Geometry.....Solve for each variable. Show your work and explain in paragraph form how you solved each problem.
Base Angles Theorem
Converse to Base Angles Theorem
Corollary
Converse to the corollary
Sum of Interior Angles
Exterior angles

Part a:  10z > 25,670; infinite integer.

Part b: Range =  2550 to 2649.

Part a:  10z > 25,670

Divide the inequality on both sides by 10.

z >  2,567

Thus, there are infinite number which are greater than 2567.

Part b:  z rounded to the nearest hundred is 2,600.

Range =  2550 to 2649.

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The colored type of led is more expensive if you order 3 strings of white led lights and 2 strings of colored led lights for 66$.

An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.

Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.

First type of white led have 3 strings=3x

Second type of colored led have 2 strings and bought only one string=2y

The total cost =3x+2y=66    ----------->(1)

In the second order ,

Each string brought only one=x+y=27 ------->(2)

Solving equations 1 and 2

From eq2, y=27-x

3x+2(27-x)=66

3x+54-2x=66

X=12

Y=27-x=27-12=15

Therefore, the type of colored led are expensive

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Answer:

Step-by-step explanation:

The outcome is Reject H0 and make a Type 1 error

What is H0?

When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H0.

Here type 1 error is defined as Rejecting H0 when H0 is true.

Therefore, the outcome is Reject H0 and make a Type 1 error.

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If Greg is at work for 10 hours a week, he spends 30 hours traveling to work.

Explanation

No of hours he works in a week = 10

No of hours he spends on travelling = 3 * no of hours he works in a week

=10 x 3 =

30 hours

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.

The repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

In addition to addition, subtraction, and division, multiplication is a mathematical operation. The four fundamental arithmetic operations are taught to students in their primary classes.

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Answer:1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

7/10-x+3/2=6/5

7/10-x=6/5-3/2

7/10-x=-3/10

-x=-10/10

x=1

[tex]\cfrac{7}{10}-x+\cfrac{3}{2}=\cfrac{6}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{7}{10}-x+\cfrac{3}{2} \right)=10\left( \cfrac{6}{5} \right)}\implies 7-10x+15=12 \\\\\\ 22-10x=12\implies 22=10x+12\implies 10=10x\implies \cfrac{10}{10}=x\implies 1=x[/tex]

For the given set of equations x/2 + y/3 = 1 and x/4 + 2y/3 = -1 the sum of x and y is 1.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given set of equations are,

x/2 + y/3 = 1,        

x/4 + 2y/3 = -1.

Simplify both the equations,

3x + 2y = 6         (1)

3x + 8y = -12       (2)

Subtract equation (2) and (1),

6y = -18

y = -3

Substitute the value of y = -3, in equation (1)

3x + 2(-3) = 6

3x - 6 = 6

3x = 12

x = 4

The sum of x and y,

x+y = 4 - 3

      = 1

The sum of x and y for the given equations, is 1.

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Answer:

x = 3

Step-by-step explanation:

First, distribute the 3.

3(x - 5) + 2x = 0

3x - 15 + 2x = 0

Next, combine the x's.

(3x + 2x) - 15 = 0

5x - 15 = 0

Then, add 15 to both sides.

5x = 15

Finally, divide by  5 on both sides.

x = 3

Answer

Step-by-step explanation:

Apple pies are $5 and pumpkin pies are $15

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

5a+12p=205............(1)

2a+1p=25.................(2)

Now, Multiply (2) by -12 to get

-24a-12p=-300

and, 5a+12p=205

-24a-12p=-300

Adding above Equations together

-19a=-95

a= 5

and, 2(5)+p=25

10+p=25

p=15

Hence, Apple pies are $5 and pumpkin pies are $15

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The phrase "given that they completed the homework" indicates that we're only looking at the students who completed the homework.  We're ignoring those students who didn't complete the homework.

Of the 19 students who completed the homework, 16 of those passed the test.

This gives us the fraction 16/19 which is about 0.842105263157895 or about 84.2%.

That's your probability that a student passed the test given that they completed the homework.

Answer:

The top right

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because for every x there is a only an y

Step-by-step explanation:

A .

1150-1090=60

60feet/5sec = 12feet/sec

B.

yes it's is constant , because is decreasing by 60 feet in every 5 sec

C.1150

Suppose 's' be a collection of 'n' plane segments. It is true to say that a transversal as well as stabber for 's' is a line that crosses every segment of 's'.

A transversal in geometry is a line, ray, as well as line segment that, on a plane, overlaps other lines, rays, including line segments at various locations.

Thus, if 's' be a collection of n plane segments. It is true to say that a transversal as well as stabber for 's' is a line that crosses every segment of s.

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The unknown value that has the solution as c = 4 of the given algebraic equation is; 2

The given algebraic expression for which we want to input a value and solve is given as; 5(2c − ?) =2(c + 11)

Now, we want to find the unknown value that has the solution as c = 4. Thus, we will plug in 4 for c into the given equation to get;

5(2(4) − ?) =2((4) + 11)

5(8 − ?) = 30

divide both sides by 5 to get;

(8 − ?) = 6

Add -6 + ? to both sides to get;

8 − ?  - 6 + ? = 6 - 6 + ?

? = 2

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Complete question is;

Complete the equation so that it has the solution c = 4.

5(2c − ?) =2(c+11)

The predicted quantity of balls in the first bin is (1/n)n.

Considering that,

There are the same number of balls and containers.

If so, then each container must always contain one ball. The probability of each ball landing in the first bin is (1/n)n.

For instance -

Three balls and three bins should be present. Next to each ball, place an A, B, and C. There are numbers 1, 2, and 3 on the containers. Ball A has a 1/3 chance of landing in bin 1. Although there is a 1/3 probability that ball B will drop in bin 1 and a 1/3 chance that ball C will do the same, both outcomes are possible. Therefore, bin 1 should be equal to 1/3 + 1/3 + 1/3. The rationale behind the projected values of bins 2 and 3 is identical.

According to the same logic, bins 2 and 3 should also have expected values of 1.

How probable is it that the first bin will receive all three balls?

In general, (1/n)n, which equals (1/3)3, or 1/3 x 1/3 x 1/3, equals 1/27.

Therefore, (1/n)n would be the expected number of balls in the first bin.

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The expected counts for each possible outcome are given by Ei = npi

What is mutually exclusive​ outcomes?

When two events cannot happen simultaneously or at the same time, they are said to be mutually exclusive in probability theory. In other words, discontinuous occurrences are described as being mutually exclusive. The likelihood of two events occurring simultaneously is 0 if they are regarded as disjoint events. Events that do not occur simultaneously are said to be mutually exclusive. When a coin is tossed, for instance, the outcome will either be head or tail, but we cannot get both outcomes.

The expected counts for each possible outcome are given by Ei = npi

Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes,

where pi represents the probability of observing the ith outcome.

The expected counts for each possible outcome are given by Ei = npi

Where,  pi is the probability of observing the ith outcome

Ei is the expected count of the ith outcome.

Hence, The expected counts for each possible outcome are given by Ei = npi.

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The shear and moment throughout the beam as functions of x are V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft and V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft

The ability to construct shear force diagrams (SFD) and bending moment diagrams (BMD) is essential for any student studying statics, mechanics of materials, or structural engineering. Both a long and a short route can be used to complete them. The extended method is more thorough and yields formulas for the internal shear and internal bending moments in beams in terms of x: V(x) and M(x), respectively. In introductory statics classes, this is typically the approach required to demonstrate understanding of the situation. The rapid method eliminates the need for calculations in terms of x and instead employs a more visual method that you may use to highlight the crucial areas on the diagrams before simply connecting the dots.

How to solve?

For 0 ≤ x ≤ 6 ft,

∑ Fy = 0

30 - 2 x - V = 0

V = ( 30 - 2x ) kip

∑M = 0

M + 216 + 2 x ( x / 2 ) - 30 x = 0

M = ( - x² + 30 x - 216 ) kip ft

For 6 ≤ x ≤ 10 ft,

∑ Fy = 0

V - 8 = 0

V = 8 kip

∑ M = 0- M - 8 ( 10 - x ) - 40 = 0

M = ( 8 x - 120 ) kip ft

the shear and moment throughout the beam as functions of x are :

V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft

V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft

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The measurements are represented by lengths of a triangle's sides by -

The triangle's three sides must satisfy the following condition:

"The total of any two triangle sides must be larger than or equal here to third side of the triangle."

We have four options in this question, so we'll go through them one at a time.

Since (1+3)<7  in this case, a triangle cannot be formed.

Since (3+3)<7 in this case, a triangle cannot be formed.

In this instance, (3+7)>8, (3+8)>7, and ((7+8)>3

Thus, a triangle will be formed by these.

In this instance, (3+5)>7, (3+7)>5, and (5+7)>3

Thus, a triangle will be formed by these.

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The options for the question are attached.

Answer:

[tex](6,1)[/tex]

Step-by-step explanation:

When reflecting over [tex]y=x[/tex], [tex](x,y) \longrightarrow (y, x)[/tex].

The average of the new list of 4 numbers is 94.

If the average of the original list of 4 numbers is 90, then the sum of these 4 numbers is:

4 x 90 = 360

If the 4th number in the original list is 80, then the sum of the first 3 numbers in the original list is:

360 - 80 = 280

If the first 3 numbers in the new list are the same as in the original list then the sum of these new first 3 numbers is also:

280

If the 4th number in the new list is 96 then the sum of the 4 numbers in the new list is:

280 + 96 = 376

Therefore, the average of the new list of 4 numbers is:

376 / 4 = 94

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Step-by-step explanation:

light blue.

our function needs to calculate r out of h.

P does not recognize h (hours after midnight) as parameter. P needs c as input.

T needs h as input and delivers c as output.

therefore (P ○ T)(h) = r is correct.

first the "inner" T function is calculated with h as parameter and then P is calculated using the result from T (c) as input and delivers r.

Answer:

1, 2, and 3

Step-by-step explanation:

5% = 0.05 = 1/20

The first expression is equal, as 5% is equal to 1/20.

The second expression is equal, as 5% in decimal form is 0.05.

The third expression is equal, as 5% is 5/100 in fraction form, which can be simplified to 1/20.

The fourth expression is NOT equal, as it is 20%, not 5%. 1/5 = 0.2.

The fifth expression is NOT equal becauase 0.5 is one half (1/2), which is not equal to 0.05.

Answer:

y=-2x+10

Step-by-step explanation:

Just use the formula y=mx+b and replace the letters with the numbers.

Answer: y = -2x + 10

Step-by-step explanation:

y = mx + b

m = -2

b = 10

x = unknown number

y = m(-2)x + b( 10)

1.42 is the base of the equation and equation [tex]y = 51 (1.42)^t[/tex] represents the exponential function

An exponential function is a function which can be defined as f(x) = aˣ, Where 'x' is a variable and 'a' is a constant.

The given equation is,

[tex]y = 51 (1.42)^t[/tex]

The given function is in exponential power of t.

Since, the 1.42 is the base of the given function

And equation [tex]y = 51 (1.42)^t[/tex] represents the exponential function.

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The statement is 1000 g = 1 kg. One thousand grams is equal to one kilo grams, to put it in words.

Given that,

The statement is 1000 g = 1 kg. One thousand grams is equal to one _____ grams, to put it in words. (Write the prefix; leave out the dashes.)

We have to fill the blank.

We know that,

The metric system's fundamental mass unit is the kilogram. In the past, it has been measured using a variety of sources. It was first calculated based on the weight of 1000 cc of water. Water density varies according to temperature. Furthermore, this reference has been abandoned since the contaminants and solutes in water also provide erroneous results when standardizing the ideal mass of 1 kg.

A gram is described as the 1/1000th of a kilogram in the reference used to define a mass of 1 kg. The maximum density of 1 g/cc was originally used to define it as the mass of 1 cc of water.

Therefore, The statement is 1000 g = 1 kg. One thousand grams is equal to one kilo grams, to put it in words.

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The number of shirts to be left for folding is 7 and the equation is F+N=22.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Boris has 22 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating N to F.

The equation will be written as,

N + F = 22

N + 15 = 22

N = 22 - 15

N = 7

Therefore, the number of shirts to be left for folding is 7 and the equation is F+N=22.

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Answer:

140 degrees

Step-by-step explanation:

first we have to find x by setting these 2 angles equal to each other

x+28=2x+16

-x.       -x

28=x+16

-16.    -16

12=x

Now we need to find the x+28 angle

12+28

40

And since PTR is next to it we subtract 180 from this

180-40

140 degrees

Hopes this helps

The total standard time required to processed for one hundred units as per given setup and run time is equal to 1120minutes.

As given in the question,

Number of units to be processed = One hundred units

Conversion used:

1 hour = 60 minutes

Time required for setup = 2 hours

                                        = 2 ( 60) minutes)

                                        = 120 minutes

Run time per piece = 10 minutes

⇒ Run time required for 100 units = 100 × 10

                                                        = 1000 minutes

Total standard time for 100 units is equal to

= Run time for 100 units + set time

= 1000 + 120

= 1120 minutes

Therefore, the total standard time required to processed 100 units is equal to 1120 minutes.

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Answer:

1/3

Step-by-step explanation:

1/9 is one piece in total of 9 but 1/3 is one piece in total of 3