Question 1 of 10
In the ellipse shown below, each point marked with a dot is called a(n)
A. vertex
B. axis
O c. center
OD. focus

Question 1 Of 10In The Ellipse Shown Below, Each Point Marked With A Dot Is Called A(n)A. VertexB. AxisO

Answers

Answer 1

In the ellipse shown below, each point marked with a dot is called a(n)  focus

What is a focus in an ellipse

In an ellipse, the focus (plural: foci) is a pair of special points that play a significant role in defining the shape of the ellipse. The focus points are located inside the ellipse along the major axis, which is the longer axis of the ellipse.

The defining property of an ellipse is that the sum of the distances from any point on the ellipse to the two foci is constant. This property is known as the "focus-directrix property."

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Related Questions

Luther bought a snack pack of crackers, and he thinks it's interesting that the cylindrical
tower of crackers came in a box shaped like a square prism. He wonders how much extra
space the box contains around the cracker tower. The box has a height of 8 inches and a side
length of 2 inches. If the tower of crackers has a height of 7.9 inches and a diameter of
1.9 inches, what is the volume of the extra space in the box?
Round your answer to the nearest tenth.

Answers

The volume of the extra space in the box is 9.0 cubic inches.

How to estimate the volume of the extra space in the box?

To estimate the volume of the extra space in the box, we shall find the difference between the volume of the box and the volume of the cracker tower.

First, volume of the box:

The volume can be calculated as the product of the height, length, and width (we assume the width is the same as the side length since it is a square prism):

Box volume = height * length * width

Given:

height = 8 inches

side length = 2 inches

Box volume = 8 * 2  * 2

= 32  in³

Next, the volume of the cracker tower:

The tower of the cracker is cylindrical, so we shall use the formula for the volume of a cylinder to estimate the volume:

Tower volume = π * (radius²) * height

Given:

height = 7.9 inches

diameter = 1.9 inches

radius = diameter / 2 = 1.9  / 2 = 0.95

Tower volume = π * (0.95)² * 7.9

≈ 22.994 in³ (rounded to three decimal places)

Then, the volume of the extra space in the box:

Volume of the extra space = Tower volume - Box volume:

= 32 in³ - 22.994 in³

≈ 9.006 in³ (rounded to three decimal places)

Therefore, the volume of the extra space in the box = 9.0 in³.

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43% of a sample of 100 visitors to a national park believes that additional funds should be used to preserve endangered species. What is the 95% confidence interval to describe the total percentage of national park visitors who support supporting endangered species?

Answers

The 95% confidence interval for the total percentage of national park visitors who support supporting endangered species is approximately 33.3% to 52.7%.

To calculate the 95% confidence interval for the percentage of national park visitors who support supporting endangered species, we can use the formula:

Confidence Interval = Sample proportion ± (Critical value * Standard error)

Given that 43% of a sample of 100 visitors believe that additional funds should be used to preserve endangered species, the sample proportion is 0.43.

To calculate the standard error, we use the formula:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size. In this case, p = 0.43 and n = 100.

Standard Error = sqrt((0.43 * (1 - 0.43)) / 100) ≈ 0.0495

The critical value for a 95% confidence interval can be obtained from a standard normal distribution table. For a 95% confidence level, the critical value is approximately 1.96.

Now we can calculate the confidence interval:

Confidence Interval = 0.43 ± (1.96 * 0.0495)

Confidence Interval = 0.43 ± 0.097

The lower bound of the confidence interval is 0.43 - 0.097 = 0.333

The upper bound of the confidence interval is 0.43 + 0.097 = 0.527

Therefore, the 95% confidence interval for the total percentage of national park visitors who support supporting endangered species is approximately 33.3% to 52.7%.

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Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?

Type the correct number below without the dollar sign.

Answers

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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Find the inverse for: f(x) = 2x^2-3

Answers

Unless we restrict its domain, a quadratic function doesn't have the inverse.

Please help me solve the following using y=mx+b
The table below models a particular physical situation.
x −8, -2, 1, 8
y 5, −9, −2, 4

Find the piecewise linear equation that models the data above.

y =____ x + −8 ≤ x ≤ −2
y= ____ x + −2 < x ≤ 1
y= _____ x + 1 < x ≤ 8

Answers

Answer:

  see below

Step-by-step explanation:

You want the piecewise function that gives straight line segments between domain boundary points (-8, 5), (-2, -9), (1, -2), (8, 4).

Slope

The two-point equation for the slope of a line is ...

  m = (y2 -y1)/(x2 -x1)

For the first pair of points, the slope is ...

  m = (-9 -5)/(-2 -(-8)) = -14/6 = -7/3

The attached calculator image shows the computation of slope for the other two segments. Those slopes are 7/3 and 6/7.

Y-intercept

The slope-intercept form of the equation for a line can be rearranged to give the y-intercept:

  y = mx + b

  b = y - mx

In the attached, we used the (x1, y1) point for each segment. For the first segment, the y-intercept is ...

  b = 5 -(-7/3)(-8) = -41/3

The other two y-intercepts are computed to be -13/3 and -20/7.

Slope-intercept function

The piecewise function that models the given data is ...

  [tex]\boxed{y=\begin{cases}-\dfrac{7}{3}x-\dfrac{41}{3}\quad&-8\le x\le-2\\\\\dfrac{7}{3}x-\dfrac{13}{3}\quad&-2 < x\le1\\\\\dfrac{6}{7}x-\dfrac{20}{7}\quad&1 < x\le8\end{cases}}[/tex]

__

Additional comment

There is nothing in this problem statement that requires the function be continuous. However, we have made it so this function is continuous in the region where it is defined.

The same repetitive computations are handled nicely by a spreadsheet.

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The assets and liabilities of a 22-year-old recent college graduate are listed below.


Furniture $4,091
Car Loan $6,060
Credit Card Balances $3,940
Savings Account Balance $2,143
Student Loans $29,400
Car Value $21,500
Equipment $4,805


The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off $25,000 in student loan debt. What is the college graduate's new net worth?
$11,309
$14,400
$23,643
$28,139

Answers

The net worth of an individual is calculated as the difference between their total assets and their total liabilities.

Before the signing bonus and student loan payment, the net worth of the college graduate can be calculated as:

Net worth = (Furniture + Car Value + Equipment + Savings Account Balance) - (Car Loan + Credit Card Balances + Student Loans)

Net worth = ($4,091 + $21,500 + $4,805 + $2,143) - ($6,060 + $3,940 + $29,400)

Net worth = $32,539 - $39,400

Net worth = -$6,861

This means that the college graduate has a negative net worth before the signing bonus and student loan payment.

After the signing bonus and student loan payment, the new net worth can be calculated as:

New net worth = (Furniture + Car Value + Equipment + Savings Account Balance + Signing Bonus) - (Car Loan + Credit Card Balances + Student Loans - Student Loan Payment)

New net worth = ($4,091 + $21,500 + $4,805 + $2,143 + $10,000) - ($6,060 + $3,940 + $29,400 - $25,000)

New net worth = $42,539 - $14,400

New net worth = $28,139

Therefore, the college graduate's new net worth is $28,139. The answer is option (D).

The value 37 is a solution for the equation 3√√2 sece +7 = 1.
A. True
B. False

Answers

The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.

Given an equation,

3√2 sec θ + 7 = 1

We have to find that whether 3π/4 is a solution for the given equation or not.

Solving the given equation, we get,

3√2 sec θ + 7 = 1

3√2 sec θ = 1 - 7

3√2 sec θ = -6

sec θ = -6 / 3√2

sec θ = -2 / √2

sec θ = -√2

Now, we know that, sec θ = 1/ cos θ

So the equation becomes,

1/ cos θ = -√2

cos θ = -1/√2

Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.

cos 3π/4 =  cos (π - π/4) = -cos (π/4) = -1/√2

So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.

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find exact value sin 9pie/ 4

Answers

The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

We have to given that;

Expression to find exact value is,

⇒ sin 9π/4

Now, WE can change it into degree as,

⇒ 9π/4

⇒ 9 × 180 / 4

⇒ 9 × 45

⇒ 405 degree

Hence, We get;

⇒ sin 9π/4

⇒ sin 405°

⇒ sin (360 + 45°)

⇒ sin 45°

⇒ 1 / √2

Thus, The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

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A normal distribution has a mean of 137 and a standard deviation of 6. Find the z-score for a data value of 155.

Round to two decimal places

Answers

Answer:

3

Step-by-step explanation:

To find the z-score for a data value of 155 in a normal distribution with a mean of 137 and a standard deviation of 6, you can use the formula:

z = (x - μ) / σ

where:

x is the data value,

μ is the mean, and

σ is the standard deviation.

Plugging in the values, we have:

z = (155 - 137) / 6

Calculating this expression:

z = 18 / 6 = 3

Emma runs 12km

Cycles 26km

Running speed X km/m

Cycling speed 10km/hr faster than running speed

Total time taken 22 hrs and 48 minutes

An expression for time in hrs he takes to run 12km is 12/x

Show time of x for the total time he takes in hrs

Answers

The value of x in the expression is 66/114.

Let's begin by addressing the issue in detail:

Emma runs 12 km, hence the time it takes her to complete that distance is 12/x hours.

Emma cycles 26 kilometers at a speed that is 10 kilometers per hour faster than she runs.

Her cycling pace is therefore (x + 10) km/hr. Her cycle distance is 26 kilometers, which can be calculated as 26/(x + 10) hours.

Emma's total time spent cycling and running is 22 hours and 48 minutes. By dividing 48 minutes by 60, we can translate it to hours: 48/60 = 0.8 hours.

We can now formulate an equation to express the entire amount of time spent:

12/x + 26/(x + 10) = 22.8

To get rid of the denominators and solve this equation, multiply both sides by x(x + 10).

12(x + 10) + 26x = 22.8x(x + 10)

To make the calculation easier:

12x + 120 + 26x = 22.8x² + 228x

Combining comparable phrases

38x + 120 = 22.8x² + 228x

Changing the equation's order:

22.8x² + 228x - 38x - 120 = 0

22.8x² + 190x - 120 = 0

By dividing the equation by 0.4, the coefficients are made simpler:

57x² + 475x - 300 = 0

Solving the equation by x = (-b ± √(b² - 4ac)) / (2a),

x = (-475 ± √(475² - 4 * 57 * -300)) / (2 * 57)

Simplifying further:

x = (-475 ± √(225625 + 68400)) / 114

x = (-475 ± √293025) / 114

x = (-475 ± 541) / 114

Now, we can calculate the two possible solutions:

x₁ = (-475 + 541) / 114

x₁ = 66 / 114

x₁ ≈ 0.579

x₂ = (-475 - 541) / 114

x₂ = -1016 / 114

x₂ ≈ -8.912

Take x = 66/114

Hence the value of x in the expression is 66/114.

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factored form of 12a-b​

Answers

The factored form of the expression 12a - b is simply 12a - b.

We have,

The concept used in the expression 12a - b is that of combining like terms. When we have an algebraic expression like this, the goal is typically to simplify or rewrite it in a more concise form.

In this case, 12a and -b are two terms in the expression.

The concept of combining like terms allows us to combine these terms together if they have the same variable(s) raised to the same power(s).

The expression 12a - b cannot be factored further using simple algebraic techniques.

Factoring typically involves breaking down an expression into its constituent factors, such as common factors or binomial factors.

However, in the case of 12a - b,

There are no common factors or binomial factors that can be extracted.

Therefore,

The factored form of the expression 12a - b is simply 12a - b.

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8. mVWY =
Segment AB and segment AD are both tangent to circle C. Find x.
Need 7-9 pls show work. Will mark you branliest

Answers

The tangent from the external point are equal, so the x value is 3 units.

7) The measure of the arc XW is 180-105=75

8) The measure of the arc VWY is 105+75+85 = 265

9) We know that, tangent from the external point are equal

In circle C, AB=AD

26=8x+2

8x=24

x=24/8

x=3 units

10) 9x-3=7x+5

9x-7x=5+3

2x=8

x=8/2

x=4

Therefore, the tangent from the external point are equal, so the x value is 3 units.

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sett up 12-5*9√49-5²​

Answers

Answer:
-328

Step-by-step explanation:

Simply use BODMAS or BIDMAS; this is the order of your operations. It is an acronym that tells you what to do in what order

Brackets: there are no brackets, move on to indices/order

Indices/Order: for the first step, do 5^2, which is 25, and √49, which is 7. The equation is no 12-5*9(7)-25

Division/Multiplication: For this step, multiply 5, 9 and 7 to get 315. The equation is now 12-315-25

Addition/subtraction: For the final step, just solve 12-315-25 in the traditional left to right way, which is -328.


I have grouped addition and subtraction as well as division and multiplication together because they are done at the same time; if a question has either both addition and subtraction or division and multiplication, just solve these parts from left to right. Division is not superior to multiplication and, likewise, addition is not above subtraction.


Warm-Up
What is the approximate area of the shaded region?
Select the correct answer.
O 15.45 cm²
O69.53 cm²
128.54 cm²
18 cm
182.47 cm²
4

Answers

Answer:

shaded area ≈ 69.53 cm²

Step-by-step explanation:

the shaded area (A) is calculated as

A = area of square - area of circle

area of square = 18² = 324

area of circle = πr² ( r is the radius )

the diameter of the circle = 18 , so r = 18 ÷ 2 = 9

area of circle = π × 9² = 81π

then

A = 324 - 81π ≈ 69.53 cm² ( to 2 decimal places )


Identify the new coordinates of polygon
ABCD after a translation of 2 units down
and 3 units right.
A. A "(-6, -5)
B. D'(2,-5)
C. C (2.0)
D. D(5,-5)
E. C'(-1,0)
F. A (-3,-5)
G. B'(-5, 0)
H. B (-2, 0)
Please help

Answers

The translated coordinates are:

A: A'(-6, -5)  ⇒ A''(-3,-7)

B:  D'(2,-5)  ⇒  D''(8, -7)

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

Here,

We have to apply a translation of 2 units down and 3 units right to these coordinates.

Translation means moving the entire polygon in a particular direction by a certain distance.

To apply the translation,

Add the same amount of distance to the x-coordinate of each vertex for the rightward motion, and subtract the same amount of distance from the y-coordinate of each vertex for the downward motion.

In this case,

the translation is 2 units down and 3 units right.

So the new coordinates will be:

A: A'(-6, -5) ⇒ A'( -6+ 3, -5-2)

              = A''(-3,-7)

B:  D'(2,-5)  ⇒ D'(5+3, -5 -2 )

                  = D''(8, -7)

Similarly apply for each coordinates we get,

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

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In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class.

Answers

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

[tex]\Huge \boxed{\bold{\text{12 Boys}}}[/tex]

[tex]\Huge \boxed{\bold{\text{30 Girls}}}[/tex]

Step-by-step explanation:

Let the number of girls be [tex]g[/tex] and the number of boys be [tex]b[/tex].

According to the problem: [tex]b = \frac{2}{5} \times g[/tex]

We also know that the total number of students is 42, so [tex]b + g = 42[/tex].

Now, we have two equations with two variables:

 [tex]b = \frac{2}{5} \times g[/tex]  [tex]b + g = 42[/tex]

We can solve these equations to find the values of [tex]b[/tex] and [tex]g[/tex].

Step 1: Solve for [tex]\bold{b}[/tex] in terms of [tex]\bold{g}[/tex]

From the first equation, we have[tex]b = \frac{2}{5} \times g[/tex]

Step 2: Substitute the expression for [tex]\bold{b}[/tex] into the second equation

Replace [tex]b[/tex] in the second equation with the expression we found in step 1.

[tex]\frac{2}{5} \times g + g = 42[/tex]

Step 3: Solve for [tex]\bold{g}[/tex]

Now, we have an equation with only one variable, [tex]g[/tex]:

[tex]\frac{2}{5} \times g + g = 42[/tex]

To solve for [tex]g[/tex], first find a common denominator for the fractions:

[tex]\frac{2}{5} \times g + \frac{5}{5} \times g = 42[/tex]

Combine the fractions:

[tex]\frac{7}{5} \times g = 42[/tex]

Now, multiply both sides of the equation by [tex]\frac{5}{7}[/tex] to isolate [tex]g[/tex]:

[tex]g = 42 \times \frac{5}{7}[/tex][tex]g = 30[/tex]

Step 4: Find the value of [tex]\bold{b}[/tex]

Now that we have the value of [tex]g[/tex], we can find the value of [tex]b[/tex] using the first equation:

[tex]b = \frac{2}{5} \times g[/tex][tex]b = \frac{2}{5} \times 30[/tex][tex]b = 12[/tex]

So, there are 12 boys and 30 girls in the class.

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help it’s past due and i have a test on it tomorrow

Answers

Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.

Stay calm: It's important to remain calm and composed to think clearly and make the best use of your time.

Prioritize: Assess the situation and determine the importance of each task. Focus on completing the task that is past due first.

Communicate: If possible, reach out to your teacher or professor and explain the situation. Apologize for the delay and request an extension or an opportunity to make up the assignment or test.

Allocate time: Allocate dedicated time to work on the overdue task. Break it down into smaller, manageable parts to make it less overwhelming.

Seek help: If you're struggling with the task or need clarification, reach out to classmates, friends, or online resources for assistance. Don't hesitate to ask for help when you need it.

Plan your study time: Make a study schedule for the test that you have tomorrow. Allocate sufficient time for each subject or topic, focusing on areas that require more attention.

Review efficiently: Prioritize the key concepts, formulas, or theories that are likely to be covered in the test. Use active studying techniques such as summarizing, creating flashcards, or teaching the material to someone else.

Take breaks: While it's important to work efficiently, don't forget to take short breaks to rest and recharge. Breaks can help improve focus and prevent burnout.

positive: Maintain a positive mindset and believe in your ability to overcome challenges. Negative thoughts can hinder your productivity and performance.

Learn from the experience: Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.

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Evaluate : 3² x (-2)³ x 5 Working out:​

Answers

Answer: 180

Step-by-step explanation:

Use the order of operations: PEMDAS

Parenthesis

Exponents

Multiplication/Division

Addition/Subtraction

3² x (-2)³ x 5               >There is nothing to simplify within parenthesis

                                   >Exponents are next in Order of Operations

(3)(3) x (-2)(-2) x 5       >This is the exponents expanded

9 x 4 x 5                      >Multiply from left to right

36 x 5

180

How do i do this problem liek i have to find a side?

Answers

Answer:

[tex]\overline{LP}=77[/tex]

Step-by-step explanation:

Given [tex]\Delta LMQ\sim\Delta LNP[/tex], then [tex]\overline{LN}=\overline{LM}+\overline{MN}=8+14=22[/tex]. This will help us find [tex]\overline{LQ}[/tex] since we know the length of [tex]\overline{QP}[/tex]:

[tex]\displaystyle \frac{\overline{LM}}{\overline{LM}+\overline{MN}}=\frac{\overline{LQ}}{\overline{LQ}+\overline{QP}}\\\\\frac{8}{8+14}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\\frac{8}{22}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\8(\overline{LQ}+49)=22\overline{LQ}\\\\8\overline{LQ}+392=22\overline{LQ}\\\\392=14\overline{LQ}\\\\28=\overline{LQ}[/tex]

Therefore:

[tex]\overline{LP}=\overline{LQ}+\overline{QP}=28+49=77[/tex]

find the general term of the arithmetic sequence if a8=8, a20=44

Answers

Answer:

[tex]a_n=3n-16[/tex]

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d\\\\a_8=a_1+(8-1)d\rightarrow 8=a_1+7d\\a_{20}=a_1+(20-1)d\rightarrow 44=a_1+19d[/tex]

[tex]-36=-12d\\3=d[/tex]

[tex]8=a_1+7(3)\\8=a_1+21\\-13=a_1[/tex]

[tex]a_n=-13+(n-1)(3)\\a_n=-13+3n-3\\a_n=3n-16[/tex]

Solving a word problem using a system of linear equations of th.. One month Alan rented 5 movies and 2 video games for a total of $21. The next month he rented 3 movies and 8 video games for a total of $50. Find the

rental cost for each movie and each video game.

Answers

Answer: The rental cost of each movie is $2 and each video game is approximately $5.5

Step-by-step explanation:

Let's assume the rental cost per movie is "m" and the rental cost per video game is "v". We can set up a system of linear equations based on the given information.

From the first month:

5m + 2v = 21 ----(1)

From the second month:

3m + 8v = 50 ----(2)

To solve the system of equations:

5m + 2v = 21 ----(1)

3m + 8v = 50 ----(2)

We can multiply equation (1) by 4 to make the coefficients of "m" the same:

4(5m + 2v) = 4(21)

20m + 8v = 84 ----(3)

Now, subtract equation (2) from equation (3):

(20m + 8v) - (3m + 8v) = 84 - 50

20m - 3m + 8v - 8v = 34

17m = 34

Divide both sides of the equation by 17:

m = 34 / 17

m = 2

Now that we have the value of "m," we can substitute it back into either equation (1) or (2) to solve for "v." Let's use equation (1):

5(2) + 2v = 21

10 + 2v = 21

2v = 21 - 10

2v = 11

v = 11 / 2

v = 5.5

Therefore, the solution to the system of equations is:

m = 2 and v = 5.5

Need to figure out how to solve this one. TIA

Answers

All the slopes of tables are,

13) m = 2

14) m = - 1/1

15) m = 0

16) m = 3

17) m = infinite

18) m = - 1/3

We have to given that;

All the tables are shown.

And, To find the slope of all the table.

Since, We know that;

Slope passing through the points (x₁ , y₁) and (x₂, y₂) is defined as,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, We get;

13) Two points are (- 2, - 3) and (- 1, - 1)

Hence, Slope is,

m = (- 1 + 3) / (- 1 + 2)

m = 2/1

m = 2

14) Two points are (- 4, 6) and (0, 4)

Hence, Slope is,

m = (4 - 6) / (0 + 4)

m = - 2/4

m = - 1/2

15) Two points are (6, 2) and (3, 2)

Hence, Slope is,

m = (2 - 2) / (3 - 6)

m = 0

16) Two points are (- 2, - 3) and (0, 3)

Hence, Slope is,

m = (3 + 3) / (0 + 2)

m = 6/2

m = 3

17) Two points are (3, 6) and (3, 4)

Hence, Slope is,

m = (4 - 6) / (3 - 3)

m = infinite

18) Two points are (- 4, 4) and (- 1, 3)

Hence, Slope is,

m = (3 - 4) / (- 1 + 4)

m = - 1/3

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A shop has jars of strawberry jam and raspberry jam in the ratio 3:1
Two customers come into the shop and randomly select a jar of jam
to purchase.

The probability that both customers select strawberry jam is 11/20

a) How many jars of jam does the shop have initially?

b) Given that the customers both chose the same type of jam, work
out the probability that they both chose strawberry.

Answers

The shop initially has 0.884 jars of jam

The probability that both customers chose strawberry jam, is 0.25.

a) Let's assume the number of jars of strawberry jam is 3x and the number of jars of raspberry jam is x.

So, the total number of jars of jam in the shop is 3x + x = 4x.

According to the given information, the probability that both customers select strawberry jam is 11/20.

So, the probability of the first customer selecting a jar of strawberry jam = (3x/4x) = 3/4,

and the probability of the second customer

=  ((3x-1)/(4x-1)).

Now, (3/4) ((3x-1)/(4x-1)) = 11/20

(3/4) ((3x-1)/(4x-1)) = 11/20

20(3/4) ((3x-1)/(4x-1)) = 11

15 (3x-1) = 44  (4x-1)

45x - 15 = 176x - 44

176x - 45x = 44 - 15

131x = 29

x ≈ 29/131

Therefore, the value of x is 0.221

To find the initial number of jars of jam in the shop, we can substitute this value of x into the equation:

4x =  0.884

b) The probability of the first customer selecting strawberry jam is

= (3x)/(4x)

= 3/4.

Therefore, the probability that both customers chose strawberry jam is:

= (3/4) x ((3x-1)/(4x-1))

= (3/4)  ((3 x 0.221 - 1)/(4 x 0.221 - 1))

= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))

≈ 0.25

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Work out the area of this circle.
Give your answer in terms of and state its units.
TC
14 cm

Answers

Answer:

49pi cm^2

Step-by-step explanation:

The area of a circle is pi(r)^2

To find our radius, we need to divide the diameter by 2.

14 / 2 = 7

Lets plug that into our equation:

pi(7)^2

Simplify:

pi(49)

rearrange:

49pi

WAIT, we need units!

49pi cm^2

~~~Harsha~~~

What is the volume of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
--
10 yd
9 yd

Answers

The volume of the given cylinder is 2543 cubic yards.

For the given cylinder,

Height of the cylinder  = 10 yard

Radius of cylinder = 9 yard yard

Then we have to calculate the volume of this cylinder.

Since we know that,

Volume of the cylinder  = πr²h

Where,

r represents radius of cylinder = 9 yard

h represents height of cylinder = 10 yard

Noe therefore,

Volume of the cylinder = π(9)²(10)

                                       = 3.14x 81 x 10

                                       = 2543 cubic yards

Thus,

⇒ Volume = 2543 cubic yards.

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School administrators asked a group of students and teachers which of two school logo ideas, logo A or logo B, they prefer. This table shows the results.
Students
Teachers
Total
Logo A
84
21
105
Logo B
16
4
20
Total
100
25
125
Are being a student and preferring logo A independent events?
Why or why not?
• A. No, they are not independent, because P(student) = 0.8 and
P(student | logo A) = 0.8.
• B. No, they are not independent, because P(student) = 0.8 and
P(student logo A) = 0.84.
• C. Yes, they are independent, because P(student) = 0.8 and
P(student logo A) = 0.84.
O D. Yes, they are independent, because P(student) = 0.8 and
P(student | logo A) = 0.8.

Answers

The statement, yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

To determine if being a student and preferring logo A are independent events, we need to compare the probabilities of these events occurring.

The probability of being a student, denoted as P(student), is given as 0.8. This means that out of the total population (125), 80% are students.

The probability of a student preferring logo A, denoted as P(student | logo A), is given as 0.8.

This means that out of the students (100), 80% prefer logo A.

If the events of being a student and preferring logo A are independent, then the probability of a student preferring logo A (P(student | logo A)) should be the same as the probability of being a student (P(student)).

However, in the given options, both options A and D state that P(student | logo A) = 0.8, which is the same as P(student).

This suggests that being a student and preferring logo A are independent events.

Hence, Yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

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1/8 of the cans in George‘s pantry are vegetables. 1/3 of the cans in George’s pantry are soup what fraction of the cans in George’s pantry are either soup or vegetables?

Answers

The fraction of the cans in George’s pantry which are either soup or vegetables is 11/24.

What fraction of the cans in George’s pantry are either soup or vegetables?

Fraction of cans in George‘s pantry that are vegetables = 1/8

Fraction of cans in George‘s pantry that are soups = 1/3

Fraction of the cans in George’s pantry which are either soup or vegetables = 1/3 + 1/8

= (8+3) /24

= 11/24

Hence, 11/24 is the fraction of the cans in George’s pantry that are either soup or vegetables.

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Can some one help me with this please

Answers

A) Area of figure is,

⇒ A = 3π (3 + √73) + 4.5π

B) Area of figure is,

A = 89 feet²

We can simplify as;

A) In figure A,

It is make with one cone and one semicircle.

Hence, Area of cone is,

A = πr (r + √h² + r²)

A = π × 3 (3 + √8² + 3²)

A = 3π (3 + √64 + 9

A = 3π (3 + √73)

And, Area of semicircle is,

⇒ A = 1/2 (π × 3²)

⇒ A = 4.5π

Hence, Total area is,

⇒ A = 3π (3 + √73) + 4.5π

B) Figure B is make with a trapezoid and triangle.

Area of trapezoid is,

A = 1/2 (7 + 13) × 5

A = 20 × 5 / 2

A = 50 feet²

And, Area of triangle is,

A = 1/2 × 6 × 13

A = 39 feet²

Hence, We get;

Area of figure is,

A = 50 + 39

A = 89 feet²

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a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

We have,

a)

The composite figure has a cone and a semicircle.

So,

Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³

Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²

b)

The composite figure has a trapezium and a triangle.

Area of the trapezium

= 1/2 x ( sum of the parallel side) x h

= 1/2 x (7 + 13) x 5

= 1/2 x 20 x 5

= 10 x 5

= 50 ft³

Area of the triangle.

= 1/2 x base x height

= 1/2 x 6 x 8

= 3 x 8

= 24 ft²

Thus,

a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

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How do you determine a the coordinates


Answers

To identify the x-coordinate of a point on a graph, read the number on the x-axis directly above or below the point. To identify the y-coordinate of a point, read the number on the y-axis directly to the left or right of the point. Remember, to write the ordered pair using the correct order (x,y) .

La ganancia obtenida después de t años de
haber realizado una inversión inicial de
$1.000.000 está dada por la expresión:
1.000.000 × 2t
¿Qué representa el número 2 en la
expresión anterior?
A)las ganancias obtenidas en el segundo año
B)las ganancias obtenidas en el último año
C) que cada nuevo año las ganancias se reducen a la mitad
D) que cada nuevo año las ganancias se duplican con respecto al año anterior

Answers

In the given expression, "2" represents that each new year the profits double with respect to the previous year. So the correct answer is D) that each new year the profits double with respect to the previous year.

How to explain the expression

In the given expression, the variable "t" represents the number of years that have passed since the initial investment was made. The expression 1,000,000 × 2t calculates the profit obtained after "t" years.

Therefore, the correct answer is D) that each new year the profits double with respect to the previous year.

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The profit obtained after t years of

have made an initial investment of

$1,000,000 is given by the expression:

1,000,000 × 2t

What does the number 2 represent in the

previous expression?

A) the profits obtained in the second year

B) the profits obtained in the last year

C) that every new year the profits are cut in half

D) that each new year the profits double with respect to the previous year

Mis disculpas por la respuesta anterior, cometí un error en la explicación. La respuesta correcta es la opción D. La expresión 1.000.000 × 2t indica que cada nuevo año las ganancias se duplican con respecto al año anterior.

                                                                                     En la expresión, el número 2 indica que las ganancias se duplican cada año con respecto al año anterior. La expresión 1.000.000 × 2t significa que la inversión inicial de un millón de dólares se multiplica por 2 elevado a la potencia de t, donde t es el número de años que han pasado.Cuando t=1, se refiere al primer año después de la inversión, y la ganancia sería 1.000.000 dividido por 2=1, es decir, dos millones. Esto significa que las ganancias del segundo año (opción A) serían de 2.000.000 de dólares.En general, las ganancias del año anterior se duplican cada año subsiguiente. Por lo tanto, la D es la opción correcta porque significa que las ganancias se duplican cada año con respecto al año anterior.

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