Answer each question about the following arithmetic series: what are the terms of the series? a1 = a2 = a3 = a4 =.

The day she runs faster is Wednesday.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

On Wednesday:

She ran 6 miles in 50 minutes.

Unit rate:

= 6/50

= 0.12 miles per minute _____(1)

On Thursday:

She ran 4 miles in 32 minutes.

Unit rate:

= 4/32

= 0.125 miles per minute _______(2)

From (1) and (2),

0.12 > 0.125

Thus,

On Wednesday she runs faster.

Learn more about unit rates here:

https://brainly.com/question/11258929

#SPJ1

The vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])

What is an orthogonal vector?

An orthogonal vector is a vector that is perpendicular to another vector in a given space. In other words, two vectors are orthogonal if their dot product is equal to zero.

To find a vector orthogonal to both 2, 2, 0 and 0, 2, 5 of the form 1, we can take the cross product of the two vectors, which results in a vector that is orthogonal to both. The cross product of 2, 2, 0 and 0, 2, 5 is given by:

(2, 2, 0) x (0, 2, 5) = (20, -10, -4)

So, a vector orthogonal to both 2, 2, 0 and 0, 2, 5 is given by (20, -10, -4). We can normalize this vector by dividing it by its magnitude, which is equal to sqrt(20^2 + (-10)^2 + (-4)^2) = sqrt(444). The normalized vector will be of the form 1:

[tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex])

Hence, the vector orthogonal for both vectors is [tex](20, -10, -4) / \sqrt{444}[/tex] = ([tex]20 / \sqrt{444}[/tex], [tex]-10 / \sqrt{444}[/tex], [tex]-4 / \sqrt{444}[/tex]).

To learn more about the orthogonal vector, visit:

https://brainly.com/question/15587050

#SPJ4

The probability that the system works under these conditions is 0.81 (0.90 x 0.90 = 0.81).

This question uses the concept of independent probabilities, Independent probabilities refer to the likelihood of two or more events occurring independently of each other.

In other words, the probability of one event occurring does not influence the probability of another event occurring.

This means that if the probability of one event occurring is known, the probability of the other event occurring can be calculated independently.

given below

Step 1: Determine the probability that both components A and B will work.

Step 2: Multiply the probability that component A will work by the probability that component B will work.

Step 3: The result of Step 2 is the probability that the system will work under these conditions.

To learn more about probability refer :

https://brainly.com/question/11234923

#SPJ4

It will take Naomi approximately 4 quarters and 8 months, or 4.67 quarters to reach her goal.

To find the number of quarters required to reach $100,000 with a quarterly payment of $1500 and an interest rate of 4.4% compounded quarterly, we will  use the  formula below:

N = log((A / P) + 1) / log(1 + r)

Where:

N = number of quarters

A = target amount ($100,000)

P = payment per quarter ($1500)

r = interest rate per quarter (4.4%/4 = 1.1%)

Substituting the values, we have that

N = log((100,000 / 1500) + 1) / log(1 + 0.011)

N = log(66.67) / log(1.011)

N = 4.67 quarters

In conclusion, It will take Naomi approximately 4 quarters and 8 months, or 4.67 quarters to reach her goal.

Learn more about interest rate per quarter at: https://brainly.com/question/25793394

#SPJ1

The range of possible values for the third side of the triangle is d)6 < x < 26.

The third side of an acute triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides. By using the Pythagorean Theorem, we can find the range of possible values for the third side.

The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. So, for this triangle, we have 10^2 + 16^2 = x^2.

Solve for x: x^2 = 256, so x = √256 = 16.

The third side must be shorter than the sum of the other two sides. So, the maximum value for x is 16 + 10 = 26.

The third side must be longer than the difference of the other two sides. So, the minimum value for x is 16 - 10 = 6.

Therefore, the range of possible values for the third side of the triangle is 6 < x < 26.

For more questions like Triangle click the link below:

https://brainly.com/question/2773823

#SPJ4

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

Which best describes the range of possible values for the third side of the triangle?

x < 12.5, x > 18.9

12.5 < x < 18.9

x < 6, x > 26

6 < x < 26

The magnitude of u × v is 0, if u and v are orthogonal

Orthogonal;

By virtue of being perpendicular to one another, orthogonal objects are connected in Euclidean geometry. Lines or line segments are said to be connected orthogonally if they are perpendicular at the point of intersection. Similar to this, if two vectors create a 90-degree angle, they are said to be orthogonal.

What use does orthogonal serve?

The orthogonal matrix's determinant has a value of 1. Its nature is symmetrical. The transpose and inverse of an orthogonal matrix are equivalent. The orthogonal matrix's eigenvalues are also equal to 1, and its eigenvectors are both orthogonal and real.

Learn more about orthogonal here;

https://brainly.com/question/14004510

#SPJ4

The expression that is equivalent to x^(2/5) is

Information given in the problem

the expression x^(2/5)

This equation represents exponents in fraction form and the basics for the calculation is from

a^(b/c) =

[tex]\sqrt[c]{a^{b} }[/tex]

Rewriting the expression is done as below

x^(2/5)

= [tex]\sqrt[5]{x^{2} }[/tex]

comparing with [tex]\sqrt[c]{a^{b} }[/tex]

gives the following values

a will be equal to x

b will be equal to 2

c will be equal to 5

Learn more about exponents here:

https://brainly.com/question/29321719

#SPJ1

Answer first 8-5=3 3-2=1 5,1  is you answer kind sir mam or them

Step-by-step explanation:

To Convert Mcg To Mg, divide your mcg figure by 1000

How To Convert Mcg To Mg?

1 milligram (mg) = 1000 micrograms (mg)

1 microgram (mcg) = 1/1000

                              =0.001 milligrams (mg)

Input:

To learn more about mcg to mg conversion refer to:

https://brainly.com/question/18829939

#SPJ4

Divide the number of mcg by 1000 to convert it to mg .A microgram is equal to 0.000001 g in micrograms because the prefix "micro-" in this context stands for 10-6.

To learn more about microgram refer

https://brainly.com/question/1643851

#SPJ4

Answer:

r=-3

Step-by-step explanation:

divide both sides by -3

-3r/-3=9/-33

r=-3

Based on the Triangle Inequality Theorem, the range is: 14 < third side < 40.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. In other words, the length of any one side of a triangle must be less than the sum of the lengths of the other two sides.

This theorem is used to determine the possible range of lengths for the sides of a triangle and to test whether a set of given lengths can form a triangle.

So, the range for the measure of the third side of a triangle given that the measures of two sides are 13 and 27 is:

14 < third side < 40.

Learn more about the Triangle Inequality Theorem on:

https://brainly.com/question/309896

#SPJ1

The mSBY is the measure of the interior angle formed when three lines meet at a point. In this case, the three lines are a regular pentagon, a regular octagon, and SBY.

To calculate the mSBY, we must first calculate the measure of each of the other two angles. A regular pentagon has five sides, and each angle measures 108°. A regular octagon has eight sides, and each angle measures 135°. To calculate the mSBY, we must use the formula mSBY = 180° - (mP + mO). Using this formula, we can calculate that the mSBY is 37°: 180° - (108° + 135°) = 37°.

To visualize this, imagine three lines coming together at a point, forming an interior angle. The measure of the interior angle is the mSBY. The measure of the regular pentagon angle is 108°, and the measure of the regular octagon angle is 135°. When these two angles are added together, they equal 243°. Since the sum of the interior angles of a triangle is 180°, the measure of the interior angle must be 180° - 243°, which is 37°.

Learn more about interior angle here:

https://brainly.com/question/12834063

#SPJ4

a. independent event  P(AuB)=P(A)+P(B) b. mutually exclusive event  P(AuB) = P(A) + P(B) - P(AnB) c.  independent event P(A and B) = P(A).P(B)

d.   complement P(A') = 1 - P(A)

a. For two events A and B the union of the two sets is  simply all the elements present in both set. This can be expressed as

P(AuB)=P(A)+P(B)

b. Two events are said to be mutually exclusive if they cannot occur at the same time. i.e no same element must be present in both events at a time. This can be expressed as

P(AuB) = P(A) + P(B) - P(AnB)

c.  event A and event B are said to be independent if the incidence of event A  does not affect the probability of the event B.

This can be expressed as

P(A and B) = P(A).P(B)

d. complement of an event are simply all the occurrence not in he set but in the universal set.

the complement of set A can be expressed as

P(A') = 1 - P(A)

learn more about of events here

https://brainly.com/question/14641698

#SPJ4

The probability of randomly drawing and immediately eating three red M&Ms in a row from a bag that contains 7 red M&Ms out of 25 M&Ms total is 1/280.

This can be calculated by using the formula for probability, which is n/(N), where n is the number of desired outcomes and N is the total number of outcomes. In this case, n is equal to 7 (the number of red M&Ms) and N is equal to 25 (the total number of M&Ms). Therefore, the probability is 7/25, which simplifies to 1/280.In this case, the probability of drawing three red M&Ms in a row is 3 out of 25, or 3/25.

To learn more about randomly probability:

https://brainly.com/question/25428940

#SPJ4

Part a) A. The population must be normally distributed

Part b) P(overbar x < 68.2​) = 0.7967

Part c)P(overbar x ≥ 65.6​)=  0.3745

a) Population is normally distributed -

b) P(overbar x < 68.2​)

Estimate the z score (z).

z = (x -  μ) / s

z = (68.2 - 64) / 19/√14

z = 0.83

Use z table,

P(overbar x < 68.2​) = P(z < 0.83)

P(overbar x < 68.2​) = 0.7967

c)  P(overbar X  ≥  65.6)

Estimate the z score (z).

z = (x -  μ) / s

z = (65.6 - 64) / 19/√14

z = 0.32

Use z table,

P(overbar x ≥  65.6)  =  P(z  ≥  0.32)

                                  = 1 -  P(z  <  0.32)

                                 = 1 - 0.6255

                                 = 0.3745

P(overbar x ≥  65.6)  = 0.3745

To know more about the normally distributed, here

https://brainly.com/question/4079902

#SPJ4

When two linear equations in two variables have no solution, it means that the equations are not compatible. This means that the equations cannot be solved simultaneously, as there is no set of values that can satisfy both equations. This can be seen by graphing the equations on a coordinate plane. If the two lines are parallel, then they will never intersect, and thus, there is no solution. If the two lines are the same line, then they will intersect at every point, and thus, any point on the line is a solution.

In the case of two linear equations in two variables, if the equations are not parallel and not the same line, then the equations will intersect at one point. This point is the solution to the two equations. If the equations are not parallel and not the same line, but do not intersect, then there is no solution. This means that the equations are incompatible and cannot be solved simultaneously.

In summary, two linear equations in two variables have no solution when the equations are incompatible. This means that the equations are either parallel or the same line, but do not intersect. In this case, there is no set of values that can satisfy both equations, and thus, there is no solution.

To learn more about linear equations:

https://brainly.com/question/2030026

#SPJ4

Two linear equations in two variables have no solution if and only if the lines represented by the equations are parallel and do not intersect.

In other words, the lines do not have a common point, which means that there is no pair of values for the variables that satisfy both equations simultaneously.

Here's an example:

y = 2x + 1

y = 2x + 3

In this case, the lines represented by the equations are parallel and do not intersect, so there is no solution for the system of equations.

You can see this graphically by plotting the lines on a coordinate plane: the lines are close to each other, but they never intersect, so there is no common point that satisfies both equations.

To know more about Linear Equation:

https://brainly.com/question/11897796

#SPJ4

Calcula cuántos litros consumes al año

el consumo medio es de 250 cm³ en 1 día

Eso significa 1000 cm³ en 4 días. 1000 cm³ = 1 litro

Entonces 1 año = 365 días.

dividelo entre 4 dias

entonces cuantos litros se consumen al año

365 días * 1 Litro / 4 días = 91,25 Litros por año

si 1 litro cuesta 0.75$.

91,75 litros * $0,75 = $68.437.

redondeado a $68.44

El litro es una unidad de medida de volumen. Sin embargo, el litro no es una unidad estándar internacional, sino que se ha identificado como una de las "unidades no estándar aceptadas para su uso con Standard". La unidad estándar internacional de volumen es el metro cúbico (m³).

1L = 1dm³ = 1000 cm³ = 1000 cc

1 ml = 1 cm³ = 1 cc l

Un litro corresponde a:

0,001 metros cúbicos

1000 centímetros cúbicos

1 decímetro cúbico

Cubo de botones de 10 centímetros de lado.

Un metro cúbico (m³) contiene 1.000 litros. Entonces los litros también se pueden dividir en unidades más pequeñas.

Aprenda más sobre litro di

https://brainly.com/question/10949125.

#SPJ4

The required percent error of the measurement is 0.8%.

Error bar, are the line through a point on a graph, axes, which emphasizes the uncertainty or variation of the corresponding coordinate of the point.

The percent error of Adrian's measurement can be calculated as follows:

(|Measured value - Actual value| / Actual value) * 100

= (|12.8 - 12.7| / 12.7) * 100

= (0.1 / 12.7) * 100

= 0.786%

Rounded to the nearest tenth of a percent, the error is 0.8%.

Learn more about the error bar here:

https://brainly.com/question/14639901

#SPJ1

Answer:6.6%

Step-by-step explanation:

If the expression is the square of a binomial, then it must have the form [tex]$(ax + b)^2 = a^2x^2 + 2abx + b^2$[/tex].

Comparing the coefficients of like terms, we have:

[tex]a^2 = x^2$, so $a = x[/tex]

[tex]2ab = 18x$, so $b = 9[/tex]

Therefore, the missing number is [tex]$\boxed{9}$[/tex].

The missing number was found by using the fact that the expression must have the form [tex]$(ax + b)^2 = a^2x^2 + 2abx + b^2$[/tex] if it is the square of a binomial.

By comparing the coefficients of like terms in this equation and in the expression given, [tex]$x^2 18x \boxed{\phantom{00}}$[/tex], we were able to solve for the values of [tex]$a$[/tex] and [tex]$b$[/tex] as follows:

[tex]$a^2 = x^2 \Rightarrow a = x$[/tex]

[tex]$2ab = 18x \Rightarrow b = 9$[/tex]

Finally, we see that the coefficient of the [tex]$x$[/tex] term in the expression is [tex]$2ab = 2 \cdot x \cdot 9 = 18x$[/tex], which matches the given expression. Hence, the missing number is [tex]$\boxed{9}$[/tex].

Learn more about Missing Number Square of Binomial here:

https://brainly.com/question/26197845

#SPJ4

There are two triangles ABC and DEF with sides are (37.5, 20, 27.5) and (y, 12, 16.5) and the value of y is 22.59.

Triangle is consists of 3 sides and there are many types of triangles like equilateral triangle, obtuse triangle and right-angled triangle and the triangle has many properties .

Triangle has three edges and three vertices.

A triangle with vertices A,B,C can be denoted as Triangle ABC

The sides of triangle ABC is (37.5, 20, 27.5)

The sides of triangle DEF is (y, 12, 16.5)

By similarity property we get,

37.5/y = 20/12 = 27.5/16.5

37.5/y = 1.66 = 1.66

so by equating values we get , y = 37.5/1.66

so the value of variable y is 22.59.

Learn more about triangle here:

https://brainly.com/question/2773823

#SPJ4

Protons are a type of subatomic particle with a positive charge. With more electrons than protons, the particle is negatively charged.

Learn more about proton and electron refer to :

https://brainly.com/question/1805828

#SPJ4

Using Priya's method to calculate (0.0015) x (0.024) gives 0.0000360

To multiply decimals using Priya's method, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Now, 15 × 24 = 360

0.0015 has 4 numbers after the decimal and  0.024 has 3 numbers after the decimal. The total is 7.

Moving the decimal point 7 spaces to the left, we get 0.0000360.

Thus,  (0.0015) x (0.024) = 0.0000360

Note: 0.0000360 = 0.000036

To learn more about Priya's method on:

brainly.com/question/11162176

#SPJ1

The height of the cone is - 3.4 centimeters.

Given data :

The total surface area of the cone is calculated by the formula -

Total surface area = πrl² + πr²

Keep the values in the formula to find the value of length or hypotenuse.

90π = πr(l² + r)

90 = 5(l² + 5)

18 = l² + 5

l² = 13

Now, find the height of the cone.

length² = perpendicular² + base²

13 = perpendicular² + 5²

Perpendicular² = 25 - 13

Perpendicular² = 12

Perpendicular = 3.4 centimeters.

Thus, the height of the cone is 3.4 centimeters

Learn more about cone refer to ;

https://brainly.com/question/27812847

#SPJ4

For the situation in part (b), the boundary condition is given by B·n = μ_0J/2πa, where n is the unit normal vector to the surface of the wire and J is the current density. This is consistent with the magnetic

(a) The magnetic field outside the wire is given by B = μ_0I/2πs, where I is the current and s is the distance from the axis of the wire. The magnetic field inside the wire is zero.

(b) The magnetic field outside the wire is given by B = μ_0J/2πs, where J is the current density and s is the distance from the axis of the wire. The magnetic field inside the wire is given by B = μ_0J/2πa, where a is the radius of the wire.

(c) For the situation in part (a), the boundary condition is given by B·n = μ_0I/2πa, where n is the unit normal vector to the surface of the wire and I is the current. This is consistent with the magnetic field outside the wire, which is given by B = μ_0I/2πs.

Learn more about vector here

https://brainly.com/question/15709504

#SPJ4

"Owning a home provides a partial tax shelter for housing-related expenses" the following is an advantage of purchasing and owning a home.

Hence, option (B) is correct choice.

The Benefits of Owning a Home:

Interest rates are low.

Creating equity: The difference between what you can sell the house for and what you owe is your equity. As you pay down your mortgage, your equity rises. Over time, more of your monthly payments will be applied to the loan balance rather than the interest, resulting in more equity.

Federal tax breaks: Mortgage interest is deductible on the first $750,000 of the house's purchase price, as are home equity loan interest, property taxes up to $10,000 if married ($5,000 if married filing separately), and various closing fees at the time of purchase.

Greater privacy: Because you own the property, you may renovate it to your desire, something tenants do not have.

Home office: The work-at-home craze may persist after the epidemic has passed, implying that more of us will require a home office. The appropriate configuration affects both comfort and productivity.

Monthly payments that are predictable: A fixed-rate mortgage requires you to pay the same amount each month for principle and interest until the loan is paid off. Rents are subject to rise with each annual lease renewal. Changes in property taxes or homeowner's insurance can affect monthly payments, although not as often as rent hikes.

Stability: People tend to stay in a house they own for a longer period of time, if only because purchasing, selling, and relocating is difficult.

For more questions on advantages of purchasing a home

https://brainly.com/question/3616137

#SPJ4

Answer:

B. Owning a home provides a partial tax shelter for housing related expenses

Hope this helps! Have an amazing day/night/afternoon!

Answer:

Option 1 is correct

Step-by-step explanation:

The solution of dy/dt = (t*y^-.5)/3 with y(0)=1 is y(1) = 1.

The solution to the given differential equation is given by the following formula:

y(t) = [tex](3/t^2)^2/3 + C[/tex]

where C is the constant of integration.

To find the value of y(1), we need to substitute t = 1 in the above formula.

y(1) =[tex](3/1^2)^2/3 + C[/tex]

y(1) = 9 + C

Since y(0) = 1, we can find the value of C by substituting t = 0 in the above formula.

y(0) = ([tex]3/0^2)^2/3 + C[/tex]

y(0) = 9 + C

1 = 9 + C

C = -8

Substituting C = -8 in the formula for y(1),

y(1) = 9 + (-8) = 1

Therefore, y(1) = 1.

Thus, the solution of [tex]dy/dt = (t*y^-.5)/3 , y(0)=1[/tex] is y(1) = 1.

Learn more about differential equation here:

https://brainly.com/question/14620493

#SPJ4

Due to the triangle being translated 1 unit down and 3 units to the right, the new x-coordinate of R is now -2+3 = 1.R's x-coordinate was 2, thus 2 Plus 3 equals 1.

Triangle PQR is formed by points P (2, 1), R (2, 5) and Q (6, 5) and is then translated 1 unit downward and 3 units to the right. This indicates that all three points move three units to the right and one unit down. We may utilise R's initial x-coordinate, which was -2, to determine its new x-coordinate. Then, as R is being translated three units to the right, we add three to it. Consequently, R's new x-coordinate is now -2 + 3 = 1. Triangle PQR has been translated one unit down and three units to the right, giving rise to a new x-coordinate of R of 1. We must first determine the coordinates of each of the three triangle's points in order to determine the new x-coordinate of R. Point P is situated at (2, 1), point R at (2, 5) and point Q at (6, 5) respectively.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

The perimeter of the entire shape that is made up of a semi circle and an equilateral triangle would be = 116.66in

The perimeter of a shape is defined as the total area of all the sides surrounding that shape.

The perimeter of the object can be calculated by the addition of the perimeter of the triangle and the circle.

The perimeter of the triangle = a+b+c = 19+19+19 = 57in

The perimeter of the circle = 2πr

where π = 3.14

r = 19/2 = 9.5 in

perimeter = 2×3.14×9.5 = 59.66in

The perimeter of the whole object = 57+59.66 = 116.66in.

Learn more about perimeter here:

https://brainly.com/question/25092270

#SPJ1

Since, the formula for variance is Variance = (σ)², where σ denotes standard deviation, the statement "the standard deviation is the positive square root of the variance" is false.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

The dispersion of the set of data values is measured by the standard deviation. The sigma symbol (σ) serves as its symbol.

This indicates that the data values tend to be more dispersed over a greater range for a higher standard deviation. While a lower number of standard deviation results from data being closer to its mean.

Variance, which is the expectation of the squared standard deviation, is a measure of how widely distributed the data are with respect to their mean.

As a result, the relationship between standard deviation and variance can be expressed numerically as, Variance = (σ)².

Therefore, standard deviation is not square root of variance.

To learn more about standard deviation from the given link

https://brainly.com/question/12402189

#SPJ4