A blood test indicates the presence of a particular disease 96​% of the time when the disease is actually present. The same test indicates the presence of the disease 0.8​% of the time when the disease is not present. Two percent of the population actually has the disease. Calculate the probability that a person has the​ disease, given that the test indicates the presence of the disease.

To complete the square, you would add (16/2)^2 = 64/4 = 16 to both sides of the equation.

x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd polynomials equation, which is guaranteed by the algebraic fundamental theorem.

In other terms, you have a quadratic equation if a times the squares of the equation after b plus b twice that the same phrase not square plus c equals 0. The initial equation will change to a quadratic equation if the value in the () is replaced with such a variable like t.

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Answer:

If angle ABD = 60°, then angle BDC can be found using the fact that the measures of the angles in a triangle add up to 180°.

So, m(angle BDC) = 180 - (m(angle ABD) + m(angle BDA))

Therefore, m(angle BDC) = 180 - (60 + m(angle BDA))

So the measure of angle BDC is not fixed, it depends on the measure of angle BDA.

Answer: 3 - 2x

Step-by-step explanation:

Product = Multiplication

Product of 2 and x = 2*x

3 minus 2x

3-2x

Answer:

3−2×x or 3-(2xx)

The equation that relates velocity, distance and time is given as follows:

v = 171/2.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

The parameters for this problem are given as follows:

d = 171, t = 2.

Hence the equation that gives the velocity in miles per hour is of:

v = 171/2.

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The area of the glacier at the start of last year was 56.31 km², based on a percentage reduction of 0.2%.

A percentage decrease represents the difference between the starting and ending values, expressed as a percentage of the starting value.

In working out the percentage reduction, we determine the difference between the ending and starting values.  This difference is divided by the starting value and multiplied by 100.

The current area of the glacier = 56.20 km²

The percentage reduction = 0.2%

Proportionately, the current area, in percentage terms = 99.8% (1 - 0.2%)

99.8% = 56.20 km²

100% = 56.31 km²

Thus, to 2 decimal points, the area of the glacier at the start of last year was 56.31 km².

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Manufacturing should pay $2206.80, Selling should pay $7356.0and Administration should pay $2452.00

Generally, To find out how much each department should pay, you can use the proportion of the cost that corresponds to their respective ratio.

First, calculate the total ratio by adding the three ratios together:

1/10 + 1/3 + 1/9 = 0.544

Then, divide the total cost by the total ratio to find the unit cost:

$12,005 / 0.544 = $22068.01

Next, multiply the unit cost by the ratio for each department to find out how much they should pay:

Manufacturing: $22068.01 x 1/10 = $2206.80

Selling: $22068.01 x 1/3 = $7356.0

Administration: $22068.01 x 1/9 = $2452.00

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Total distance travelled by the cyclist is 131/40 km in fraction.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.

Total distance travelled by the cyclist is 7/8 + 9/10 + 3/2 = 131/40 km

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Answer: A quadratic of the form $ax^2 + bx + c$ has rational roots if and only if its discriminant, $b^2 - 4ac$, is a perfect square. In this case, the discriminant is $(20)^2 - 4(3)(c) = 400 - 12c$. So, we need to find the positive integers $c < 100$ that make $12c$ a perfect square.

The perfect squares that are less than $100$ are $1,4,9,16,25,36,49,64,81$, so the possible values for $c$ are $33,44,55,66,77,88$.

So, the positive integers $c$, with $c < 100$, that make the quadratic have rational roots are $33,44,55,66,77,88$

Step-by-step explanation:

We can conclude that the division property of equality was done between step 4 and step 5.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

a/c = b/c

At step 4: The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

-6x = 57

---- Divide both sides by -6 (Step 4)

-6x / -6  = 57 / -6

---- (Intermediary between step 4 and 5)

x = -9.5

----- Step 5

Hence, we can conclude that the division property of equality was done between step 4 and step 5

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The  Pinewoods Trail is longer than the Outlook Trail.

The definition of a fraction is a portion of a whole. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin.

Given the length of Lake Trail = 4 and 3/5 mile

length of Lake Trail = 23/5 miles

length of Outlook Trail = 5 and 5/6 mile

length of Outlook Trail = 35/6 miles

length of Pinewoods Trail = 1 and 3/10 miles longer than Lake Trail

length of Pinewoods Trail = 33/10 + 23/5

length of Pinewoods Trail = (33 + 46)/10

length of Pinewoods Trail = 79/10 miles

comparing the length of  Outlook Trail  and  Pinewoods Trail,

which is 35/6 and 79/10 miles respectively,

the common denominator for both is 30,

35/6 = (35*5)/(6*5)

35/6 = 175/30

and 79/10 = (79*3)/(10*3)

79/10 = 273/30

here 273/30 > 175/30

Hence  Pinewoods Trail is longer.

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Answer: 38

Step-by-step explanation:

You can split this shape into 2 rectangles. The area of the two rectangles = 5 * 4 + 6 * 3

= 20 + 18

= 38

Take the original data and divide it by the standard deviation to determine the z-scores. X is a symbol for the relevant data point. For the population from which you selected your sample, mu and sigma stand in for the mean and standard deviation.

In terms of standard deviations above or below the mean, a data point's z-score quantifies this exact distance.

A z-score is calculated using the following formula:

data point = mean standard deviation

Data point means with standard deviation equal to z

The same equation is given below in symbol form:

z=  x−μ / σ

Some significant z-score details are as follows:

An elevated z-score indicates that the data point is.

When a data point has a negative z-score, it is below average.

The data point is considered to be roughly average if the z-score is near to 0.00.

If a data point's z-score is higher or lower than 3 33 or 3 3minus, the data point is deemed uncommon.

At Almond, the average score on a history midterm is

= 85 = 85mu, which is equivalent to 85 with a standard deviation of

= 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2

On the test, Michael received a score of 86.866.668.

Calculate Michael's exam grade in Z-score form.

His Grade = Mean Grade Standard Deviation

= 86 − 85 / 2

= 1 /2 = 0.5 z z z

= standard deviation of his grade and mean grade.

= 2 / 86−85

= 2 / 1 =0.5.

The z-score for Michael is 0.5, 0.50, and 5. He received a grade that was half a standard deviation higher than the mean.

​

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Answer:

(A+7)^4

Step-by-step explanation:

Answer: 16/81

Step-by-step explanation:

To do this you have to do 2^4 which is 16.
Next, you have to do 3^4 which is 81
This gives you 16/81.

Now check if you can simplify it.
You can't so this is your answer :D

I hope this was able to help you :D

The earliest time at which they can be finished moving all of the boxes is: d. 9:44 a.m

To determine the earliest time at which Quincy and Celine can finish moving all of the boxes, we need to determine the maximum amount of time it will take for them to move all of the boxes. We can do this by calculating the time it will take for each person to move each type of box individually, and then adding those times together.

Quincy takes 1 minute to move a small box and 2 minutes to move a large box. Celine takes 2 minutes to move a small box and 3 minutes to move a large box.

Time to move 16 small boxes: 16 boxes * 1 minute/box = 16 minutes

Time to move 10 large boxes: 10 boxes * 2 minutes/box = 20 minutes

Total time for Quincy: 16 minutes + 20 minutes = 36 minutes

Time to move 16 small boxes: 16 boxes * 2 minutes/box = 32 minutes

Time to move 10 large boxes: 10 boxes * 3 minutes/box = 30 minutes

Total time for Celine: 32 minutes + 30 minutes = 62 minutes

To get the earliest time they can finish moving all the boxes, we take the maximum of the two times:

Max(36 minutes, 62 minutes) = 62 minutes

Start time: 9:00 a.m.

End time: 9:00 a.m. + 62 minutes = 9:62 a.m.

So the earliest time they can finish moving all the boxes is 9:62 a.m.

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Answer:

102

Step-by-step explanation:

34x3=102

A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic.

Quadratic equations or quadratic functions. A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic. Equations using quadratics is another name for it. The quadratic equation is expressed in its general form as ax2 + bx + c = 0.

For instance, 6x2 + 11x - 35 = 0, 2x2 - 4x - 2 = 0, 2x2 - 64 = 0, x2 - 16 = 0, x2 - 7x = 0, 2x2 + 8x = 0, etc. are examples of quadratic equations.

Three kinds of quadratics are frequently employed:

Standard Form: y = an x 2 + b x + c y = an x 2 + b x + c

y = a (x r 1, x r 2) is the factored form. y=a(x-r 1)(x-r 2) y=a(x−r1)(x−r2)

Vertex Formula: y=a (x h) 2 + k y=a (x-h)2 + k y=a (x-h) 2+k.

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The conclusion of the proportion is if a and bare not coprime, when it share a factor greater than 1

Here we have given that if and are not coprime that is share a factor greater than.

And we need to find the examples that contradict the conclusions of proposition.
While we looking into the given question, we have identified that  if and  are not coprime.

In order to find the conclusion to this one, we must know the definition of co prime.

The term co prime is referred as those umbers that do not have any common factor other than 1.

As per the definition, we have clearly know that if the two number has the factor greater than one then it will not a co prime to each other.

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Answer:

1 or 0

Step-by-step explanation:

in order for a number's square equals to itself, it has to be 1 or 0.

Answer:

3 1/10 as a fraction

Step-by-step explanation:

3.3 as a fraction is 3 3/10. The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''. However, the second 3 to the right of the decimal point represents a decimal amount. Because this 3 is in the tenths place, we say it as ''3 tenths.

33 is repeating

    When converting a percent in fraction form, you must know its place value of each number, and you can easily transform it to fraction.

3.3% - the place value is ones. It is a whole number and called as three.

3.3% - the place value is tenths. It is called as three-tenths.

When you convert a percent to decimal, you must divide it by 100.

3.3 ÷ 100

The verbal expression that best represents the equation 2(n - 7) = -14 is: c) seven less than twice a number is equal to negative fourteen.

Verbal expression can be defined as the way of writing mathematical expression into words or translating  equation into words.

Now let interpret this  equation 2(n - 7) = -14 into verbal expression.

n = a number

2n = twice a number

2n - 7 = seven less than twice a number

-14 = negative fourteen

Therefore we can conclude that the correct option is C.

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The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.

The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:

f(x) = (2x + 1)(x² - 8x + 8) + 5

Simplifying the above gives the following:

f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5

f(x) = 3x³ - 15x² + 8x + 13

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Answer: If you are reporting on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, you are using a population.

A population is a complete set of all the individuals or elements that share a common characteristic, such as all breast cancer patients seen at a hospital in a given year. A sample, on the other hand, is a subset of a population that is selected for analysis or study.

In this case, since you are reporting on all breast cancer patients seen at the hospital last year, you are using the entire population of breast cancer patients, rather than just a sample of them.

Step-by-step explanation:

a = amount invested at 6%

how much is 6% of "a"? (6/100) * "a", namely 0.06a.

b = amount invested at 4%

how much is 4% of "b"? (4/100) * "b", namely 0.04b.

we also know that the yielded amount in interest or the annual income he's got from both is $116, so if we simply add their interest, that'd be 0.06a + 0.04b = 116.

We also know that he invested 400 more in "b" than in "a", so whatever "a" might be, we know that b = a + 400.

[tex]0.06a~~ + ~~0.04(\stackrel{b}{a+400})~~ = ~~116\implies 0.06a+0.04a+16=116 \\\\\\ 0.10a+16=116\implies 0.10a=100\implies a=\cfrac{100}{0.10} \\\\\\ \boxed{a=1000}\hspace{5em}\stackrel{1000+400}{\boxed{b=1400}}[/tex]

a) The discount on the loan is $1,862.

b) The amount of money the borrower received on the discount loan is $11,438.

c) The true interest rate paid on the discounted loan is 4.1%.

A discount loan is a type of loan in which the interest (cost of borrowing) is deducted upfront or at the time the loan is granted.

The implication of getting a discount loan is that the amount received is less than the principal amount because the grantor has reduced it by interest and other fees (finance charges).

The principal = $13,300

Discount rate = 3¹/₂%

Time = 4 years

Discount = $1,862 ($13,300 x 3.5% x 4)

Amount received = $11,438 ($13,300 - $1,862)

Real interest rate = 4.1% ($1,862/$11,438 x 100)/4

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Answer:

Yes, (x-3) is a factor of (x^4-13x^2+36) using synthetic division.

Synthetic division:

| x -3 |

x^4 -13x^2+36

x^3 -10x^2+27x-108

The remainder is zero, so (x-3) is a factor of the polynomial (x^4-13x^2+36).

Step-by-step explanation:

The histogram that accurately summarizes the data in this problem is given by the second image presented at the end of the answer.

The histogram of a data-set shows the number of times that each item was observed in the data-set.

From the first image given at the end of the answer, the absolute frequencies are given for each observation, which is the height of each bin of the histogram.

The problem is given by the first image presented at the end of the answer.

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Answer:

191.5

Step-by-step explanation: