how do you solve this?

Answer:

l=10.5 in , w=16.5 in

Step-by-step explanation:

p=2l+2w
54=2(w-6)+2(w)
54=2w-12+2w
54=4w-12
66=4w
w= 16.5
l=w-6
l=16.5-6

l=10.5 in
w=16.5 in

hope this helps

1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment

2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive

3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism

4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle.  Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion

According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.

Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.

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The expected number of the real workers in any sample of size 50 is 35

Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done. Assume James and Natalie had the notion to arrange the matchsticks into numerical patterns while they were fiddling with them.

Given that : A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers.

n= 50

30 % are ghost workers

= 30% 0f 50

= 0.3×50

= 15 are ghost workers

50 - 15 = 35 are real workers

The expected number of the real workers in any sample of size 50 is 35

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Source of magnetic force - Nail

Source electric force - battery cell

We know that the electromagnet is a type of magnet whose magnetic property depends on the interaction of the magnetic material with an electric field. We can see in the image that the nail which serves as the magnetic material is connected to a cell which is the source of the given electric current.

It the follows that the nail above is the source of the magnetic force because the coils of wire while the battery cell is the source of the electrical force.

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Answer:

You cannot multiply or divide for 4 and 3 so no false

Step-by-step explanation:

Answer:

mean: 86 median: 85 mode: 85

Step-by-step explanation:

Answer:

72 m

Step-by-step explanation:

We observe that 7y+6=18, and thus y=12/7.

So, the perimeter is:

[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]

Answer:

First option is correct.

Step-by-step explanation:

Normally, Pete's dad deposits $25 into his bank account every week.

Now, he wants to deposit x extra dollars for 8 weeks. So, the total deposits for these 8 weeks will be:

8*(25 + x)

He wants to keep the total deposits above 500. So

8*(25 + x) > 500

Now we solve the inequality similarly to how we would solve an equality.

8*(25 + x) > 500

200 + 8x > 500

8x > 500 - 200

8x > 300

x > 300/8

x > $37.50

So the first option is correct.

Given,

The measure of side YZ is 21.

The measure of side XY is 20.

The measure of side XZ is 29.

Required:

The value of tanX.

The trigonometric ratio is calculated as,

Substituting the values,

ence, the value of tanX is 21/290.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

he detiails of the solution are as follows:

sing the Laws of logarithm which says that:

Hence,

Answer:

160,000

Step-by-step explanation:

Answer:2.225

Step-by-step explanation:

If you add all the numbers and then divide by the number of numbers given you get the average.

The equation that represents the daily production cost based on the number of pairs of boots manufactured each day is C(x) = 4.75x + 400.

What are linear equations?
Linear equations are a subset of first order equations. Linear equations are defined for lines in the coordinate system. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.

Given, the daily production cost (in $) = C(x)
The number of pairs of boots manufactured = x
The cost of making a pair of boots = $ 4.75
The fixed cost of production each day = $ 400
Thus, net cost of making 'x' boots added to the daily fixed production cost will give the  daily production cost.
Therefore, C(x) = 4.75x + 400, is the correct equation.

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Answer:

yellow 75 gallons

white 45 gallons

red 15 gallons

Step-by-step explanation:

yellow (5) + white (3) + red (1) equal 9 total parts.

5/9 is yellow

3/9 is white

1/9 is read

5/9 x 135 = 75

3/9 of 135 = 45

1/9 of 135 = 15

The peaches required for every cup of water is 4/3

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

so;

    A.T.Q:-                  

Is there two columns of data and two data points? Like this:

peaches          Water

40                    30

400                  300

If so, then there are two ways to do it.

1) You can set up a ratio like this

40/30 = x

:-Where x is the number  of peaches for every cups of water .

So;

x = 40/30  peaches

x = 4/3  peaches

2) Look at the increase from one to the other.

3 cups of water requires 4 peaches.

∵ Hence by unitary method

1 cup of water requires 4 /3  peaches.

:- so; 4/3 peaches are required for every cup of water.

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Answer:  x = 3

x = ± √3 = ± 1.7321

Step-by-step explanation:

those are 2 solutions

(a) 291/2020

(b) 77/465

(c) 437/1010

(d) 145/376

(e) 32/157

(f) 53/157

(g) 433/465

(h) 335/376

Find the inverse of:

a. To sketch f(x), we use the graph of the parent function

Translated 3 units to the left:

b. The part of the function f(x) that is one-to-one and non-decreasing is in the domain [-3, ∞). Expressing in inequality notation: x ≥ -3.

c. The function f(x) can be written as:

Applying square root on both sides:

Solving for x:

Swapping letters:

Since we have chosen only the non-negative part of the domain for f(x), we use only the positive sign:

Both functions, f(x) and its inverse are shown below:

Answer:

Step by step explanation:

To solve this situation we can create a system of linear equations, with the given information for the customers:

Let x be the price for each hamburger

Let y be the price for each drink

To solve for x and y. We can use the substitution method, which consists of isolating one variable in one of the equations and substitute it into the other.

Let's isolate y in (1):

Now, substitute it into equation (2).

Solve for x:

With the x-value, we can substitute it into the equation (1) to find the price for each drink:

Therefore, the price for each hamburger is $3.5 and for each drink is $1.5.

Now, if we want to buy 8 drinks and 9 hamburgers:

The surface area and volume of the polyhedron are mathematically given as

This is further explained below.

Generally, The surface area of a three-dimensional object is equal to the total of areas of all of its faces, also known as surfaces. A cuboid has six faces that are rectangular in shape.

Add together the areas of each of the cube's six sides to get the surface area of the cube. To get the surface area of the prism, we may additionally label its length (l), width (w), and height (h), and then use the formula surface area = length (l) times width (w) times height (h).

To refresh your memory, the surface area of an item is the entire area of the exterior surfaces of the three-dimensional object or the total sum of the area of the faces of the object.

In other words, the surface area of an object is its "face area." It is expressed in terms of square units as a measurement.

In conclusion, Generally, the Surface area is mathematically given as

SA= 9+35+35+33+36+12

SA=160 Sqr Units

Generally, the equation for Volume is mathematically given as

V=(11*9)+6

V=99+6

V=105 cubic units

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CQ is attached  surface area

The degree of the polynomial is even.

Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and [tex]x^{2}[/tex] + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.

The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).

The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.

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Step-by-step explanation:

we have to find the equation, that's why we select the data

(t, n) = (50, 52) and (14,148)

we look as follows

n-52 = ((148-52) / (14-50)) * (t-50)

We perform the indicated operations

n-52 = (96/24) * (t-50)

n-52 = 4 (t-50)

finally we get the result

n = 4t-148

Answer:

Linear equation n = 4t-148

B)

Therefore,

Hence, the answer is 61degrees.

x = Number of posts

y = samuel's savings

If he order 2 posts with words and pictures:

y = 2(10) + 35 = 55

If he order 2 posts with words only and 2 posts with pictures only.

y = 2(5) + 2(10) + 5 + 25 = 10 + 20 + 5 + 25 = 60

Therefore, he could have save 5 dollars

Therefore the equation is:

y = 5x - 5

The composite function F(1) has a value of 2

The definition of the composite function is given as

F(x) = f(xf(xf(x)))

Also, we have

f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5, and f '(5) = 6,

Substitute 1 for x in the equation F(x) = f(xf(xf(x)))

So, we have

F(1) = f(xf(xf(1)))

From the question

f(1) = 2

So, we have

F(1) = f(xf(2))

From the question

f(2) = 5

So, we have

F(1) = f(5)

As a general rule

If f '(2) = 5 then f(5) = 2

So, we have

F(1) = 2

Hence, the value of the function F(1) is 2

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By definition, the work is given by:

Where W is the work in Joules (J), F is the force in Newtons (N) and d is the distance in meters (m).

In this problem we have:

• W = 280J,

• d = 35m.

We can find the force F in terms of W and d:

Replacing the values of W and d, we find that the force F is:

In the last step, we used that J = N m.

Answer: The force is F = 8N.

Using integrals, the 90th percentile of the given probability distribution is of $53.58.

The amount exceeded only 10% of the time is the 90th percentile of the distribution, which is the value of p for which:

[tex]\int_0^p f(y) dy = 0.9[/tex]

The integral represents the cumulative density function of the distribution, which is the reason why we use it to find the 90th percentile of the distribution.

The function is given by:

f(y) = 3(1 - y)²

Hence the integral is calculated as follows:

[tex]\int_0^p 3(1 - y)^2 dy[/tex]

Applying the integral of the power of y rule, along with the substitution, it is found that:

[tex]\int 3(1 - y)^2 dy = -(1 - y)^3[/tex]

Hence:

[tex]\int_0^p 3(1 - y)^2 dy = -(1 - y)^3|_{y = 0}^{y = p}[/tex]

Applying the Fundamental Theorem of Calculus, considering the value of the definite integral, it is found that:

-(1 - p)³ + 1 = 0.9

-(1 - p)³ = -0.1

(1 - p)³ = 0.1

Applying the cube root to both sides:

1 - p = 0.4642.

p = 1 - 0.4642

p = 0.5358.

This amount is in hundredths of dollars, hence the 90th percentile of the given probability distribution is of $53.58, as 0.5358 x 100 = $53.58.

The problem is missing, and is given by the image at the end of the answer.

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Measure of the angle m ∠ RQS = 58 ° for the given circle with arc RS subtending m ∠RPS=14 x + 46 ° at the center P and m ∠ RQS = 3 x + 43 ° at Q, on the circumference.

As given in the question,

Measure of the angle is given by :

m ∠ RPS=14 x + 46 °                                  

m ∠ RQS=3 x + 43 °                                      

m ∠ RPS = twice m ∠RQS (angle subtended at center of the circle)

14 x +46 =2(3 x + 43)

⇒ 14x + 46 = 6x +86

⇒ 14x-6x=86-46

⇒8x=40

⇒ x=5°

m ∠ RQS = (3 x + 43) °  

                 =[3(5) + 43 ]°

                 = 58°

Therefore, measure of the angle in the given circle m ∠RQS is equal to the  58 °

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Answer: ? = 1/2

Step-by-step explanation:

Your question is a bad example, so let me come up with one.

2/8 = 1/4

This is done by dividing both the numerator and denominator by the same value: 2/8 / 2/2

or

2/2 = 1, 8/2 = 4

We now have 1/4

or 9/36

What can we divide 36 by, 9 by? We need to divide by both for it to work.

9/3 = 3

36/3 = 12

3/12 But we can divide this again

3/3 = 1

12/3 = 4

1/4, we could also have divided 9/36 by 6/6 to get 1/4

For 1/8 to get ?/4, we do

8/? = 4

? = 1/2

, so the answer is 1/2/4 = 1/2*4 = 1/8

If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube

The shape of the monument  is cylinder

The base radius of the cylinder = 1.5 meter

The altitude of the monument = 3.5 meters

The volume of the cylinder = [tex]\pi r^{2}h[/tex]

Where r is the radius of the cylinder

h is the height of the cylinder

Substitute the values in the equation

The volume of the cylinder = [tex]\pi (1.5)^{2}(3.5)[/tex]

= 24.74 meter cube

Hence, If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube

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