An image of a rectangular pyramid is shown below:

A right rectangular pyramid is shown.

Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section? Explain your answer.

Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? Explain your answer.

Answer:

a) 95% Confidence interval = (0.026%, 0.037%) to 3 d.p

b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (131/420076) = 0.0003118483 = 0.0312%

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 95% confidence interval for sample size of 420,076 is obtained from the z-tables because the sample size is large enough for the properties of the sample to approximate the population properties.

Critical value = 1.960 (from the z-tables)

Standard error = σₓ = √[p(1-p)/n]

n = sample size = 420,076

σₓ = √(0.0003118×0.999688/420076) = 0.0000272421 = 0.0000272

95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.000312 ± (1.96 × 0.0000272)

CI = 0.000312 ± 0.0000534

95% CI = (0.0002586055, 0.0003653945)

95% Confidence interval = (0.000259, 0.000365)

95% Confidence interval = (0.0259%, 0.0365%) = (0.026%, 0.037%) to 3 d.p

b) The result of the 95% confidence interval does not agree with the previous rate of such cancer because the value 0.0224% does not lie within this confidence interval obtained.

Hope this Helps!!!

Answer:

150 kg

Step-by-step explanation:

The diagonal Piece: √5²+12² = 13

6 pieces: 5, 12, 5, 12, 13, 13

Total length: 2 x(5 + 12 + 13) = 60

Total weight: 60 x 2.5 = 150 kg

Answer:

150 kg

Step-by-step explanation:

The length of the diagonal:

sqrt(12² + 5²)

sqrt(169)

13

Total length:

2(13 + 12 + 5)

2(30)

60m

Mass;

60 × 2.5

150 kg

Answer:

(-7,-6)

Step-by-step explanation:

-10 + 3 = -7

6 - 12 = -6

(-7,-6)

Answer:

 x2 + 8x - 3

Step-by-step explanation:

 1 . ((2x2 +  4) -  5) -  (x2 - 8x + 2)  

2.  Factoring  x2+8x-3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   8 .

Step 3. -3

  +    

1

  =    

-2

-1

  +    

  3

  =    

2

Observation : No two such factors can be found !!  

Conclusion : Trinomial can not be factored

So that the answer

Answer:

2. The transformation rule is (x, y) -> (x + 0, y + 4).

Step-by-step explanation:

The true statements about the translation are:

2. The transformation rule is (x,y) = (x+0.7+4).

3. The transformation is a vertical translation.

The vertices are given as:

V(-2, 3) to V-2,7)

From the above vertices, we have the following transformation rule

(x,y) = (x+0.7+4).

Notice that the x-coordinate remains unchanged,

This means that the transformation is a vertical translation.

Hence, the true statements about the translation are: (2) and (3)

Read more about translation at:

https://brainly.com/question/11468584

Answer:

B ) Negative

Step-by-step explanation:

Given the expression 3xy

when x>0 and y<0

The value of the expression 3xy will be negative.

This is because the product of a positive and negative number will always be negative.

For illustration,

Let x=5>0 and y=-5<0

3xy=3(5)(-5)=-75

NOTE:

[tex]-X-=+\\-X+=-\\+X+=+[/tex]

Answer:

Step-by-step explanation:

First let's figure out the scale Alexander is using by relating the base in his drawing 10 in/3​000 ft = 1 in/300 ft

The scale for the drawing is 1 in:300 ft.

We know the actual Federal Triangle has a height of 1200 ft Let's use the scale to find the height of Alexander's triangle.

1200 ft times 1 in/300 ft = 4 in.

Alexander is using a scale of 1 in: 300 ft.His triangle has a height of 4 in.

Answer:

Step-by-step explanation:

Look at where -2 is on the x-axis (the left side of the horizontal line), and go another half a box in, that is -2.5. But then go down one box from there, and plot the point. that is (-2.5,-1).

Next go half a box to the right and two boxes up, and plot your point there. that is (.5,2).

Answer:

3a + b = 7

6x + 8y = 40

9a + 3b is 3*(3a + b)  or 7*3 = 21

3x + 4y is (6x + 8y) /3 = 40 / 3 ≅ 13.3

So now we know that 9a + 3b = 21 and 3x + 4y = 13.3 which means that it is greater because 21 > 13.3

Answer:-x+8

Step-by-step explanation:

So in this case we have to combine alike variables for this question.

(6x+9)-(7x+1)

     -9       -9

6x-7x+-8

We had to isolate in this case thats why both alike terms were getting subtracted by 9.

Then we just combining 6x-7x since they are alike terms.

-1x+8

-1x and -x are the same thing but if you want to make it more complex, the real answer is  -x+8

(I hope you find this helpful ;w;)

Answer:

-x+8

Step-by-step explanation:

Answer:

162 mL

Step-by-step explanation:

1.Convert all volumes to millilitres

(a) Chlorpheniramine

V = 100 mL

(b) Lidocaine

V = \text{2 oz} \times \dfrac{\text{29.57 mL}}{\text{1 oz}} = \text{ 59.14 mL)

(c) Banana flavouring

V = \dfrac{1}{2}\text{ tsp} \times \dfrac{\text{4.93 mL}}{\text{1 tsp}} = \textbf{2.46 mL} }

2.Calculate the total volume

Chlorpheniramine = 100      mL

Lidocaine               =   59.14

Banana flavouring =    2.46          

TOTAL                    = 162      mL

Answer:

Step-by-step explanation:

[tex]x^{-2}=16\\\\\frac{1}{x^{2}}=16\\\\[/tex]

Cross multiplication,

[tex]1=16x^{2}\\\\\frac{1}{16}=x^{2}[/tex]

Given:

Given that O is the center of the circle.

AB is tangent to the circle.

The measure of ∠AOB is 68° and we know that the tangent meets the circle at 90°

We need to determine the measure of ∠ABO.

Measure of ∠ABO:

The measure of ∠ABO can be determined using the triangle sum property.

Applying the property, we have;

[tex]\angle ABO+\angle BAO+\angle AOB=180^{\circ}[/tex]

Substituting the values, we get;

[tex]\angle ABO+90^{\circ}+68^{\circ}=180^{\circ}[/tex]

Simplifying, we get;

[tex]\angle ABO+158^{\circ}=180^{\circ}[/tex]

          [tex]\angle ABO=22^{\circ}[/tex]

Thus, the measure of ∠ABO is 22°

To solve this you need to use this formula: 1/2Pi x D

So we can multiply 0.5 x 3.14 x 1.7

Your answer is 2.669

Answer:

A

Step-by-step explanation:

A: will be the connect with 2 sides of hypotenuse of the triangle

Answer: what is the question??

Step-by-step explanation:

Answer:

[tex] = 13 \frac{2}{5} [/tex]

Step-by-step explanation:

[tex] \: \: \: \: \: \: 13\\ 5 \sqrt{67} \\ \frac{ \: \: - 65}{ \: \: \: \: \: 02} \\ \\ \\ = 13 \frac{2}{5} [/tex]

Answer:

It is 80.

Step-by-step explanation:

It's pretty simple-> Thousands, Hundreds, Tens, Ones.

Answer:

The tens place

Step-by-step explanation:

place values:

6000

400

80

2

Answer  :  Define F as fathers age and S as sons age right now.

Then now they are

(1) 3S = F

and six years ago they were

(2) 5*(S-6) = F-6

calculate 5*(S-6)

5S - 30 = F-6

Subtract left and right side by -F

Add 30 to left and right side

5S - F = 24

Put (2) 3S = F into the equation above

5S - 3S = 24

2S = 24

S = 12

insert result in (2) 3S = F

3*12 = F

36 = F

So the son is 12 years, and the father is 36 years.

"The correct system of equations to represent Kevin's and Daniel's ages is:

1.  k = d + 3

2.  k - 2 = 4(d - 2)

To solve for Kevin's and Daniel's current ages, we can substitute  k  from equation 1 into equation 2.

From equation 1:

k = d + 3

Substitute  k  into equation 2:

(d + 3) - 2 = 4(d - 2)

Now, simplify the equation:

d + 1 = 4d - 8

Combine like terms:

4d - d = 8 + 1

3d = 9

Divide both sides by 3 to solve for  d :

d = [tex]\frac{9}{3}[/tex]

d = 3

Now that we have Daniel's age, we can find Kevin's age by substituting  d  back into equation 1:

k = d + 3

k = 3 + 3

k = 6

Therefore, Kevin is 6 years old and Daniel is 3 years old. The final answer is:

Kevin's age:  k = 6

Daniel's age:  d = 3 "

Answer:

5.6 thousand

Step-by-step explanation:

To find the mean absolute deviation (MAD), first find the mean (or average).

μ = (41 + 38 + 36 + 57 + 43) / 5

μ = 43

Next, subtract the mean from each value and take the absolute value.

|41 − 43| = 2

|38 − 43| = 5

|36 − 43| = 7

|57 − 43| = 14

|43 − 43| = 0

Sum the results and divide by the number of animals.

MAD = (2 + 5 + 7 + 14 + 0) / 5

MAD = 5.6

Answer:

43 thousand dollars

Answer: the answer is 200

Step-by-step explanation:

The second line has a greater rate of change by 13/4.

To determine the rate of change, or slope, of the given graphed line, we employ the formula for calculating the slope between two points, expressed as:

a = (y2 - y1)/(x2 - x1)

Observing the graphed function, we identify two points, (0, -2) and (4, 0), and apply these coordinates to the slope formula

a = (0 - (-2))/(4 - 0) = 2/4 = 1/2

Having established that the slope of the first line is 1/2, we move on to the second line, which has a slope of 15/4. To find the difference in slopes, we subtract the slope of the first line from that of the second:

15/4 - 1/2 = 15/4 - 2/4 = 13/4

This calculation reveals that the second line has a greater rate of change by 13/4.

In summary, the step-by-step analysis indicates that the slope of the second line exceeds that of the first by 13/4.

The question probable may be:

Consider the two functions. Which statement is true?

A)Function 1 has a greater rate of change by 13/4

B)Function 2 has a greater rate of change by 13/4

C)Function 1 has a greater rate of change by 13/2

D)Function 2 has a greater rate of change by 13/2

Answer:

see below

Step-by-step explanation:

Angle ACE = DCE since they are vertical angles

Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles

Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles

When all three angles are equal, the triangles are similar.

We can use ratios to find DE

DE         CE  

------- = ----------

AB           AC

DE         8

------- = ----------

12           10

Using cross products

10 DE = 8*12

10 DE = 96

Divide by 10

DE = 9.6

Answer:

1) they are similar by AAA postulate

2) 9.6 cm

Explanation:

Triangles CAB and CED are similar

because:

1) both have the same angle C

(vertically opposite angles)

2) Angle A = Angle E

(alternate angles)

3) Angle B = Angle D

(alternate angles)

CA/CE = AB/ED

10/8 = 12/DE

DE = 12 × 8/10

DE = 9.6 cm

Answer:

7.875 (not sure what your unit is but include it here)

Step-by-step explanation:

3/4 of 4.5 is 3.375

3.375+4.5=7.875

Answer:

A, C, and D

Step-by-step explanation:

The rate of change will simply be the slope of the line, which we can find by taking the change in y and dividing that by the change in x:

slope = [tex]\frac{6-3}{4-2} =\frac{3}{2}[/tex]

Thus, the slope is 3/2 = 1.5.

Since the slope remains constant throughout the graph, we know that A is correct. In addition because the points 0, 2, 4, and 6 are on the graph, the rate of change between any of the two points will still be the constant 1.5, making C and D correct as well.

So, we can choose A, C, and D.

Hope this helps!

Answer:

The rate of change of a linear function is always the same.

The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

Step-by-step explanation:

Slope = rate = (6 - 3)/(4 - 2) = 3/2

Slope of a straight line is constant hence the rate of change is also constant

Answer:

fish. pink salmon. 50. i like fish btw

Step-by-step explanation:

Experimental probabilities: Pink Salmon 22%, Yellowfin Tuna 32%, Bluegill 46%. Total probability equals 100%.

To find the experimental probability of each type of fish, we first need to calculate the percentage of each type of fish out of the total number of fish caught.

Experimental Probability ($P$) is given by:

[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \times 100 \][/tex]

Let's calculate:

1. Pink Salmon:

[tex]\[ P(\text{Pink Salmon}) = \frac{11}{50} \times 100\% = \frac{11}{50} \times 100\% = 22\% \][/tex]

2. Yellowfin Tuna:

[tex]\[ P(\text{Yellowfin Tuna}) = \frac{16}{50} \times 100\% = \frac{16}{50} \times 100\% = 32\% \][/tex]

3. Bluegill:

[tex]\[ P(\text{Bluegill}) = \frac{23}{50} \times 100\% = \frac{23}{50} \times 100\% = 46\% \][/tex]

Now, let's check if the total probability sums up to 100%:

[tex]\[ 22\% + 32\% + 46\% = 100\% \][/tex]

Yes, it does.

So, the experimental probability of catching pink salmon is [tex]\(22\%\),[/tex]yellowfin tuna is[tex]\(32\%\)[/tex], and bluegill is [tex]\(46\%\).[/tex]

Complete question;

What is the probability of selecting each type of fish in an experimental study when the total frequency of fish sampled is 50? The types of fish sampled are pink salmon, yellowfin tuna, and bluegill. The frequencies of each fish type are 11, 16, and 23 respectively.

Answer:

C) cos²(theta)

Step-by-step explanation:

csc(X) = 1/sin(X)

cos(-X) = cos(X)

tan(-X) = -tan(X)

cot(-X) = -1/tan(X) = -cos(X)/sin(X)

[cos(X) × -cos(X)/sin(X)] ÷ -1/sin(X)

-cos²(X)/sin(X) × -sin(X)

cos²(X)

Answer:

x = 3 , y = 0

Step-by-step explanation:

Solve the following system:

{y = (2 x)/3 - 2 | (equation 1)

y = 3 - x | (equation 2)

Express the system in standard form:

{-(2 x)/3 + y = -2 | (equation 1)

x + y = 3 | (equation 2)

Swap equation 1 with equation 2:

{x + y = 3 | (equation 1)

-(2 x)/3 + y = -2 | (equation 2)

Add 2/3 × (equation 1) to equation 2:

{x + y = 3 | (equation 1)

0 x+(5 y)/3 = 0 | (equation 2)

Multiply equation 2 by 3/5:

{x + y = 3 | (equation 1)

0 x+y = 0 | (equation 2)

Subtract equation 2 from equation 1:

{x+0 y = 3 | (equation 1)

0 x+y = 0 | (equation 2)

Collect results:

Answer: {x = 3 , y = 0

To solve the given system of equations, we can use the method of substitution. After obtaining the value of x, we can substitute it back into one of the original equations to solve for y. The solution to the system is x = 3 and y = 0.

The given system of equations is:

y = \frac{2}{3}x - 2

y = -x + 3

To solve this system, we can use the method of substitution. We can rearrange the second equation to solve for y:

y = -x + 3

Now, substitute this value of y into the first equation:

\frac{2}{3}x - 2 = -x + 3

Add x to both sides:

\frac{2}{3}x + x - 2 = 3

Multiply both sides by 3 to eliminate the fraction:

2x + 3x - 6 = 9

Combine like terms:

5x - 6 = 9

Add 6 to both sides:

5x = 15

Divide both sides by 5:

x = 3

Now, substitute the value of x back into one of the original equations to solve for y:

y = -x + 3

y = -3 + 3

y = 0

Therefore, the solution to the system of equations is x = 3 and y = 0.

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