Find the area under the χ 2 -curve with 5 degrees of freedom to the right of 9.24.

Answer:

Step-by-step explanation:

To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.

Let's first find the vector that points from point A to point B:

�

�

⃗

=

(

4

−

3

)

−

(

−

3

−

2

)

=

(

7

−

1

)

AB

=(

4

−3

​

)−(

−3

−2

​

)=(

7

−1

​

)

The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:

3

4

�

�

⃗

=

3

4

(

7

−

1

)

=

(

21

4

−

3

4

)

4

3

​

AB

=

4

3

​

(

7

−1

​

)=(

4

21

​

−

4

3

​

​

)

Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:

(

−

3

−

2

)

+

(

21

4

−

3

4

)

=

(

3

4

,

−

11

4

)

(

−3

−2

​

)+(

4

21

​

−

4

3

​

​

)=

(

4

3

​

,−

4

11

​

)

​

Answer: 3+(-8+1) or 3+-8+1

Step-by-step explanation: Rita rewrote the equation so instead of it being negative 8 it is negative 1.

One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:

$4a^5 - 3a^4 + 2a^3 - 7a^2$

A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.

For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.

Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.

One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:

$4a^5 - 3a^4 + 2a^3 - 7a^2$

Learn more about polynomials expression below.

https://brainly.com/question/4142886

#SPJ1

Hi !

[tex]2x + 3 > 11\\\iff 2x > 8\\\iff x > \frac{8}{2}\\ \iff x > 4[/tex]

Have a nice day ;)

Answer:

x > 4

Isolate the variable by dividing each side by the factors that don't contain the variable

The y-intercept of the tangent line is b. -1

The y-intercept of a line is the value of y at which the line crosses the y axis

To determine the value of y-intercept of a line with the given slope -3 that is a tangent line to the curve y = -x² - 5x -5.

We proceed as follows

First we differentiate the equation of the curve.

So,  y = -x² - 5x -5.

dy/dx = d(-x² - 5x -5)/dx

=  d-x²/dx - d5x/dx - d5/dx

= -2x - 5 - 0

= -2x - 5

Since the derivative of the curve equals the value of the tangent at the point, we have that

dy/dx = -3

-3 = -2x - 5

-3 + 5 = -2x

2 = -2x

x = 2/-2

x = -1

So, substituting x = -1 into the equation for y to find the y intercept, we have that

y = -x² - 5x -5.

y = -(-1)² - 5(-1) -5

= -1 + 5 - 5

= -1 + 0

= -1

So, the y-intercept is b. -1

Learn more about y-intercept of line here:

https://brainly.com/question/31142381

#SPJ1

Answer:

[tex]6(4x - 3) > 30 \\ divide \: both \: sides \: of \: the \: \\ inequality \: by \: 6 \\ = 4x - 3 > 5 \\ = 4x > 5 + 3 \\ = 4x > 8 \\ = x > \frac{8}{4} \\ = x > 2[/tex]

hope it helps

Answer: x=4

Step-by-step explanation:

Isolate x using opposite operations.

2x + 3 = 11

2x = 8

x = 4

Answer:

4

Step-by-step explanation:

subract 3 from 11

2x=8

divide by 2

x=4

After Derek drinks 1/4 ounce of water, he is left with 95/3 ounces of water in his glass.

Derek initially had 10 2/3 ounces of water in his glass. To find out how much water is left after he drinks 1/4 ounce of water, we need to subtract 1/4 from 10 2/3. To do that, we need to convert the mixed number (10 2/3) into an improper fraction.

To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. In this case, we have:

10 x 3 + 2 = 32/3

Therefore, Derek initially had 32/3 ounces of water in his glass.

To subtract 1/4 from 32/3, we need to make sure the denominators are the same. We can convert 1/4 into twelfths by multiplying both the numerator and denominator by 3. This gives us:

1/4 x 3/3 = 3/12

Now that we have a common denominator of 12, we can subtract:

32/3 - 3/12 = 383/12 - 3/12 = 380/12

To simplify, we can divide both the numerator and denominator by 4:

380/12 ÷ 4/4 = 95/3

To learn more about quantity click on,

https://brainly.com/question/5060881

#SPJ4

Complete question is:

Derek had 10 2/3 ounce of water in a glass He drank 1/4 of an ounce of the water from his glass how much water is left in Derek's glass?

The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.

The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.

The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:

Radius of sphere = (102mm - 76mm)/2 = 13mm

Now we can calculate the volume and surface area of each component:

Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3

Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2

Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3

Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2

Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:

Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3

Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2

To learn more about Volume click on,

https://brainly.com/question/24254068

#SPJ4

The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.

The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.

Therefore, the height of the tank can be calculated as follows:

7.48 liquid gallons = 1 ft³

1100 liquid gallons = ?

cross multiply

volume of the tank = 1100 / 7.48 = 147.058823529 ft³

Therefore, let's find the volume of the cylindrical tank.

volume of the cylindrical tank = πr²h

where

Therefore,

r = 3.2 feet

h = ?

The volume of the cylindrical tank in feet cube is 147.058823529 ft³

Let's find the height, h

volume of the cylindrical tank = 3.14 × 3.2² × h

147.058823529 = 3.14 × 10.24 × h

32.1536h = 147.058823529

divide both sides by 32.1536

h = 147.058823529 / 32.1536

h = 4.57363405653

Therefore,

height of the water tank = 4.6 feet

Learn more on volume here: brainly.com/question/8827822

#SPJ1

The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.

Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.

The exponential probability distribution with a mean of 12 seconds is given by

f(x) = (1/12) × e^(-x/12)

where x represents the time between arrivals of vehicles.

To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12

P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx

=  [tex]\int\limits^{12}_0[/tex]  (1/12) × e^(-x/12) dx

= [(-e^(-x/12))]_[0,12]

= (-e^(-12/12)) - (-e^(0/12))

= 1 - e^(-1)

≈ 0.6321

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?

The statement " Time plots are special scatterplots where the explanatory variable, x, is a measure of time" is true because time plots are scatterplots where the x-axis represents time, and they are commonly used to visualize trends and patterns in time series data.

A time plot is a type of scatterplot where the x-axis represents time and the y-axis represents a response variable. Time plots are useful for displaying data that change over time and can reveal trends, patterns, and seasonality in the data. They are commonly used in fields such as economics, finance, and social sciences to analyze time series data.

By visualizing data over time, time plots can help to identify relationships, outliers, and potential forecasting models. Overall, time plots are a powerful tool for analyzing and understanding trends and patterns in time series data.

Learn more about time plot here

brainly.com/question/28481310

#SPJ4

The given question is incomplete, the complete question is:

Time plots are special scatterplots where the explanatory variable, x, is a measure of time. True or false

The ice cream factory could make 720 quarts of ice cream in 36 hours.

We can use a proportion to solve this problem:

quarts / hours = constant rate of production

Let x be the number of quarts that could be made in 36 hours. Then we have:

200 quarts / 10 hours = x quarts / 36 hours

Cross-multiplying, we get:

10x = 200 * 36

Simplifying, we get:

10x = 7200

Dividing both sides by 10, we get:

x = 720

Therefore, the ice cream factory could make 720 quarts of ice cream in 36 hours.

Read more about proportions at

https://brainly.com/question/1781657

#SPJ1

According to the function, the rate of change with respect to the number of minutes purchased is $1.05 per minute.

The function given in the problem is y = 5.45 + 1.05(x + 7), where y represents the cost in dollars for a prepaid cell phone plan of x minutes. This means that if you want to know how much it will cost to purchase a certain number of minutes, you can simply plug in that number for x and the equation will give you the corresponding cost in dollars.

Now, the rate of change with respect to the number of minutes purchased is also known as the slope of the function. This tells us how much the cost will change for each additional minute purchased. To find the slope, we need to take the derivative of the function with respect to x.

The derivative of y with respect to x is given by:

dy/dx = 1.05

This means that for each additional minute purchased, the cost will increase by $1.05.

To know more about function here

https://brainly.com/question/28193995

#SPJ4

The y-component of the force that the wall exerts on the beam (f) is -400.5 N.

The y-component of the force that the wall exerts on the beam (f) can be found using the following steps:

Step 1: Calculate the magnitude of the force (f):

f = √[f_x² + f_y²]

f = √[(-500 N)² + (-300 N)²]

f = 600 N

Step 2: Calculate the angle of the force relative to the y-axis:

θ = tan-1(-300 N/500 N)

θ = -53.13°

Step 3: Calculate the y-component of the force (fy):

fy = f × sin(θ)

fy = 600 N × sin(-53.13°)

fy = -400.5 N

Therefore, the y-component of the force that the wall exerts on the beam (f) is -400.5 N.

To learn more about magnitude visit:

https://brainly.com/question/30699700

#SPJ4

The answer of the given question based on the rectangle is , The MNOP congruence is shown by  Side-Angle-Side (SAS) and the steps are given below.

In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.

To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:

Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.

To know more about Side-Angle-Side (SAS) congruence visit:

https://brainly.com/question/4111714

#SPJ1

Answer:

Prove the following identitics: tan 0 + cot 0 = I/(sin 0 cos 0) 0 + tan 0 sec 0 = cosec 0 'sec? 0. 18 cosec = cosec? 0 = tan? 0 cot2 19 sec? 0 sin ' 0 =cos? 0 'sin? 20 cos4 (sec 0 + tan 0) (sec 0 _ tan 0) = 1 2 sin? 0 = cOs? 0 _ 'sin? 0. 22 2 cos? 0_I=1 23 sec? 0 + cosec 0 = sec? 0 cosec? sin? , COs? 24 sec" 0 cosec" 0 = cos 0 sin" 0 25 =I tan 0 + 1 cot? 0 +4 26 (sec? 0 1) (cosec? 0 1) = [ 27 ((sec? 0 _0)+ V(cosec" 0 _ !) = sec € cosec 0 28 (sec? tan? 0) + V(cosec? 0 ~ cot? 0) = 2 cos? 0 29 =1 sin sec? 0 _ 1 sec 0 cosec 0 tan 0 + cot 0 30 tan 0 cot 0 sec 0 + cosec 0 cos 0 sin 0 31 =l V( + tan? 0) V( + cot? 0) Eliminate 0 from the following equations: 32 x = 4 cos 0, y = b sin 0. 33 x = 4 cot 0,y = b cosec 0. 34 x=a tan 0,y =b cos 0. 35 x = ] sin 0, y = [ + cos 0, 36 x =a sec 0,y = b +c cos 0. 37 x=a cosec 0, y = b sec 0. 38 X=l+ tan 0,y = cos 0. 39 x=sin 0 + cos 0,y = sin 0 40 cos X = sCc 0 + tan 0, y = sCc 0 ~ tan 0.

The first option, "one half," corresponds to the scale factor of 0.5.

Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.

We can contrast the side lengths of triangles D and D′ to determine the scaling factor.

Let's contrast the side lengths for the two triangles.

Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The first option, "one half," corresponds to the scale factor of 0.5.

To know more about scale factor, visit:

brainly.com/question/25722260

#SPJ1

Answer:

x = 52.5

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360.

2x+100 +95+60 = 360

Combine like terms.

2x+255=360

Subtract 255 from each side

2x+255-255= 360-255

2x = 105

Divide each side by 2

2x/2 = 105/2

x = 52.5

Answer:

x = 52.5

Step-by-step explanation:

The sum of the interior angles of a quadrilateral is 360°.

Accordingly, let us find the value of x.

2x + 100 + 95 + 60 = 360

2x + 255 = 360

Subtract 255 from both sides.

2x = 360 - 255

2x = 105

Divide both sides by 2.

x = 52.5

(C.) reflection and (D.) rotation produce congruent images.

What three transformations are congruent?

We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.

(A) Dilation, (B) horizontal stretch, and (E) translation do not produce congruent images because they change the size, shape, and/or orientation of the original object.

(C) Reflection produces congruent images because the resulting image is a mirror image of the original object, and therefore has the same size and shape.

(D) Rotation produces congruent images because the resulting image is the same shape and size as the original object, just rotated to a different orientation.

To know more about congruent images visit,

brainly.com/question/30493724

#SPJ1

Answer:

its taking the immage on the right and moving it ounter clockwise 90°

The solution to the system of equations is:

x = -1/42

y = -11/6

In mathematics, a variable is a symbol that represents a value that can vary or change. It is often represented by a letter, such as x, y, or z. Variables are used to write algebraic expressions and equations that can be solved to find unknown quantities. The value of a variable can be determined by solving an equation that involves the variable, or by assigning a specific value to the variable. In algebra,

To solve this system of equations by the method of elimination, we need to eliminate one of the variables by adding the two equations together. We can do this by multiplying the first equation by 3, which will make the y terms cancel out when we add the equations:

7x - y = 2 (multiply by 3)

-21x - 3y = 5

21x - 3y = 6 (first equation multiplied by 3)

-21x - 3y = 5

Now we can add the two equations together:

(21x - 3y) + (-21x - 3y) = 6 + 5

0x - 6y = 11

Simplifying, we get:

-6y = 11

Dividing both sides by -6, we get:

y = -11/6

Now that we have solved for y, we can substitute this value back into either equation to solve for x. Let's use the first equation:

7x - y = 2

7x - (-11/6) = 2

Multiplying both sides by 6 to eliminate the fraction, we get:

42x + 11 = 12

Subtracting 11 from both sides, we get:

42x = -1

Dividing both sides by 42, we get:

x = -1/42

Therefore, the solution to the system of equations is:

x = -1/42

y = -11/6

To know more about variables visit:

https://brainly.com/question/28248724

#SPJ1

Answer:

To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:

Length = 70 ft

Width = 60 ft

Depth = 4 in = 4/12 ft = 1/3 ft

Volume = Length x Width x Depth

Volume = 70 ft x 60 ft x (1/3) ft

Volume = 1400 ft³

Option 1: Bags of topsoil

Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:

Number of bags = Volume / Bag size

Number of bags = 1400 ft³ / 3 ft³ per bag

Number of bags = 467 bags

The total cost of bags of topsoil is:

Cost = Number of bags x Cost per bag

Cost = 467 bags x $2.50 per bag

Cost = $1167.50

Option 2: Bulk topsoil

The volume of topsoil needed is 1400 ft³, which is equivalent to:

Volume = 1400 ft³ / 27 ft³ per yd³

Volume = 51.85 yd³ (rounded to two decimal places)

The cost of bulk topsoil is:

Cost = Volume x Cost per yd³ + Delivery fee

Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee

Cost = $1153.70

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50

Answer:

Bulk is less expensive

Step-by-step explanation:

First convert inches to feet:  4 in x 1 ft/12 in =0.333 ft

Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³

Bagged topsoil:   1400 ft³ x $2.50/3 ft³ = $1166.67

Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74

Bulk is just a little cheaper

The reasonable estimate of the median home cost in the US in 2025 is  $340,000

To assess the middle domestic taking a toll within the US in 2025, ready to utilize the verifiable drift and expect that the relationship between the middle domestic fetched and time (measured in a long time since 1975) is straight.

Let`s begin with calculating the rate of increment in median domestic fetched per year utilizing the information from 1975 to 2005. Ready to utilize the equation for the slant of a direct relapse line:

slant(slope) = (y2 - y1) / (x2 - x1)

where

y1 and y2 are the middle domestic costs in 1975 and 2005,

separately, and x1 and x2 are comparing a long time (0 and 30).

incline = ($240,000 - $40,000) / (30 - 0) = $6,000

This implies that the middle domestic taken a toll expanded by a normal of $6,000 per year amid this period.

Presently, ready to utilize this rate of increment to appraise the middle domestic taken a toll in 2025, which is 50 long times after 1975.

The year 2025 will be 50 a long time after 1975, so the number of a long time since 1975 will be x = 50. Utilizing the incline we fair calculated, able to assess the middle domestic fetched in 2025 as takes after 

y = y1 + slant(slope) * x = $40,000 + $6,000 * 50 = $340,000

Therefore, a sensible assessment of the middle domestic taking a toll within the US in 2025, based on the presumption that the slant watched from 1975 to 2005 proceeds, is $340,000. 

To know more about median problems refer to this :

https://brainly.com/question/14532771

#SPJ4

The first term represents area of the two triangular faces having base of pyramid, second term represents area of two triangular faces having length of the rectangle, third term represents area of rectangular base.

A rectangular pyramid is a solid figure with a rectangular base and four triangular faces that meet at a single point, known as the apex. To find the surface area of a rectangular pyramid, we need to calculate the area of each face and add them together.

The formula for the surface area of a rectangular pyramid is:

Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base)

The first term, 2(1/2 x base x height), represents the area of the two triangular faces that share the base of the pyramid. The second term, 2(1/2 x length x height), represents the area of the two triangular faces that share the length of the rectangle. The third term, (length x base), represents the area of the rectangular base.

By multiplying each term by its appropriate values and adding them together, we can find the total surface area of the rectangular pyramid.

To learn more about Surface area click on,

https://brainly.com/question/12141919

#SPJ4

Complete question is:

Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base). Explain what each term represents?

Answer:-91 is an integer

1/2 is not an integer

51 is an integer

-6/2 is not an integer

-99.34 is an integer

Step-by-step explanation: An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Answer:

-91 - yes

1/2 - no

51 - yes

-6/2 - yes

-99.34 - no

Answer:  option C - Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips, is the most likely scenario.

Step-by-step explanation:

Based on the Law of Huge Numbers, the more times a coin is flipped, the closer the test likelihood will be to the hypothetical likelihood of 0.5 for heads and 0.5 for tails. In this manner, Sandy's exploratory likelihood is most likely to be closest to the hypothetical likelihood within the test with 1,000 flips.

In spite of the fact that it is conceivable that Sandy's exploratory likelihood might be near to the hypothetical likelihood within the explore with 100 flips or 500 flips, it is more likely that the bigger test measure of 1,000 flips will result in a more precise representation of the hypothetical likelihood.

x = 108 is 3.10 standard deviations to the left of the mean.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

The z-score when x = 108 is:

z = (108 - 153) / 14.5

z = -3.10

This tells us that x = 108 is 3.10 standard deviations to the left of the mean.

Learn more about standard deviation on:

https://brainly.com/question/475676

#SPJ4