"National survey released in 2003 showed that among U.S. adults ages 70 and older, 21.1% had been told by a doctor that they had some form of cancer. Use this result as valid for the population of U.S. adults, 70 yrs. old and older. What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

Answer:

Step-by-step explanation:

A parallelogram is a quadrilateral with congruent opposite sides and pair of opposite angles.

Given: parallelogram ABCD

          AD≅ BC

          AD ║ BC

Thus;

<ABC + DAB = [tex]180^{o}[/tex] (supplementary angle property)

ΔABD = ΔCBD (each diagonal divides a parallelogram into two congruent triangles)

<ABC = <ADC (both pairs of opposite angles are congruent)

<DAB = <BCD (both pairs of opposite angles are congruent)

AB ≅ CD (opposite sides are congruent)

AB ║ DC (pair of opposite sides are parallel)

Therefore, the quadrilateral ABCD is a parallelogram.

Answer :

I have solved for the points.

Explanation :

Just get a protractor and plot out the angles into a circle. Starting with the largest angle.

Answer:

each bag of candy is $6.00

Step-by-step explanation:

1 bag would cost $6.00

1×$6.00=$6.00

6 bags × $6.00 = $36.00

Answer:

the constant of proportionally is 6

the prices of 6 bags of candy is 36

Step-by-step explanation:

to find the constant u divide 6 by 1 to find how they multiplying it by

the prices for six bags is 36 bc u can do 6 times 6 or look at the graph and see that it lands on 36

hope this helps

Answer:

Step-by-step explanation:

Let the number of children's tickets sold =c

Let the number of adult's tickets sold =a

Let the number of student's tickets sold =s

A total of 204 tickets were sold, therefore: c+a+s=204

Child tickets are $6, adult tickets are $12, and student tickets are $8.

Total revenue =$2,008

Therefore:

6c+12a+8s-2008

We are also told that 4 more adult tickets were sold than the total number of student and child tickets combined.

c+s=a+4

We then solve the resulting system of equation.

Substituting c+s=a+4 into the first equation

c+a+s=204

a+4+a=204

2a=204-4

2a=200

a=100

Substitute a=100 into the second and third equation

6c+12(100)+8s=2008

6c+8s=2008-1200

6c+8s=808

From the third equation

c+s=100+4

c=104-s

Substitute c=104-s into 6c+8s=808

6(104-s)+8s=808

624-6s+8s=808

2s=808-624

2s=184

s=92

Since c=104-s

c=104-92

c=12

Therefore:

Answer: -1

Step-by-step explanation:

to calculate f(-1), you know that x = -1. so all you have to do is substitute:

f(-1) = (-1)2 + 1

f(-1) = -2 + 1

f(-1) = -1

Answer:

0

Step-by-step explanation:

Answer:

  Annuity C:  Deposit $72,000 one lump sum

Step-by-step explanation:

The yield is improved when the money is on deposit for a longer period.

If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.

If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.

  Annuity C will provide the largest yield.

Answer:

(a)f(4) square cm.

(b)f(10.91)-f(10.9) Square centimeter.

Step-by-step explanation:

f(r)=the area of a circle (in square cm) that has a radius of r cm.

(a)Area (in square cm) of a circle whose radius is 4 cm.

Since r=4cm

Area of the circle = f(4) square cm.

(b) When the radius of the increases from 10.9 to 10.91 cm.

Change in the Area = f(10.91)-f(10.9) Square centimeter.

Answer:

13-n=4

Subtract both sides by 13

-n=-9

n=9

Step-by-step explanation:

13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you

Answer:

Distance between line and point =

4√5 -3/2√10

Step-by-step explanation:

Distance between the line is

= √ ((9-0)²+(0+1)²)

= √ (89+1)

= √90

= 3√10

Half of the line = 3/2√10

Distance of one side of the line and the point.

= √((9-1)²+(0-4)²)

= √((8)²+(-4)²)

=√64+16

= √80

= 4√5

Distance between line and point =

4√5 -3/2√10

Answer: 2 square root 10 units

Step-by-step explanation: A

Answer:

[tex]x=2$\pm$\sqrt{42}[/tex]

Step-by-step explanation:

The given equation is:

[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]

Formula:

A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:

[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]

Where [tex]D= b^{2} -4ac[/tex]

Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]

a = 1

b = -4

c= -38

Calculating D,

[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]

Now, finding the roots:

[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]

So, the solution is:

[tex]x=2$\pm$\sqrt{42}[/tex]

Answer is A or the first one

Answer

value of x is 34 degrees  

Step-by-step explanation:

Answer:

4y = -3x +18

Step-by-step explanation:

Let's get the gradient from this line equation first.

4x-3y=10

4x-10=3y

Y= 4/3x -10/3

The gradient is 4/3.

For a line perpendicular to another line.

M*M'= -1

M= -/(4/3)

M = -3/4

So the gradient to be used is -3/4

Formula for solving is

(Y-y1)/(x-x1)= M

X1= 2

Y1= 3

M = -3/4

(Y-y1)/(x-x1)= M

(Y-3)/(x-2)= -3/4

4(y-3)= -3(x-2)

4y -12 = -3x +6

4y = -3x +18

Answer:

Option (2)

Step-by-step explanation:

The given table represents the relation between the velocity and the time for an object is falling under the gravity.

Change in velocity with respect to time is directly proportional so the change is linear.

Acceleration due to gravity of this object is defined by the slope of the line joining the ordered pairs given in the table.

Let the two points lying on the line are (0, 0) and (1, 9.8)

Slope of the line passing through two points = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

                                                                          = [tex]\frac{9.8-0}{1-0}[/tex]

                                                                          = 9.8 [tex]\frac{m}{s^{2} }[/tex]

Option (2) will be the answer.

Answer:  4.4 seconds

Step-by-step explanation:

h(t) = -16t² + 315

Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0

  0  = -16t² + 315

-315 = -16t²

[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]

Answer:

≈ 4.44 sec

Step-by-step explanation:

h= 315 ft

h= 16t²

315 = 16t²

t²=315/16

t=√315/16 ≈ 4.44 sec

Answer:  55.6 days

Step-by-step explanation:

[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]

Answer:

[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=21-1=20[/tex]  

the p value for this case would be given by:

[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]  

For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm

Step-by-step explanation:

Information given

[tex]\bar X=2567[/tex] represent the mean height for the sample  

[tex]s=\sqrt{121}= 11[/tex] represent the sample standard deviation

[tex]n=21[/tex] sample size  

[tex]\mu_o =2564[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to check if the true mean is equal to 2564 mm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 2564[/tex]  

Alternative hypothesis:[tex]\mu \neq 2564[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]t=\frac{2567-2564}{\frac{11}{\sqrt{21}}}=1.250[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=21-1=20[/tex]  

the p value for this case would be given by:

[tex]p_v =2*P(t_{(20)}>1.250)=0.2113[/tex]  

For this case we see that the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2564 mm

Answer:

[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]  

And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg

Step-by-step explanation:

Information given

[tex]\bar X=595[/tex] represent the sample mean

[tex]s=20[/tex] represent the sample standard deviation

[tex]n=65[/tex] sample size  

[tex]\mu_o =600[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is different from 600 mg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 600[/tex]  

Alternative hypothesis:[tex]\mu \neq 600[/tex]  

The statistic would be given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{595-600}{\frac{20}{\sqrt{65}}}=-2.016[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{(64)}<-2.016)=0.048[/tex]  

And for this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mena is different from 600 mg

Answer:

It  was gained 4 1/4 points.

Step-by-step explanation:

- 7 1/8 - 1 5/8 + 13 = - 8 6/8 + 13 = - 8 3/4 + 13 = - 8 - 3/4 + 12 + 4/4 =  4 1/4

Answer:

[tex]\boxed{\sf \ \ \ k = 1 \ \ \ }[/tex]

Step-by-step explanation:

hello,

saying that p-1 is a factor of [tex]p^4+p^2-p-k[/tex]

means that 1 is a root of this expression, so it comes

1+1-1-k=0

<=> 1-k=0

<=> k = 1

Answer:  see table below

Step-by-step explanation:

Simply add the digit on the left to the digit on the top

1, 2 --> 1 + 2 = 3

3, 4 --> 3 + 4 = 7

4, 2 --> 4 + 2 = 6

6, 6 --> 6 + 6 = 12

[tex]\begin{array}{c|c|c|c}&\underline{\quad 2\quad }&\underline{\quad 4\quad }&\underline{\quad 6\quad }\\\underline{\quad 1 \quad}&\bold{\underline{\quad 3\quad}}&\underline{\quad 5\quad}&\underline{\quad 7\quad}\\\underline{\quad 2 \quad}&\underline{\quad 4\quad }&\underline{\quad 6\quad }&\underline{\quad 8\quad}\\\underline{\quad 3 \quad}&\underline{\quad 5\quad }&\bold{\underline{\quad 7\quad}}&\underline{\quad 9\quad}\\\end{array}[/tex]

[tex]\begin{array}{c|c|c|c}{\underline{\quad 4 \quad}&\bold{\underline{\quad 6\quad }}&\underline{\quad 8\quad }&\underline{\quad 10\quad }\\\underline{\quad 5 \quad}&\underline{\quad 7\quad}&\underline{\quad 9\quad}&\underline{\quad 11\quad}\\\underline{\quad 6 \quad}&\underline{\quad 8\quad }&\underline{\quad 10\quad }&\bold{\underline{\quad 12\quad}}\\\end{array}[/tex]

Answer:

combine 4m -8m to get -4m

[tex] - 4m - 2[/tex]

Answer:

− 4m-2

Step-by-step explanation:

Answer:

$23161.10

Step-by-step explanation:

Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t

Step 1: Convert months to years

60 months/12 month/year = 5 years

Step 2: Plug in known variables

A = 18400(1 + 0.0471)^5

Step 3: Solve

When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.

Answer:

B.

Step-by-step explanation:

The correct table that shows the justified solution steps is the second table.

The correct option is B.

The correct table that shows the justified solution steps is:

A 2-column table with 4 rows.

Column 1: Solution step

3x - 15 + 7x = 65

10x - 15 = 65

10x = 80

x = 8

Column 2: Method to Justify

Distributive property

Combine like terms

Addition property of equality

Division property of equality

In this table, the solution steps are correctly listed in the first column, showing the step-by-step process of solving the equation. The methods to justify each step are accurately provided in the second column, demonstrating the mathematical properties used at each stage.

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Answer: 2x²-√3

Step-by-step explanation:

Another way to say the conjugate is the opposite. All you have to do is to change the sign in the binomial, which is 2x²+√3. When you change the sign, it becomes 2x²-√3.

Answer:

no

Step-by-step explanation:

No, it is not a random sample of the students in school.

Answer:

No

Step-by-step explanation:

A random sample is a sample that is taken from a larger set. Molly specifically chose to interview the youngest students, so the sample is not random.

Answer:

P = [tex]\frac{19}{7}[/tex] or the decimal answer is 2.71

Step-by-step explanation:

Answer:

12/40=0.3

0.3 car parts per minute

9 / 0.3 = 30 minutes

30 minutes for 9 parts

Hope this helps

Step-by-step explanation:

Jose required 30 minutes to assemble 9 parts.

Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.

In mathematics it deals with numbers of operations according to the statements.

Here,
40 minute = 12 parts
40/12 = 1 part

Time to assemble 9 parts: = 40/12 x 9
                                             = 10/3 x 9
                                             =  30

Thus, Jose required 30 minutes to assemble 9 parts.

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