what is the area of a rectangle that has sides measuring (7x-1) units and (2x+3)​

Therefore, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is 0.25, or 25%.

The probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 can be found using the formula:

P(event) = number of favorable outcomes / total number of possible outcomes

In this case, the number of favorable outcomes is 3, since there are 3 preparation stations that we are interested in (6, 7, and 8). The total number of possible outcomes is 12, since there are 12 preparation stations in total.

So, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is:

P(event) = 3 / 12

P(event) = 0.25

Therefore, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is 0.25, or 25%.

To know more about probability, refer here:

https://brainly.com/question/30034780#

#SPJ11

Answer:

The object falls 4.9 meters in the first second, 14.7 meters in the second second, 24.5 meters in the third second, and 34.3 meters in the fourth second. We can see that the object is falling 9.8 meters per second per second, which is the acceleration due to gravity.

To find how far the object falls in 10 seconds, we can use the formula for the sum of an arithmetic sequence:

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

where S is the sum of the sequence, n is the number of terms, a is the first term, and d is the common difference between the terms.

In this case, we have:

n = 10 (since we want to find the total distance in 10 seconds)

a = 4.9 (the first term is the distance fallen in the first second)

d = 9.8 (the common difference is the acceleration due to gravity)

Plugging in these values, we get:

S = 10/2(2(4.9) + (10-1)9.8) = 10/2(9.8 + 88.2) = 10/2(98) = 490

Therefore, the object will fall a total of 490 meters in 10 seconds.

The object will fall 495 meters in 10 seconds.

It is a sequence where the difference between each consecutive term is the same.

We have,

We can see that the object is falling with a constant acceleration of 9.8 meters per second squared (which is the acceleration due to gravity near the surface of the Earth).

Each second, the distance the object falls increases by an additional 9.8 meters.

So, during the fifth second, the object will fall 44.1 meters (34.3 + 9.8), during the sixth second it will fall 53.9 meters, during the seventh second it will fall 63.7 meters, during the eighth second it will fall 73.5 meters, during the ninth second it will fall 83.3 meters, and during the tenth second it will fall 93.1 meters.

The total distance the object will fall in 10 seconds is:

= 4.9 + 14.7 + 24.5 + 34.3 + 44.1 + 53.9 + 63.7 + 73.5 + 83.3 + 93.1

= 495 meters

The object will fall 495 meters in 10 seconds.

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ2

Answer:

Rectangle, yes yes or no rectangle

Step-by-step explanation:

There will be 4 small boxes and 2 large boxes of granola bars.

A variable is an attribute or a phenomenon that can be measured and has a changing value over time.

Given,

Number of granola bars in the small box = 10

Number of granola bars in the large box = 30

The number of small boxes = three times the number of a large boxes

To Find,

The number of small boxes purchased =?

The number of large boxed purchased =?

Let the number of large boxes be y

The number of small boxes be x

Total number of boxes, x + y = 6         ..... equation i

Total number of granola bars in small box = 10x

Total number of granola bars in large box = 30x

So, 10x + 30x = 100

After dividing by 10 we get

x + 3y = 10                                               ..... equation ii

Subtracting equation ii from equation i

We get,   2y = 4

y = 2

Putting the value of y in equation i we get x = 4

So, there will be 4 small boxes and 2 large boxes of granola bars.

Learn more about variables on:

https://brainly.com/question/2466865

#SPJ1

Therefore , the solution of the given problem of equation comes out to be required equation is 0.05b = 4.80 .

Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection integer between each sign part and the number of lines. The significance of a symbol usually contradicts itself.

Here,

The following equation can be set up to represent the circumstance if x is the procedure's cost:

=>  5% of x = $4.80

The percentage must first be divided by 100 to become a decimal before we can answer for x:

=>  0.05x = $4.80

Then, by dividing both lines by 0.05, we can separate out x:

=>  x = $96

Consequently, the process will cost you $96. It is possible to confirm that the gratuity is 5% of $96:

=>  5% of $96 = 0.05 × $96 = $4.80

So, the solution is:

=> 0.05b = 4.80

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].

To subtract the rational expressions and find the answer in its fully factored form, we first need to find a common denominator for the two expressions.

The denominators of the two expressions are (m^(2)-64) and (2m^(2)-128). We can factor both of these to find the common denominator.

(m^(2)-64) = (m+8)(m-8)

(2m^(2)-128) = 2(m^(2)-64) = 2(m+8)(m-8)

The common denominator is 2(m+8)(m-8).

Now we can rewrite the two expressions with the common denominator and subtract them:

[(m^(2)+4m-12)(2) - (m^(2)+11m+24)(m+8)(m-8)] / [2(m+8)(m-8)]

= [(2m^(2)+8m-24) - (m^(3)+11m^(2)+24m+8m^(2)+88m+192)] / [2(m+8)(m-8)]

= [m^(3)-17m^(2)-104m-216] / [2(m+8)(m-8)]

= (m-9)(m^(2)-8m-24) / [2(m+8)(m-8)]

= (m-9)(m-12)(m+2) / [2(m+8)(m-8)]

So the answer in its fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].

To know more about rational expressions click on below link:

https://brainly.com/question/17134322#

#SPJ11

Hence, there is a 38.2% likelihood that the group chosen will consist of two men and two women.

A committee's primary responsibility is to aid in the smooth operation of the company. The majority of the time, the main concerns of a committee are information sharing and assisting the leadership in making decisions by providing them with the necessary knowledge.

We may employ the formula of combinations to determine the likelihood of choosing a group comprising two men plus two women from of the committee. C(7,2) = 21 ways to choose two males from a group of seven, and C(4,2) = 6 ways to choose two women from a group of four. Hence, there are 21 x 6 = 126 different ways to choose a team of two men and two women.

C(11,4) = 330 different techniques can be used to choose any four members of the committee. Thus, the following is the likelihood of choosing a team of two men and two women:

126 / 330 = 0.382 or 38.2%

To know more about committee's function visit:

https://brainly.com/question/11621970

#SPJ1

The equation of the line that passes through the point (14,3) and is perpendicular to the given equation is y = x - 11.

To solve the equation 5(y+x)-6(x-y)=-8, we need to use the distributive property and combine like terms.

5(y+x)-6(x-y)=-8

Distribute the 5 and -6:

5y + 5x - 6x + 6y = -8

Combine like terms:

11y - x = -8

Now, we need to find the slope of the line that passes through the point (14,3) and is perpendicular to the given equation.

The slope of the given equation is -1, so the slope of the perpendicular line is the negative reciprocal, which is 1.

Using the point-slope form, we can write the equation of the perpendicular line:

y - 3 = 1(x - 14)

Distribute the 1:

y - 3 = x - 14

Add 3 to both sides:

y = x - 11

To know more about perpendicular click on below link:

https://brainly.com/question/11707949#

#SPJ11

It is not possible to use Cramer's Rule to solve the system of equations you provided. This is because Cramer's Rule can only be applied to systems of linear equations that have the same number of equations as there are unknowns.

In the system you provided, there are four equations but only two unknowns. This means that Cramer's Rule cannot be applied.

Instead, you can use other methods such as substitution or elimination to solve the system. However, it is important to note that with more equations than unknowns, it is possible that there may be no solution or an infinite number of solutions.

To know more about Cramer's Rule refer here:

https://brainly.com/question/30682863

#SPJ11

For 0 miles cost is 3 dollars, for 4 miles cost is 7 dollars, for 6 miles cost is 9 dollars, for 8 miles cost is 11 dollars.

Distance refers to the measurement of the space or length between two points, objects, or locations.  In mathematics, the distance between two points in a coordinate plane can be calculated using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

In physics, distance is an important concept in understanding motion and energy. For example, the distance traveled by an object can be used to calculate its speed and acceleration, and the distance between two objects can affect the strength of their gravitational attraction.

In everyday life, distance is often used to describe physical space between objects, such as the distance between two buildings, the distance between two cities, or the distance between two people. It is also used in the context of travel, such as the distance between two destinations and the time it takes to travel that distance.

C = 3 + m

Distance in miles (m)              Cost in dollars (c)

0                                               3

4                                               7

6                                               9

8                                               11

To know more about cost visit:

https://brainly.com/question/1853254

#SPJ1

The complete question is:

Check the picture below.

The ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.

To write the ratio as a fraction in simplest form, we will follow the steps below:

Step 1: Write the ratio as a fraction. In this case, we have 3.5cm:1.4cm, which can be written as 3.5cm/1.4cm.

Step 2: Simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF). In this case, the GCF of 3.5 and 1.4 is 0.7. So we will divide both the numerator and denominator by 0.7 to get:

(3.5cm/0.7) / (1.4cm/0.7) = 5/2

Step 3: Convert the fraction to simplest form with whole numbers in the numerator and denominator. In this case, we can multiply both the numerator and denominator by 10 to get:

(5*10)/(2*10) = 50/20

Step 4: Simplify the fraction by dividing both the numerator and denominator by the GCF. In this case, the GCF of 50 and 20 is 10. So we will divide both the numerator and denominator by 10 to get:

(50/10)/(20/10) = 5/2

Therefore, the ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.

To know more about fractions, refer here:

https://brainly.com/question/10354322#

#SPJ11

To find the rational roots of the equation x^(4)-4x^(3)-5x^(2)+16x+4=0, we can use the Rational Roots Test. This test states that any rational root of the equation can be expressed as p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is 4 and the leading coefficient is 1. The factors of 4 are 1, 2, and 4, and the factors of 1 are 1. Therefore, the possible rational roots are 1, 2, 4, -1, -2, and -4.

We can use synthetic division to test each of these possible roots. If the remainder is 0, then the root is a rational root of the equation. For example, let's test the root 1:

1 | 1 -4 -5 16 4
 |   1 -3 12 28
 ---------------
 | 1 -3 -8 28 32

The remainder is 32, which is not 0, so 1 is not a rational root of the equation.

We can continue to test the other possible roots in the same way until we find the rational roots of the equation. Once we have found the rational roots, we can use them to factor the equation and find the remaining roots.

Learn more about equation

brainly.com/question/29657983

#SPJ11

The distance between Jason's school and his house is 8 miles.

What is the Cartesian system?

Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be plotted as an ordered pair (x, y) known as Coordinates. The origin, symbolized by the letter "O," is the point where the two number lines intersect. The horizontal number line is known as the X-axis, and the vertical number line is known as the Y-axis.

Given that the coordinates of Jason's house is (-4,-5). The coordinates of his school is  (-10,-11).

The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

Here, x₁ = -4, y₁ = -5,x₂= -10, y₂ = -11

The distance between points is

√[(-10-(-4))² + (-11 - (-5))²]

=√(6² + 6²)

= √(36+36)

= √72

= 6√2

= 8.48

≈ 8 miles

To learn more about distance, click on the below link:

https://brainly.com/question/17252855

#SPJ1

This statement is false. A right exact functor preserves exactness of short exact sequences at the right-hand side, but it does not necessarily preserve exactness at the left-hand side. An example of a right exact functor that is not left exact is the tensor product functor.

The following statements can be proved or disproved as follows:
(a) Every ring is an IBN ring.
This statement is false. A ring is said to be an IBN (Invariant Basis Number) ring if all of its finitely generated free modules have unique rank. However, not all rings have this property. For example, the ring of polynomials over a field F, F[x], is not an IBN ring.
(b) In a ring R, if for any a,b∈R,ab=0, then ba=0.
This statement is true. If ab=0, then b is a zero divisor in the ring R. Since zero divisors are symmetric, this implies that ba=0 as well.
(c) The characteristic of a finite field is a prime number.
This statement is true. The characteristic of a finite field is the smallest positive integer n such that n*1=0 in the field. Since a finite field is also an integral domain, it cannot have zero divisors, and therefore the characteristic must be a prime number.
(d) Every right exact functor is also left exact.
This statement is false. A right exact functor preserves exactness of short exact sequences at the right-hand side, but it does not necessarily preserve exactness at the left-hand side. An example of a right exact functor that is not left exact is the tensor product functor.

Learn more about Finitely

brainly.com/question/29732670

#SPJ11

Answer:

  -119/169

Step-by-step explanation:

You want cos(2α) where cos(α) = 5/13 and 270° < α < 360°.

The desired function is ...

  cos(2α) = 2cos²(α) -1

In the given quadrant, sin(α) < 0. Since the sine is squared in the double-angle identity, whether it is positive or negative is irrelevant.

  [tex]\cos(2\alpha)=2\cos^2(\alpha)-1=2\left(\dfrac{5}{13}\right)^2-1=\dfrac{2(25)-169}{169}\\\\\boxed{\cos(2\alpha)=-\dfrac{119}{169}}[/tex]

The restrictions for this equation are that y must be greater than or equal to 0, since the square root of a negative number is not a real number. So, the restrictions for this equation are y ≥ 0.

To solve the equation √y + 6 = 4, we first need to isolate the square root on one side of the equation. We can do this by subtracting 6 from both sides of the equation:
√y = 4 - 6
√y = -2

Now, we need to square both sides of the equation to get rid of the square root:
y = (-2)^2
y = 4

So, the solution to the equation is y = 4. However, we need to verify this solution by plugging it back into the original equation:
√(4) + 6 = 4
2 + 6 = 4
8 = 4

This is not true, so there are no solutions to the equation.

The restrictions for this equation are that y must be greater than or equal to 0, since the square root of a negative number is not a real number. So, the restrictions for this equation are y ≥ 0.

For more information about equation, visit:

https://brainly.com/question/22688504

#SPJ11

Answer:

It is D

Step-by-step explanation:

Its D it has to be 5 and bigger than 5

Triangle IJK is an isosceles triangle.

The slope of IJ is -2, the slope of JK is 1, and the slope of IK is 2. The length of IJ is 8, the length of JK is 4, and the length of IK is 6. Triangle IJK is an isosceles triangle.
√Correct

Learn more about isosceles trianlge

brainly.com/question/2456591

#SPJ11

The Big Ideas or Focal Points in the mathematics curriculum in grades 4 are as follows:

Learn more about focal points

brainly.com/question/16188698

#SPJ11

Ryan needs to make a  monthly deposit of $774.08 in order to have $30,000 for a down payment on a home.

To calculate the monthly deposit that Ryan needs to make in order to have $30,000 in 3 years, we can use the formula for the future value of an annuity:

FV = Pmt * [(1 + r)ⁿ - 1] / r

where FV is the future value (in this case, $30,000),

Pmt is the monthly deposit,

r is the monthly interest rate (5% / 12 = 0.00417), and

n is the number of compounding periods (36 months).

Substituting the values we have:

30,000 = Pmt * [(1 + 0.00417)³⁶ - 1] / 0.00417

38.75564454Pmt = 30,000

Pmt = 30,000/38.75564454

Pmt = $774.08

Therefore, Ryan needs to deposit approximately $774.08 each month in order to have $30,000 for a down payment on a home.

Learn more about future value of an annuity on:

https://brainly.com/question/14702616

#SPJ1

Answer: In each of the terms 3x 2 and 7x, x is a variable, and in both terms, we are multiplying a number by the variable. In the first term, 3x 2, 3 is being multiplied by the variable, so 3 is a coefficient. In the second term, 7x, 7 is being multiplied by the variable, so 7 is a coefficient.

Step-by-step explanation:

An expression that looks like Sarah's expression but is not equivalent is:

10(5j + j + 3).

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. This statement is represented mathematically by the expression x/2 + 6. Using mathematical expressions, complex puzzles can be solved.

now in the question,

We can write a look alike expression which is not equivalent is:

10(5j + j + 3).

Now translating the new expression into verbal:

Sarah gets paid $10 for every shark tooth she finds. After finding 3, she asked Jhon for help. When Jhon finds a tooth, by that time Sarah finds 5 of them.

To know more about expressions, visit:

https://brainly.com/question/14083225

#SPJ1

Overproduction of uric acid in the body is a condition known as hyperuricemia. It occurs when the body produces more uric acid than it can excrete. Uric acid is a waste product that is formed when the body breaks down purines, which are found in certain foods and drinks. If the body is unable to get rid of the excess uric acid, it can build up and form crystals in the joints, causing a painful form of arthritis known as gout.

Hyperuricemia can also be an indication of other health conditions, such as leukemia and lymphoma. These are types of cancer that affect the blood cells and the immune system, respectively. When cells in the body break down, they release uric acid into the bloodstream. If there is an overproduction of cells, as in the case of leukemia and lymphoma, this can lead to an excess of uric acid in the body.

It is important to monitor the levels of uric acid in the body, as it can be an early indication of these serious health conditions. A healthcare professional can conduct tests to measure the levels of uric acid in the body and determine the cause of the overproduction.

Know more about Hyperuricemia here:

https://brainly.com/question/14368274

#SPJ11

Correct question is" Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advanced indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.75 mg/dl. (a) Find a 95 % confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) (b) Find the sample size necessary for a 95 % confidence level with a maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)"

The value of x in the triangle given the midsegment points and sections is 1.35 units

The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.

The midsegments of triangle UWY are VR, VZ, ZR

To find the value of x, we use a theorem called the mid segment theorem which states that:

"The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle."

The third side of triangle UWY is WY and it measures 2.7.

Therefore, x will be 2.7 divided by 2 2.7/2 which will give us the value 1.35 i.e. x = 1.35

To learn more about midsegment triangles visit

https://brainly.com/question/11412750

#SPJ1

So, by resolving the given, we obtain the result: As a result, the range of standard deviation timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.

A statistic called standard deviation may be used to represent the variability or variation of a collection of statistics. A low standard deviation means that the values often tend to be closer to the set mean, whereas a large standard deviation shows that the values are widely spread. The standard deviation is an indicator of how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is small, and are more scattered when it is big. Standard deviation is the average degree of variability in the data collection. It displays each score's standard deviation from the mean.  

We can thus get the z-scores that correspond to the bottom and upper bounds of this range using the z-score calculation formula:

Lower bound: z = (x - )/z = (x - 80)/z = 2.5 z = -3

The maximum value is z = (x - ) / z = (x - 80) / 2.5 z = 3.

The area under the curve between z = -3 and z = 3 can be calculated using a calculator or a conventional normal distribution table.

The minimum value is z = -3 (x - 80) / 2.5 = -3 x - 80 = -7.5 x = 72.5.

z = 3 (x - 80) / 2.5 = 3 x - 80 = 7.5 x = 87.5 is the upper limit.

As a result, the range of timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ1

cost = 3/√34,  csct = √34/5, sect =√34/3 , and cott = 3/5

explanation:-

The given equation is: tant = 5/3, so, cot t = 3/5 as cot t= 1/tan t

we know sec² t - tan² t = 1

or, sec²t= 1 + tan²t = 1+(25/9) = 34/9

or, sect = √(34/9) = √34/3

or, cos t=√(9/34) = 3/√34 as cos t= 1/sec t

now, also, csc²t - cot²t = 1

or, csc²t = 1+cot²t = 1+ 9/25 = 34/25

or, csc t= √34/5

learn more about trigonometry here. https://brainly.in/question/2685053

#SPJ11

The round-off of the number 216,777777 to 2 decimal places​ is 216.78.

When a number is rounded off, its value is preserved while it is moved closer to the next number. simplifying the number. It is done for whole numbers as well as decimals at different places of hundreds, tens, tenths, and so on.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. If the number after it is between 5 and 9, it will be rounded up to its higher value.

To round 216,777777 to 2 decimal places, we look at the third decimal place, which is 7. Since 7 is greater than or equal to 5, we round up the second decimal place, which is 7. Therefore, 216,777777 rounded to 2 decimal places is 216,78.

To know more about rounding off numbers follow

brainly.com/question/10340128

#SPJ1

Answer:

Without more information about the diagram, it is impossible to determine the term that describes GI. The terms median, angle bisector, perpendicular bisector, and altitude are all related to different types of lines and segments in triangles. Depending on the context and information given in the diagram, GI could be any of these.

Step-by-step explanation:

wag na pa delete nito na bweweset ako ang bob0 ng admin