A line runs tangent to a circle at the point (4, 2). The line runs through the origin. Find the slope of the tangent line.

Answers

Answer 1

Answer:

Slope of the tangent line (m) = 1 / 2

Step-by-step explanation:

Given:

Point A = (4,2)

Origin point = (0,0)

Find:

Slope of the tangent line (m)

Computation:

Slope of the tangent line (m) = (y2-y1) / (x2-x1)

Slope of the tangent line (m) = (2-0) / (4-0)

Slope of the tangent line (m) = 2 / 4

Slope of the tangent line (m) = 1 / 2


Related Questions

What is the biggest value of probability?

Answers

Answer:

1

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is 1 as that means its certain that the event will happen.

hope thus helps,have a great day!!

~Pinky~

What number comes next in this series 7,10,10,13,16,16,

Answers

19
you’re just adding 3
you’re welcome :)

. In statistics, a data set has the following characteristics: (Choose all that apply) A:A data set is a collection of similar data. B:A data set can contain only quantitative data. C:A data set is any piece of descriptive or quantitative information on any object of study. D:A data set contains data all of which have some common characteristic.

Answers

Answer:

A. A data set is a collection of similar data.

D. A data set contains data all of which have some common characteristic.

Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about 13% of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York). The resulting relative frequency can be used as an estimate of the true probability of all Americans who can wiggle their ears. The resulting relative frequency can be used as an estimate of the true probability of all Americans who cannot wiggle their ears. The resulting relative frequency is the true probability of all Americans who can wiggle their ears. The resulting relative frequency cannot be used as an estimate of the true probability of all Americans who can wiggle their ears.

Answers

Answer:36

Step-by-step explanation:

In the diagram, ∆ABC and ∆DBE are similar. What is the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE? A. 1.33 B. 0.75 C. 0.66 D. 0.55

Answers

Answer:

B

Step-by-step explanation:

Calculate the ratio of corresponding sides, image to preimage, that is

scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B

The scale factor of the dilation will be 1.33. Then the correct option is A.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

In the diagram, ∆ABC and ∆DBE are similar.

Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be

⇒ 16.12 / 12.09

⇒ 1.33

Then the correct option is A.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ2

800,000+700 standard form

Answers

Answer:

800700

Step-by-step explanation:

800000 + 00000 + 0000 + 000 + 00 + 0

000000 + 00000 + 0000 + 700 + 00 + 0

------------------------------------------------------------

= 800700

Answer:

Hey there!

800000+700=800700

Hope this helps :)

Help me I’m stuck please

Answers

Answer:

choice 1,2,4,5 from top to bottom

Step-by-step explanation:

1:the points given are in the line where both planes intersect

2:point H is not on any plane

3:in the diagram point F is on plane R so false

4:if you connect the points given they will intersect so not collinear

5:the points F and G are on the plane R

6:so F is on plane R but H is not on any do false

Please! David has several chains of length 5 and of length 7. By joining chains one after the other, David can create different lengths. Which of these lengths is impossible to make? A)10 B)12 C)13 D)14 E)15

Answers

Answer:

13

Step-by-step explanation:

A)5+5=10

B)5+7=12

C) impossible

D)7+7=14

E)5+5+5=15

how can i solve this factorial? A 6,2- P6- A 5,3 + P5

Answers

I’m very confused! Is this a math problem!?

x+3y-Z=0
2x+y+Z=1
3X-y+Z=3

Answers

Answer: x = 1, y = -1/2 and z = -1/2

Explanation:

I added a picture

Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36. Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0 Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Ordered pair negative square root 65 comma 0 and ordered pair square root 65 comma 0 Center: (0, 0); Vertices: (0, -3), (0, -3); Foci: Ordered pair 0 comma negative square root 5 and ordered pair 0 comma square root 5 Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Ordered pair 0 comma negative square root 65 and ordered pair 0 comma square root 65

Answers

Answer:

Option A.

Step-by-step explanation:

The given equation of ellipse is

[tex]4x^2+9y^2=36[/tex]

Divide both sides by 36.

[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]

[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]

[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex]    ...(1)

The standard form of an ellipse is

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]    ...(2)

where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.

On comparing (1) and (2), we get

[tex]h=0,k=0,a=3,b=2[/tex]

Now,

Center [tex]=(h,k)=(0,0)[/tex]

Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]  

We know that

[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]

Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]

Therefore, the correct option is A.

33 points
1. A sandwich vendor offers a choice of hamburger, chicken, or fish on
either a plain or sesame seed bun. How many different types of
sandwiches are there to choose from?
*
4
6
12
3

Answers

Answer:

6 sandwiches to choose from because

3×2 = 6

A house m by m is surrounded by a walkway m wide. 27 9 1.8 a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway.

Answers

Answer:

A. 385.56 square meters.

B. 142.56 square meters.

Step-by-step explanation:

A house 27m by 9m is surrounded by a walkway 1.8m wide.

a) Find the area of the region covered by the house and the walkway.

​b) Find the area of the walkway.

Let

Length of the house=l=27m

Width of the house=w=9m

Wideness of the walkway=x=1.8m

Area of the region covered by the house and the walkway

=( L + 2*x) * (w + 2*x)

= (27+2*1.8)*(9+2*1.8)

=(27+3.6)*(9+3.6)

=(30.6)*(12.6)

=385.56 square meters.

​b) Area of the walkway

= (L + 2*x)*(w + 2*x) - l*w

= (27+2*1.8)*(9+2*1.8) - 27*9

=(27+3.6)*(9+3.6) - 243

=(30.6)*(12.6) - 243

=385.56 - 243

=142.56 square meters.

At a sale, dresses were sold for $39 each. This price was 65% of a dress's original price. How much did a dress originally cost?

Answers

Answer:

Hey there!

We can write the equation:

0.65x=39

x=60

The dress originally sold for 60 dollars.

Hope this helps :)

A scatter plot is shown below.. PLEASE HELPPP!!

Answers

Answer:

(0,9.8) and (10, 1.2)

Step-by-step explanation:

These are the only points that are the best fit for the garph correlation.

Answer:

(0, 9.8) and (10, 1.2)

Step-by-step explanation:

:) hope this helped

The graph shows the weight of a jar when filled with different numbers of marbles.

What does the y-intercept represent?
A) The weight of the marbles without the jar.
B) The weight of the jar without the marbles.
C) The weight of one marble and the jar.
D) The unit rate for each marble added.

Answers

Answer:

B

Step-by-step explanation:

The weight of the jar depends on the number of marbles in it, therefore the weight is the dependent variable (y) and the number of marbles is the independent variable (x). The y-intercept is when x = 0 and since the number of marbles is x, the answer is that the y-intercept represents the weight of the jar without the marbles.

I need help with this

Answers

Answer:

The fraction that represents the heart in the diagram shown is 7/3

Step-by-step explanation:

For this problem, we have to find the fraction expressed by the number line in the diagram shown.

First off, we know that the fraction will be between 2 and 3. Second, we know that each little dash between 2 and 3 represents 1/6.So, let's use this information to find the fraction.

Since the heart is two dashes away from 2, then this part of the fraction is 2/6 which can also be simplified to 1/3.

2 1/3

Since we can not have a mixed fraction, then we are going to turn this mixed number into an improper fraction. We do this by multiplying 2 with the denominator (which is 3) and adding the numerator (which is 1) to that product. Our denominator will stay the same in the final fraction.

2 1/3 = 7/3

So, the fraction represented by the heart is 7/3

Answer:

16/7

Step-by-step explanation:

There are 7 divisions between the numbers 2 and 3

So the denominator is 7

The heart is at the second mark

We are past the 2 mark so it is

2 2/7

Changing this from a mixed number to an improper fraction

(7*2+2) /7

16/7

Consider the following. C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1), starting at (0, 0)

a. Find a piecewise smooth parametrization of the path C.
r(t) = { 0
b Evaluate

Integral of (x+2y^1/2)ds

Answers

Answer:

a.

[tex]\mathbf{r_1 = (t,0) \implies t = 0 \ to \ 1}[/tex]

[tex]\mathbf{r_2 = (2-t,t-1) \implies t = 1 \ to \ 2}[/tex]

[tex]\mathbf{r_3 = (0,3-t) \implies t = 2 \ to \ 3}[/tex]

b.

[tex]\mathbf{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}+11}{6}}[/tex]

Step-by-step explanation:

Given that:

C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1), starting at (0, 0)

a. Find a piecewise smooth parametrization of the path C.

r(t) = { 0

If C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1),

Then:

[tex]C_1 = (0,0) \\ \\ C_2 = (1,0) \\ \\ C_3 = (0,1)[/tex]

Also:

[tex]\mathtt{r_1 = (0,0) + t(1,0) = (t,0) }[/tex]

[tex]\mathbf{r_1 = (t,0) \implies t = 0 \ to \ 1}[/tex]

[tex]\mathtt{r_2 = (1,0) + t(-1,1) = (1- t,t) }[/tex]

[tex]\mathbf{r_2 = (2-t,t-1) \implies t = 1 \ to \ 2}[/tex]

[tex]\mathtt{r_3 = (0,1) + t(0,-1) = (0,1-t) }[/tex]

[tex]\mathbf{r_3 = (0,3-t) \implies t = 2 \ to \ 3}[/tex]

b Evaluate :

Integral of (x+2y^1/2)ds

[tex]\mathtt{\int \limits ^1_{c1} (x+ 2 \sqrt{y}) ds = \int \limits ^1_{0} \ (t + 0) \sqrt{1} } \\ \\ \mathtt{ \int \limits ^1_{c1} (x+ 2 \sqrt{y}) ds = \begin {pmatrix} \dfrac{t^2}{2} \end {pmatrix} }^1_0 \\ \\ \mathtt{\int \limits ^1_{c1} (x+ 2 \sqrt{y}) ds = \dfrac{1}{2}}[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \int \limits (x+2 \sqrt{y} \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2 \ dt } }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \int \limits 2- t + 2\sqrt{t-1} \ \sqrt{1+1} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} \int \limits^2_1 2- t + 2\sqrt{t-1} \ dt }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} 2t - \dfrac{t^2}{2}+ \dfrac{2(t-1)^{3/2}}{3} (2) \end {pmatrix} ^2_1}[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} 2 -\dfrac{1}{2} (4-1)+\dfrac{4}{3} (1)^{3/2} -0 \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} 2 -\dfrac{3}{2} + \dfrac{4}{3} \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} \dfrac{12-9+8}{6} \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \sqrt{2} } \ \begin {pmatrix} \dfrac{11}{6} \end {pmatrix} }[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \dfrac{ \sqrt{2} }{6} \ (11 )}[/tex]

[tex]\mathtt{\int \limits _{c2} (x+ 2 \sqrt{y}) ds = \dfrac{ 11 \sqrt{2} }{6}}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \int \limits ^3_2 0+2 \sqrt{3-t} \ \sqrt{0+1} }[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \int \limits ^3_2 2 \sqrt{3-t} \ dt}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \int \limits^3_2 \begin {pmatrix} \dfrac{-2(3-t)^{3/2}}{3} (2) \end {pmatrix}^3_2 }[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = -\dfrac{4}{3} [(0)-(1)]}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = -\dfrac{4}{3} [-(1)]}[/tex]

[tex]\mathtt{\int \limits _{c3} (x+ 2 \sqrt{y}) ds = \dfrac{4}{3}}[/tex]

[tex]\mathtt{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}}{6}+\dfrac{1}{2}+ \dfrac{4}{3}}[/tex]

[tex]\mathtt{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}+3+8}{6}}[/tex]

[tex]\mathbf{\int \limits _{c} F \ dr =\dfrac{11 \sqrt{2}+11}{6}}[/tex]

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows. Color Purple Yellow Red Orange Green Blue Brown Percentage 22% 20% 23% 10% 6% 6% 13% Suppose you have a large bag of plain M&M candies and you choose one candy at random. (a) Find P(green candy or blue candy). Are these outcomes mutually exclusive? Why? Yes. Choosing a green and blue M&M is possible. Yes. Choosing a green and blue M&M is not possible. No. Choosing a green and blue M&M is not possible. No. Choosing a green and blue M&M is possible. (b) Find P(yellow candy or red candy). Are these outcomes mutually exclusive? Why? Yes. Choosing a yellow and red M&M is possible. No. Choosing a yellow and red M&M is not possible. Yes. Choosing a yellow and red M&M is not possible. No. Choosing a yellow and red M&M is possible. (c) Find P(not purple candy).

Answers

Answer:

A) 0.12. Yes. Choosing a green and blue M&M is possible

B) 0.43. Yes. Choosing a yellow and red M&M is possible

C) 0.78

Step-by-step explanation:

First of all, the summation of the distribution of all colours is;

Σ(all colors ) = 22% + 20% + 23% + 10% + 6% + 6% + 13% = 100%, or 1.

Thus;

a) P(green candy or blue candy) is;

P(GREEN ∪ BLUE) = P(G) + P(BL)

P(GREEN ∪ BLUE) = 6%+6%

P(GREEN ∪ BLUE) = 12% or 0.12

Now, due to the fact that we have to choose ONE candy and only ONE candy at random, then they are mutually exclusive: Yes. Choosing a green and blue M&M is possible

b)P(yellow candy or red candy is;

P(YELLOW ∪ RED) = P(Y) + P(R)

P(YELLOW ∪ RED) = 20% + 23% = 43% or 0.43

Yes. Choosing a yellow and red M&M is possible

c) P(NOT PURPLE)

the probability of having a purple is;

P(PURPLE) = 22% or 0.22

So, the Probability of NOT having a PURPLE is 1 - 0.22 = 0.78

Please help me on question a
I would really appreciate it

Answers

Answer:

[tex]x = 3.6[/tex]

Step-by-step explanation:

To find the area of a rectangle, you multiply its length by its width. The formula is [tex]lw = a[/tex].

We already know the length, 5, and the area, 18, so we can plug it into the equation.

[tex]5\cdot w=18[/tex]

We can simplify this equation by dividing both sides by 5.

[tex]5\cdot w \div5 = 18\div5\\\\w = 3.6[/tex]

Hope this helped!

Answer: x= 13

Step-by-step explanation:

Which is the ratio of the number of months that begin with the letter M to the total number of months in a year? 2 to 12 2 to 10 10 to 12 12 to 2

Answers

Answer:

the answer will be 2 to 12

Answer:

2 to 12

Step-by-step explanation:

just did a quiz got it right

A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 2 percentage points and with 95% confidence the difference in the proportion of her male and female constituents who favor the bill. What sample size should she obtain?

Answers

Answer:

The sample size is  [tex]n = 2401[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of  error is  [tex]E= 2\% = 0.02[/tex]

Given that the  confidence level is  95% then the level of significance is mathematically evaluated as

          [tex]\alpha = (100 - 95)\%[/tex]

            [tex]\alpha = 5\% = 0.05[/tex]

The  critical value of [tex]\frac{\alpha }{2}[/tex]  obtained from the normal distribution table is   [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]  

Let assume that the sample proportion is  [tex]\r p = 0.5[/tex]

 Generally the sample size is evaluated as

            [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p ( 1- \r p )[/tex]

            [tex]n = [\frac{1.96}{0.02} ]^2 * 0.5 ( 1- 0.5 )[/tex]

            [tex]n = 2401[/tex]

   

Blake bought two iced coffees from Dutch Bros. He originally had $13.50 and now has $9. Write and solve an equation to find out how much each iced
coffee cost.

Answers

Answer:

each ice coffee is $2.25

Step-by-step explanation:

13.50 - 9 = 4.50

4.50 / 2 = 2.25

(05.06A LC)

Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B'. What is the length

of A'B'?

1 unit

4 units

5 units

6 units

Answers

Answer:

4 units

Step-by-step explanation:

A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.

If a shape is transformed, the length of its sides and shape remains the same, only the position changes.

If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:

Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:

[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

AB = A'B' = 4 units

Find the interquartile range of the following data set. Number of Points Scored at Ten Basketball Games 57 63 44 29 36 62 48 50 42 34 A.21 B.28 C.6 D.34

Answers

Answer:

total number(n)=10

divided the total number into two equal parts so

in one group of number =5

ln first phase group of number middle value =44

In second phase group of number middle value=50

then using formula,q1=44 q3=50

inter quartile range =q3_q1

=50-44

=6

therefore interquartile range =6

Answer: The answer is 6

For an ordered pair (x,y) in a relation, the y element represents the

a.) range
b.) domain
c.) function
d.) input

Answers

Answer: y represents the range

Explanation:

x represents the domain
y represents the range

y represents the range for an ordered pair (x, y). Option A is correct.

For an ordered pair (x, y), What y represents is to determine.

What is range?

Range of the function is the output value of the function.

Here, in ordered pair (x, y) x represents the values of independent variable terms as domain. And for every value of x their is exist or output values y this  set of y values is called as range.

Thus, y represents the range for an ordered pair (x, y).

Learn more about range here:

https://brainly.com/question/17553524

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solve the following inequalities 7 x minus 5 / 8 x + 3 >4

Answers

Answer:

[tex]x> \frac{8}{51} [/tex]

Step-by-step explanation:

[tex]7x - \frac{5}{8} x + 3>4[/tex]

Bring constants to one side, simplify:

[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]

*Note that the inequality sign only changes when you divide the whole inequality by a negative number.

Answer:

[tex]x>\frac{8}{51}[/tex]

Step-by-step explanation:

[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]

I hope it helps :)

* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.​

Answers

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

Complete the square: x2+7x+?=(x+?)2

Answers

Answer:

x² + 7x + 49/4 = (x + 7/2)²

Step-by-step explanation:

x² + bx + c is a perfect square when c = (b/2)².

b = 7, c = (7/2)² = 49/4.

x² + 7x + 49/4 = (x + 7/2)²

Answer:

x² + 7x + 12.25 = (x+3.5)²

Step-by-step explanation:

(a+b)² = a²+ 2ab + b²

then:

7x = 2ab

7/2 = 3.5

then:

(x+3.5)² = x² + 2*3.5*a + 3.5²

x² + 7x + 12.25 = (x+3.5)²

Jasmine is making 150 bracelets and she needs 26 cm of silver wire for each bracelet. She will buy either the 3.7 metre or the 10.5 metre packs. She wants to pay as little as possible for the silver wire. How much will she have to pay for the silver wire to make 150 bracelets? £

Answers

Answer:

The least possible price is  p  =  £110

Step-by-step explanation:

From the question we are told that

     The number of bracelets to be made is  [tex]n = 150[/tex]

      The length of silver require for on bracelet is  [tex]x = 26 \ cm = 0.26 \ m[/tex]

      The option of silver length packs that she buys is  a =  10.5 m  packs

                                                                                           b  =  3.7 m packs

    Generally

                   1 bracelet   [tex]\to[/tex]  0.26 m  

                   150 bracelet [tex]\to[/tex]  z

=>        [tex]z = \frac{150 * 0.26}{1}[/tex]

=>        [tex]z = 39 \ m[/tex]

Now for option a  i.e  10.5 m  per pack

    The number of packs require is

        [tex]v = \frac{z}{a}[/tex]

=>     [tex]v = \frac{39}{ 10.5}[/tex]

=>      [tex]v = 3.7 1[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase v =  4

and that 4 packs would equal  t  =  4 * 10.5 =  42 meters of  silver

 Now for option d  i.e  3.7 meters per pack  

 The number of packs requires is  

           [tex]w = \frac{z}{b}[/tex]

=>        [tex]w = \frac{39}{3.7}[/tex]

=>        [tex]w = 10.54[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase w= 11

and that 11 packs would equal  t  = 11 * 3.7 =  40.7 meters of  silver

So the comparing the option and option b we see that for her to pay as little as possible she needs to go for option b since option be will produce the 150  bracelet with a little excess while option a will produce the 150 bracelet with much excess

    Assuming the price for the 3.7 m  pack is    £10

     And the price for the 10.7 pack is  £30

The least possible amount she would pay is  

                 [tex]p = 10 * 11[/tex]

                 p  =  £110  

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