x³ is 3 times x. So here, 9x³ is a perfect cube

Answer:

(a)k=44.245

(b)39820.50 PHP

Step-by-step explanation:

Part A

Let the number of PHP =y

Let the number of USD =x

The number of Philippine Pesos(y) received is directly proportional to the number of US Dollars(x) to be exchanged.

The equation of proportion is: y=kx

If 550 USD can be converted into 24,334.75 PHP.

Substitution into y=kx  gives:

[tex]24,334.75=550k\\$Divide both sides by 550$\\k=24,334.75 \div 550\\k=44.245[/tex]

The constant of proportionality k=44.245

Part B

The equation connecting y and x then becomes:

y=44.245x

If x=900 USD

Then:

y=44.245 X 900

y= 39820.50

Therefore, given that you have 900 USD to convert. You will receive 39820.50 PHP

Answer:

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Answer:

so the distance between two points is (2√13)

Step-by-step explanation:

we have to find the distance between two points

d=√(x2-x1)²+(y2-y1)²

putting the values of coordinates

d=√(4--2)²+(-1-3)²

d=√(6)²+(-4)²

d=√36+16

d=√52

d=2√13

i hope this will help you :)

Answer:

y = - 16.1779 + 14.1087*In(x)

y = 37.5

Step-by-step explanation:

Given the data:

X:5,10,15,20,25,30

Y:6,15,25,27,29,30

General form of a logarithmic fuction:

y = A + BIn(x)

Using the logarithmic regression calculator :

The logarithmic regression model is :

y = - 16.1779 + 14.1087*In(x)

The estimated value of y when x = 45

y = - 16.1779 + 14.1087*In(45)

y = - 16.1779 + 14.1087*3.8066624

y = - 16.1779 + 53.707059

y = 37.529159

y = 37.5

Answer:

25, 55, 100

Step-by-step explanation:

Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:

x + x + 30 + 4x = 180

6x + 30 = 180

6x = 150

x = 25°

x + 30 = 25 + 30 = 55°

4x = 25 * 4 = 100°

The sum of angles is 180.

[tex] \alpha + \beta + \gamma = 180 [/tex]

[tex] \alpha + ( \alpha + 30) + (4 \alpha ) = 180[/tex]

[tex]6 \alpha = 150[/tex]

[tex] \alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100[/tex]