Does this graph represent a function?
-3
-2 -1
-1
OA. No, because some of the y-values are paired with two x-values
OB. Yes, because it touches the y-axis exactly one time
OC. No, because there are no closed circles to show where the graph
ends
O D. Yes, because each x-value has exactly one corresponding y-value
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Does This Graph Represent A Function?-3-2 -1-1OA. No, Because Some Of The Y-values Are Paired With Two

Answers

Answer 1

The correct option is,

D. Yes, because each x-value has exactly one corresponding y-value

We have to given that,

The graph of a quadratic equation is shown in image.

Since, We know that,

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable (the dependent variable).

Now, When we apply Vertical line test on the graph.

We get;

Each x-value has exactly one corresponding y-value.

Therefore, The graph of equation is function because each x-value has exactly one corresponding y-value.

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Related Questions

The front view of a podium is shown. Bryan wants to paint the front of the podium blue. He decomposed the shape into two triangles and a rectangle to find the area.

Which are the correct steps to find the area of the front of the podium?

Answers

To find the area of the front of the podium add the area of two triangle and one rectangle.

To find the area of the front of the podium by decomposing it into two triangles and a rectangle, you can follow these steps:

Measure the dimensions: Measure the necessary dimensions of the triangles and rectangle. Typically, you would need to measure the base and height of each triangle and the length and width of the rectangle.

Calculate the area of each shape: Use the appropriate formulas to calculate the area of each shape.

The formula for the area of a triangle is (1/2) x base x height,

and for a rectangle, it is length x width.

Sum up the areas: Add up the areas of the two triangles and the rectangle to find the total area of the front of the podium.

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The table shows the average number of miles traveled per person in the United
States for different years.
Year 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005
Average
miles
traveled 194 1056 1796 1788 3650 4569 6147 7460 9099 10,181
per
person
Use the Desmos graphing calculator to find the quadratic regression equation using
the years since 1900 for the input variable, and the average number of miles for the
output variable. Round each coefficient in the equation to the nearest thousandth.
Using your regression equation with rounded values, what is the best estimate for
the average number of miles traveled per person in 1961?
1001

Answers

Answer: 4191

Step-by-step explanation: i took the quiz

The estimated average number of miles traveled per person in 1961 is approximately 4567 miles.

The given table is

Year    1915   1925   1935   1945   1955   1965   1975   1985   1995   2005

Average

miles  194     1056   1796   1788   3650   4569   6147   7460   9099  10,181

traveled

The equation for the linear regression is:

y = -211.902x² + 779.914x - 8742.14

To estimate the average number of miles traveled per person in 1961, we use the equation with the input value of 61 (1961 since 1900):

y = -211.902(61)² + 779.914(61) - 8742.14

y ≈ 4567 miles

Therefore, the estimated average number of miles traveled per person in 1961 is approximately 4567 miles.

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A school supervisor wants to determine the percentage of students that bring their lunch to school. What method would assure random selection of a sample population?

Answers

To assure the random selection of a sample population for determining the percentage of students who bring their lunch to school, a method known as simple random sampling can be employed.

Simple random sampling is a technique that provides each member of the population an equal chance of being selected for the sample. Here's an explanation of how simple random sampling can be implemented in this scenario:

Define the population: The school supervisor needs to clearly define the population of interest, which would be all the students in the school.Assign a unique identifier: Each student should have a unique identifier, such as a student ID number, to differentiate them from one another.Generate a sampling frame: A sampling frame is a list of all the unique identifiers of the students. This could be obtained from the school's records or databases.Determine the sample size: The school supervisor needs to decide on the desired sample size, ensuring it is representative of the population while being practical to manage.Use a random selection method: Employ a random selection method, such as using a random number generator or a random number table, to select the required number of unique identifiers from the sampling frame.Contact selected students: Once the sample has been selected, the chosen students can be contacted to participate in the survey or data collection regarding whether they bring their lunch to school.

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An expression is given 42r3s2 - 35r2s3 which expression is equivalent

Answers

The given expression is:

42r^3s^2 - 35r^2s^3

To find an equivalent expression, we can factor out the common terms, r^2s^2, from both terms:

42r^3s^2 - 35r^2s^3 = r^2s^2(42r - 35s)

Therefore, an equivalent expression is r^2s^2(42r - 35s).

Geometry Section 5BC/School Year/Week 30/Day 148
1. For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your re
Part B, and Part C.
Use the figure below to answer the following questions.
R
Type here to search
O
Ħi
PREVIOUS 1 of 23
NEXT
A44

Answers

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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An artist paints a mural that measures 25 feet by 18 feet. The artist adds a border around the mural that increases the total area to 588 square feet. The area of the mural and border is modeled by the given equation, where x represents the width of the border.
(25 + 2x) (18 + 2x) = 588
What is the width, in feet, of the border?

Answers

The width, in feet, of the border is,

⇒ x = 1.5 feet

We have to given that,

An artist paints a mural that measures 25 feet by 18 feet. The artist adds a border around the mural that increases the total area to 588 square feet.

Here, The area of the mural and border is modeled by the given equation,

⇒ (25 + 2x) (18 + 2x) = 588

where x represents the width of the border.

Now, WE can simplify as,

⇒ (25 + 2x) (18 + 2x) = 588

⇒ 450 + 50x + 36x + 4x² = 588

⇒ 4x² + 86x + 450 - 588 = 0

⇒ 4x² + 86x - 138 = 0

⇒ 2x² + 43x - 69 = 0

⇒ x = (- 43 ± √43² - 4×2×- 69) / 2×2

⇒ x = (- 43 ± √1849 + 552) / 4

⇒ x = (- 43 ± 49) / 4

This gives two solution,

⇒x = (- 43 + 49) / 4

⇒ x = 6/4

⇒ x = 3/2

⇒ x = ( -43 - 49) / 4

⇒ x = - 92 / 4

⇒ x = - 23

Since, Width is never negative.

Hence, the width, in feet, of the border is,

⇒ x = 1.5 width

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Terri and mary ellen are members of the drama club at school who are participating in a candy bar fundraiser for a club trip,. Terri sold 9 fewer candy bars this week thsn dhe did last week. She sold 4 times as many candy bars as mary ellen this week. Mary ellen was only able to sell 25 candy bars this week. How many candy bars did mary and terri sell last week

Answers

Let's assume that Terri sold "x" candy bars last week.

According to the given information, Terri sold 9 fewer candy bars this week than she did last week. So, this week Terri sold (x - 9) candy bars.

It is also mentioned that Terri sold 4 times as many candy bars as Mary Ellen this week, and Mary Ellen sold 25 candy bars. Therefore, Terri sold 4 * 25 = 100 candy bars this week.

Since Terri sold (x - 9) candy bars this week, we can set up the equation:

x - 9 = 100

To find out how many candy bars Terri sold last week, we solve for x:

x = 100 + 9
x = 109

Therefore, Terri sold 109 candy bars last week. And Mary Ellen also sold 25 candy bars last week.

What are the coordinates of the image R(90°,0)(JKLO)=J'K'L'O'

Answers

The image of the figure after rotating by counterclockwise about the origin is J' = (-1, -1), K' = (-2, -1), L' = (-1, 4,) and O' = (-3, -2)

Rotating the figure 90 counterclockwise about the origin

From the question, we have the following parameters that can be used in our computation:

The coordinates are

J = (-1, 1)

K = (-1, 2)

L = (4, 1)

O = (-2, 3)

The rule of rotating a figure 90 counterclockwise about the origin is

(x,y) = (-y,x)

So, we have

J' = (-1, -1)

K' = (-2, -1)

L' = (-1, 4,)

O' = (-3, -2)

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Question

What are the coordinates of the image R(90°,0)(JKLO)=J'K'L'O'

J = (-1, 1) K = (-1, 2) L = (4, 1) O = (-2, 3)

The Robinson family had a race and the referee recorded in the event.The difference between the first and last finisher is 2 seconds.


True or false

Answers

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

True

Reason

Use the last person time to minus the first person time which is

53.3 - 51.3

A letter of the alphabet is chosen at random. Find the odds in favor of picking an A, E,I,O or U.

Answers

There are 5 chances out of 21 of picking an A, E, I, O, or U.

There are 5 vowels in the English alphabet (A, E, I, O, U) out of a total of 26 letters. So, the probability of picking a vowel is 5/26.

To find the odds in favor of picking a vowel, we divide the probability of picking a vowel by the probability of not picking a vowel:

odds in favor = probability of picking a vowel / probability of not picking a vowel

The probability of not picking a vowel is 1 - 5/26 = 21/26.

So, the odds in favor of picking an A, E, I, O, or U are:

5/26 / 21/26 = 5/21

This means that there are 5 chances out of 21 of picking an A, E, I, O, or U.

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In the diagram below, quadrilateral QRST is inscribed in circle U. Solve for x and
Y.
a
73
U
(x+6)
T
111°
R
(3y+44)
S

Answers

The solutions are x = 29° and y = 27°.

In the given quadrilateral, the angles are mentioned.

So,

Q = 79°

R = 109°

S = (6y - 61)°

T = (4x - 45)°

A quadrilateral is a polygon with four vertices, four sides, and four angles with a total angle of 360 degrees.

The quadrilateral makes two triangles when its diagonals are drawn. These two triangles have an angle total of 180 degrees. The quadrilateral's total angle sum is hence 360°.

So,

T + R = 180°

(4x - 45) + 109 = 180

4x + 64 = 180

4x = 180 - 64

4x = 116

Therefore, x = 116/4

x = 29°

S + Q = 180°

(6y - 61) + 79 = 180

6y + 18 = 180

6y = 180 - 18

6y = 162

Therefore,

y = 162/6

y = 27°

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What must be added to 1⅔ gross to make 15 cm scores​

Answers

There is no quantity that can be added to 1⅔ gross to make 15 cm scores, as it would result in a negative value.

To solve the problem, we need to determine the quantity that needs to be added to 1⅔ gross to make a total of 15 cm scores.

First, let's convert 1⅔ gross to a more manageable unit. One gross is equal to 144 units, so 1⅔ gross can be expressed as:

1⅔ gross = 1 gross + ⅔ gross = 144 + (2/3) * 144 = 144 + 96 = 240 units.

Now, let's denote the quantity that needs to be added as "x" units.

Therefore, we can set up an equation to represent the given situation:

240 + x = 15.

To solve for x, we subtract 240 from both sides of the equation:

x = 15 - 240 = -225.

The result, x = -225, indicates that we need to add -225 units to 1⅔ gross to make a total of 15 cm scores. However, since quantities cannot be negative in this context, it means that it is not possible to add a negative value to the given quantity.

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solve it and show full calculus.
thank you!

Answers

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

15 POINTS
Using Pythagoras' theorem, calculate the length
of XY.
Give your answer in centimetres (cm) to 1 d.p.

Answers

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:
13.3cm
Step-by-step explanation:
The Pythagorean theorem is a^2+ b^2 = c^2
Plug the values into the equation.
7^2+ b^2 = 15^2
Simplify.
49 ÷ b^2 = 225
Subtract 49 from both sides.
b^2 = 176
Take the square root of both sides.
vb^2 = v176
b=13.266
b=13.3cm

A tumor is a collection of cancerous cells. Suppose each cancerous cell is spherical and has a radius of 5 x 10-³ cm, and that the doubling time for a population of cancerous cells is 30 hours.

If the tumor has an initial volume of 0.3 cm³, how many cancerous cells does it contain? (For simplicity, assume that the tumor is entirely made of cells, that there is no space between them.) Round your answer up to the next whole number. ​

Answers

The 5 × 10⁻³ cm radius of one spherical cancerous cell indicates that the number of cells in the initial volume of 0.3 cm³ of the tumor is; 572,958 cells

What is the volume of a sphere?

The volume, V, of a sphere is the product of the cube of the radius of the sphere, pi, and (4/3); V =  (4/3) × Pi × (The radius of the sphere, r)³

The volume of each cancerous cell can be calculated as follows;

The shape of each cancerous cell = A sphere

Volume of a sphere = (4/3) × π × r³

Where;

r = The radius of the sphere

The radius of the cancerous sphere, r = 5 × 10⁻³ cm

The volume of each cancerous cell = (4/3) × π × (5 × 10⁻³)³

The number of cancerous cells = The initial volume of the tumor ÷ The volume of one cancerous cell

The number of cancerous cells = 0.3/((4/3) × π × (5 × 10⁻³)³) ≈ 572958

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The sphere has a diameter of 10 in. What is the volume of the sphere?

Answers




Volume of sphere = 3/4 πr^3

r=radius
Given:
diameter(d)=10 in
radius(r)= d/2
=
10/2
=5 in

4/3 πr^3= 4/3 ∗3.14∗5^3


= 4/3 * 5∗5∗5∗3.14
= 4/3∗125∗3.14
= 1570/3


=523.33 in^3

Answer: 523.8 cubic inches

Step-by-step explanation:

Volume of the sphere, V = (4/3) * π * r^3

where r is the radius of the sphere.

Given, the diameter of the sphere (d) = 10 inches

Therefore, the radius of the sphere, r = d/2 =10/2 = 5 inches

Now, substituting the value of the radius to the volume formula,

V = (4/3) * π * (5^3)

= (4/3) * (22/7) * 125

≈ 523.8 cubic inches

a) C.P. = Rs 120, profit = Rs 25​

Answers

If cost price is Rs. 120, profit is Rs. 25 then the selling price is Rs.145.

We have to find the selling price

The formula for find the selling price is given below:

Selling Price = Cost Price + Profit

Given that the Cost Price (C.P.) is Rs 120 and the profit is Rs 25.

we can substitute these values into the formula:

Selling Price = 120 + 25

When one hundred twenty is added with twenty five we get One hundred twenty five.

Selling Price = 145

Therefore, the selling price is Rs 145.

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C.P. = Rs 120, profit = Rs 25​ then find the selling price?


Polynomials - Factor this polynomial, and identify the x-intercepts
y = 15x³ + 5x² - 60x - 20

Answers

The x-intercepts of the polynomial are -1/3, 2, and -2.

Given is a polynomial, we need to factor the polynomial, and identify the x-intercepts,

y = 15x³ + 5x² - 60x - 20

To factor the polynomial y = 15x³ + 5x² - 60x - 20, we can follow these steps:

Step 1: Factor out the greatest common factor (GCF) if possible.

In this case, the GCF of all the terms is 5:

y = 5(3x³ + x² - 12x - 4)

Step 2: Use factoring by grouping or other factoring techniques to factor the remaining polynomial.

Group the terms:

y = 5[(3x³ + x²) + (-12x - 4)]

Factor out common terms from each group:

y = 5[x²(3x + 1) - 4(3x + 1)]

Notice that we now have a common binomial factor of (3x + 1):

y = 5(3x + 1)(x² - 4)

Step 3: Factor any remaining quadratic expressions if possible.

The quadratic expression x² - 4 can be factored as the difference of squares:

y = 5(3x + 1)(x - 2)(x + 2)

Now we have factored the polynomial completely.

To find the x-intercepts (also known as zeros or roots), we set y = 0 and solve for x:

0 = 5(3x + 1)(x - 2)(x + 2)

Setting each factor equal to zero and solving for x, we get:

3x + 1 = 0 ⇒ x = -1/3

x - 2 = 0 ⇒ x = 2

x + 2 = 0 ⇒ x = -2

Therefore, the x-intercepts of the polynomial are -1/3, 2, and -2.

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Write an explanation of how you would solve the following equation
4/5 x = -15

Answers

Answer:

-18.75

Step-by-step explanation:

Since the x is being multiplied by 4/5, we have to divide by 4/5 on both sides.

How to divide by 4/5? Take the reciprocal. The reciprocal to 4/5 is 5/4 (flip it).

Multiply both sides by 5/4.

5/4(4/5x)=5/4(-15)

x=-18.75

Answer:

[tex]x = -\frac{75}{4}[/tex]

Step-by-step explanation:

Question:

[tex]\frac{4}{5}x = -15[/tex]

Now, we multiply both sides by 5:

[tex]\frac{4}{5} x*5 = -15*5[/tex]

Simplify:

[tex]4x = -75[/tex]

Divide both sides by 4:

[tex]x = -\frac{75}{4}[/tex]

2. How much should you have in your emergency fund? ​

Answers

Building an emergency fund may take time, but it can provide peace of mind and financial security in the event of an unexpected emergency.

The amount you should have in your emergency fund depends on your personal circumstances. Experts typically recommend having three to six months' worth of living expenses saved in an emergency fund.

However, if you have a high-risk job or irregular income, you may want to consider saving up to nine months' worth of expenses.

Additionally, if you have a lot of debt or dependents, you may want to have a larger emergency fund to ensure you can cover unexpected expenses or job loss.

It's important to regularly reassess your emergency fund and adjust it as needed based on changes in your financial situation

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PLEASE HELP WILL GIVE LOTS OF POINTS

Answers

The number of square feet tile he needs to purchase is 45.9 feet squared.

How to find the square feet of the tile needed?

Kyle is going to retile the bottom of his pool. He first needs to drain the pool.  

The pool hold 321 cubic feet of water and has a height of 7 feet. Therefore, the number of square feet tile he needs to purchase can be calculated as follows:

Therefore,

volume of the pool = base area × height

321 = 7b

divide both sides of the equation by 7

b = 321 / 7

b = 45.85

b =   45.9 feet squared

Therefore,

amount of square feet tiles to purchase = 45.9 feet squared

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What is the modulus and argument of (1+i)^2 divided by (1-√3 i)^4

Answers

The Modulus = 1 / √37, Argument ≈ -0.9828 radians

To find the modulus and argument of the expression (1+i)^2 / (1-√3i)^4, let's first simplify the expression.

(1+i)^2 can be expanded as follows:

[tex](1+i)^2 = (1+i)(1+i) = 1 + 2i + i^2 = 1 + 2i - 1 = 2i[/tex]

Similarly, (1-√3i)^4 can be expanded as:

(1-√3i)^4 = (1-√3i)(1-√3i)(1-√3i)(1-√3i)

Expanding this further requires using the properties of complex numbers, namely (a+b)(c+d) = ac + ad + bc + bd and i^2 = -1.

Simplifying the expression, we get:

(1-√3i)^4 = ([tex]1^4 - 4(1^3)(\sqrt{3i} ) + 6(1^2)(\sqrt{3i} )^2 - 4(1)(\sqrt{3i} )^3 + (\sqrt{3i} )^4)[/tex]

= (1 - 4√3i - 6(-3) + 4(√3i)(-√3) + (-3)^2)

= (1 - 4√3i + 18 + 4(-3) - 9)

= (10 - 4√3i)

Now, we can calculate the modulus and argument of the expression:

Modulus: The modulus of a complex number is calculated by taking the square root of the sum of the squares of its real and imaginary parts.

The modulus of (1+i)^2 / (1-√3i)^4 is the modulus of (2i) / (10 - 4√3i), which can be simplified as:

Modulus = √(([tex]2^2 + 0^2[/tex]) / (10^2 + (-4√3)^2))

= √(4 / (100 + 48))

= √(4 / 148)

= √(1 / 37)

= 1 / √37

Argument: The argument of a complex number is the angle it makes with the positive real axis in the complex plane.

The argument of (1+i)^2 / (1-√3i)^4 can be calculated as the argument of (2i) / (10 - 4√3i), which is the argument of 2i minus the argument of (10 - 4√3i).

The argument of 2i is π/2 (or 90 degrees), as it lies on the positive imaginary axis.

The argument of (10 - 4√3i) can be calculated using the inverse tangent function:

Argument = atan((-4√3) / 10)

= atan(-2√3 / 5)

≈ -0.9828 radians (or approximately -56.31 degrees)

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What value of X makes KM the angle bisector of LKN

Answers

Then , if KL is 45 units long, then KM will be the angle bisector of LKN.

To find the value of X that makes KM the angle bisector of LKN, we need to use the angle bisector theorem. According to the theorem, if a line bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle.

Let's apply this theorem to triangle LKN. Suppose that KM bisects angle LKN, and let X be the length of KL. Then, according to the angle bisector theorem:

LK / KN = KL / KN
LK = KL * (KN / KN)
LK = KL

This tells us that LK and KL have the same length, which means that triangle LKN is isosceles. Therefore, we can write:

LK = KN

Now, we can use the fact that the sum of the angles of a triangle is 180 degrees to find the measure of angle LKN. We know that angle LKN is bisected by KM, so we can write:

angle LKM = angle MKN

Let's call this angle x. Then, we have:

angle LKN = 2x

And since triangle LKN is isosceles, we also have:

angle LNK = angle KLN = (180 - angle LKN) / 2
angle LNK = (180 - 2x) / 2
angle LNK = 90 - x

Now, we can use the fact that the sum of the angles of a triangle is 180 degrees to write:

angle LKM + angle LKN + angle LNK = 180

Substituting the values we found earlier, we get:

x + 2x + (90 - x) = 180

Simplifying, we get:

x = 45
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Can somebody help? Find the sum of the first 22 terms of the arithmetic sequence, if the first term is 5 and the common difference is 2.

Answers

To find the sum of the first 22 terms of an arithmetic sequence, we can use the formula:

Sn = (n/2)(2a + (n-1)d)

where Sn represents the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

In this case, the first term a is 5, the common difference d is 2, and the number of terms n is 22. Substituting these values into the formula, we get:

S22 = (22/2)(2(5) + (22-1)(2))
= 11(10 + 21(2))
= 11(10 + 42)
= 11(52)
= 572

Therefore, the sum of the first 22 terms of the arithmetic sequence is 572.

Identify the number types that describe √7.

O A. Real, irrational
OB. Real, rational
C. Real, rational, integer, whole, natural
OD. Real, rational, whole

Answers

The correct answer is:

A. Real, irrational

Given is a number √7, we need to identify the category of the number.

The number √7 is a real number because it exists on the number line.

We see that the imaginary numbers are those which can not be drawn on number line.

It is also an irrational number because it cannot be expressed as a ratio of two integers.

The number √7 cannot be written as a fraction or a terminating or repeating decimal.

It is a non-repeating, non-terminating decimal that goes on forever without a pattern.

Hence, it is considered irrational.

Therefore, the correct answer is:

A. Real, irrational

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1. It is hypothesized that the average production cost in
making a movie is ₱24.6 million. This year, a random
sample of 15 movies have shown an average production
cost of ₱28.3 million with a standard deviation of ₱9.5
million. At 0.01 level of significance, is the hypothesized
average production cost true?































































































































































































































































































































































































































Answers

From the data given, we do not have enough evidence to conclude that the hypothesized average production cost of P24.6 million is false.

What is the hypothesized average production cost?

To test the hypothesis that the average production cost in making a movie is P24.6 million, we can perform a hypothesis test using the sample data.

Let's define the null hypothesis (H₀) and the alternative hypothesis (H₁) as follows:

H₀: The average production cost is P24.6 million.

H₁: The average production cost is not P24.6 million.

We will use a t-test since we have a sample size smaller than 30 and the population standard deviation is unknown.

Given the sample information, the sample mean (x) is P28.3 million, the sample size (n) is 15, the hypothesized population mean (μ) is P24.6 million, and the sample standard deviation (s) is P9.5 million.

We can calculate the t-statistic using the formula:

t = (x - μ) / (s / √n)

Substituting the values:

t = (28.3 - 24.6) / (9.5 / √15)

t = 3.7 / (9.5 / √15)

t = 1.51

To determine whether the hypothesis is true at a 0.01 level of significance, we need to compare the calculated t-value to the critical t-value from the t-distribution table for a two-tailed test with 14 degrees of freedom (n - 1 = 15 - 1 = 14) and a significance level of 0.01.

The critical t-value for a two-tailed test with 14 degrees of freedom and a significance level of 0.01 is approximately ±2.977.

If the calculated t-value falls within the range of ±2.977, we fail to reject the null hypothesis; otherwise, we reject the null hypothesis.

Since the calculated t-value of 1.51 does not exceed the critical t-value of ±2.977 for a two-tailed test at a 0.01 level of significance, we fail to reject the null hypothesis.

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• 1) write an equation of that
passes through the points through
the points (-2, -3) and (2,5)
Show all work.

Answers

The equation of the line passing through the points (-2, -3) and (2, 5) is y = 2x + 1.

To find the equation of a line passing through the points (-2, -3) and (2, 5), we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents one of the points on the line, and m represents the slope of the line.

First, let's calculate the slope (m) using the given points:

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

  = (5 - (-3)) / (2 - (-2))

  = 8 / 4

  = 2

Now, we have the slope (m) as 2. Let's choose one of the points, (-2, -3), and substitute its coordinates into the point-slope form equation:

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

y + 3 = 2(x + 2)

Simplifying further:

y + 3 = 2x + 4

y = 2x + 4 - 3

y = 2x + 1

Therefore, the equation of the line passing through the points (-2, -3) and (2, 5) is y = 2x + 1.

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The segment CD is tangent to O T. Find mZTDC.

Answers

Answer:

The answer is 32°

Step-by-step explanation:

TC is perpendicular to CD.

90 + 3x + 8 + 7x + 2 = 180

x = 8

/_TDC = 3x + 8 = 32

Dzani bought some candy. If he packs them equally into 4 jars, he will have 3 candies left. If he packs them equally into 5 jars, he will have 1 candy left. What is the smallest possible number of candies Dzani bought?

Answers

The smallest possible number of candies Dzani bought is 11

How to determine the smallest possible number of candies Dzani bought?

From the question, we have the following parameters that can be used in our computation:

4 jars and 3 remaining candles5 jars and 1 remaining candle

Represent the number of jars with x

So, we have

4x + 3 = 5x + 1

Collect the like terms

So, we have

5x - 4x = 3 - 1

Evaluate

x = 2

So, we have

Candles = 4 * 2 + 3

or

Candles = 5 * 2 + 1

Evaluate

Candles = 11

Hence, the smallest possible number of candies Dzani bought is 11

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The volume of the larger cylinder is 150π.

Let's assume the ratio of the radii of the two cylinders is 3x and 5x.

We know that the volume of a cylinder is given by the formula:

V=πr²h, where r is radius and h is height.

Given that the volume of the smaller cylinder is 54π cubic centimeters  we can write the equation:

54π =π(3x)²h₁

54π =π9x²h₁

h₁=6/x²

ow, we need to find the volume of the larger cylinder. Let's denote it as V₂:

V₂=π(5x)²h₂

V₂=150π

Therefore, the volume of the larger cylinder is 150π.

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