Question 3 (1 point)
What is the correct solution for the following addition, reported to the correct
number of significant digits? Assume all numbers are measurements.
3001+ 20.3 +0.009
a) 3021
b) 3021.3
c) 3021.309
d) 3021.30

Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Step-by-step explanation:

What does it mean converse in geometry?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

So, in the figure below, if we can choose n║m, then ∠1≅∠2

Since  n║m , by the corresponding Angles Postulate,

∠1≅∠2.

Therefore, by the definition of congruent angles,

m∠1=m∠2

Since ∠1 and ∠2 form a linear pair, they are supplementary, so

m∠1+m∠2=180°.

Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

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8x+y=31

perpendicular means the slopes are opposite reciprocals of each other.  perpendicular to: y +5= 8(x +4)   →   m = 8   m⊥ = -8

Input the slope (m⊥ = -8) and the point (x₁, y₁) = (4, -1) into the Point-Slope formula: y - y₁ = m(x - x₁)

y - (-1) = -8(x -4)

y + 1 = -8 x + 32      simplified

8x+y =31      

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Answer:  87/100

Step-by-step explanation:

f(x)>=-7

Functions:

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x

Given :

f(x) = -3|x+1|-4

using the table of values for g(x) = |x|

Solution :

f(x) = -3|x+1|-4

f(x) = -3|g(x)+1|-4

f(x) = -3||x|+1|-4

which means |x| is always positive |x|>0

f(x) = -3||x|+1|-4

f(x) = -3x-3-4

f(x) = -3x-7

f(x)>=-7

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Answer:

Step-by-step explanation:

A)

A - the population after its decrease

x - the number of years in which there has been a decrease in population

Hence,

[tex]\displaystyle\\A=30000-475x\\A+475x=30000-475x+475x\\A+475x=30000\\A+475x-A=30000-A\\475x=30000-A[/tex]

Divide both parts of the equation by 475:

[tex]\displaystyle\\x=\frac{30000-A}{475}[/tex]

B)

[tex]\displaystyle\\x=\frac{30000-24300}{475} \\\\x=\frac{5700}{475}\\\\x=\frac{12*475}{475} \\\\x=12\ years[/tex]

A : all real numbers

Answer:

A. All real numbers.

Step-by-step explanation:

The z test statistic needed for this hypothesis test is 0.75 .

Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.

NOW,

sample proportion =  p = x / n = 0.23

Test statistics

z = ( p - p0 ) / [tex]\sqrt{ p0*(1-p0)}[/tex] / n

= ( 0.23 - 0.20) /  [tex]\sqrt{ (0.20*0.80) / 100}[/tex]

= 0.75

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Answer: D

Step-by-step explanation: 2,6

Answer:

the is X=4

Step-by-step explanation:

Distribute

5(x-6)+3= -7

5x-30+3= -7

add numbers

5x-30+3= -7

5x-27= -7

add 27 to both sides

5x-27= -7

5x-27+27= -7 + 27

simplfly

5x=20

divide both sides by 5

5x = 20

-- ----

5. 5

5 and 5 are off

divide 20 by 5

20/5= 4

therefore x= 4

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Answer:

42°, 101°

Step-by-step explanation:

These answers come from the angle subtraction postulate.

Answer: The slope of the line that goes through the points is = ¼

Step-by-step explanation:

Define Slope:

The slope is a numerical value that describes the steepness of a line and is usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise over run) between two points.

The slope of the line that goes through the points (-4,2) and (8,5).

Let, X1=-4

Y1=2

X2=8

Y2=5

We can use m=(y2-y1) / (x2-x1)

replace with x1, y1 and x2, y2 values in this equation  

We can write: m=[(5-2) / (8-(-4))]

Solve it: M= 3/12

M=1/4

So, the slope of the line that goes through the points is = ¼.

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The number such that one-half of the number is three more than one-fourth of the number is 12.

It is given in the question that a number  is such that one-half of the number is three more than one-fourth of the number.

We have to find the number.

Let the number be x.

According to the question, we can write,

x/2 = x/4 + 3

Solving the linear equation, we get,

x/2 - x/4 = 3

(2x - x)/4 = 3

x/4 = 3

x = 4*3

x = 12

Hence, the number such that one-half of the number is three more than one-fourth of the number is 12.

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the thickness in scientific notation is:

4.3* 10⁻³ inches

Here we know that the thickness of a dollar bill is 0.0043 inches.

Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.

To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.

Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:

0.0043 = 4.3* 10⁻³

From this, we conclude that the thickness in scientific notation is:

4.3* 10⁻³ inches

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The sum will be negative.

The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.

Here, we are given an expression 4a + (-3b)

Also we are told that a < b and b is a negative number

Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.

Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.

Here, in fact, since a < b, a will always be negative only

Let us take an example, say a = -3 and b = -2

Then the sum becomes 4(-3) + (-3)(-2)

= -12 + 6

= -6

If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.

Thus, we can conclude that 4a > (-3b) for all values of a and b

and since 4a will always be negative, the sum will also be negative.

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We get the dimensions of the park as length = 75 feet and width = 20 feet.

We are given that:

A yard has a perimeter of 190 feet.

Also, four times the length of the yard equals 15 times the width.

Now,

Let the length of the yard be x.

ATQ, we get the width of the yard as:

15 width = 4 x

Width = 4 / 15 x

Perimeter = 2 ( l + b )

190 = 2( x + 4 / 15 x )

95 = 19 x / 15

19 x = 95 × 15

19 x = 1425

x = 1425 / 19

x = 75 feet.

Length = 75 feet

Width = 4 / 15 x = 20 feet.

Therefore, we get the dimensions of the park as length = 75 feet and width = 20 feet.

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Answer:

-35

Step-by-step explanation:

Question =7-24÷8×4+6

=7-192÷4+6

=7-49+6

=-41+6

=-35

Therefore,right answer is (-35)

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The number of students those who will most likely have their preference  to do their classwork online is 238 out of 350

According to the question statement, A teacher surveys a random group of students about their preference for doing classwork online or on paper.

17 Preferred Online and 8 Preferred on paper.

We are supposed to find the number of students who will most likely have their preference to do their classwork online.

We will be using the concept of Probability for solving this.

[tex]Probability(Event)=\frac{Favourable Outcomes}{Total Outcomes}[/tex]

Probability(Event) = Favorable Outcomes/Total Outcomes

For the survey probability of students preferring online mode of classwork is = [tex]\frac{17}{17+8} =\frac{17}{25}[/tex]

                     = [tex]0.68[/tex]

Now if we consider a group of 350 students and probability of students preferring online mode of classwork as 0.68

Let the number students preferring online mode of classwork be "x"

so  [tex]\frac{x}{350} =0.68[/tex]

or  [tex]x=0.68*350\\x =238[/tex]

Therefore, the number of students those who will most likely have their preference  to do their classwork online is 238 out of 350

where P(A) is the probability of an event “A”,  n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.

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Justin should have multiplied 3.8 and 7.9 first

He is trying to evaluate the expression 12.5 + 3.8x, when x = 7.9.

This was Justin solution to the expression

12.5 + 3.8(7.9)

16.3(7.9)

128.77

Now let's do our own arithmetic,

12.5 + 3.8x

we have to substitute the value of x in the equation.

12.5 + 3.8(7.9)

Using PEMDAS principle, we have to multiply before addition.

Therefore,

12.5 + 3.8(7.9)

12.5 + 30.02

42.52

Hence, Justin should have multiplied 3.8 and 7.9 first

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Answer: Continuous data

Step-by-step explanation:

Answer:

16π m²

Step-by-step explanation:

area of circle = πr²

area = π × (4 m)²

area = 16π m²

Answer: 51.33

Step-by-step explanation:

7+8.75+12.5+15.33+7.75 = 51.33

Answer:

-3x>24

Step-by-step explanation:

-3x-10>14

now we add 10 to both sides, 10+14 is 24

so, the missing step is -3x>24

Answer:

The equivalent fraction of 6/9 is 4/6

By taking the measure of the given line segment and making arc on one of the end points from one point of the line segment and joining those three points will be the line as twice as the given segment.

Following are the steps to construct a line segment that is twice the given segment :

Step 1 : Take the compass and measure the length of the given line segment let’s say AB

Step 2 : Now with that measure put one end of the compass on one of the points of a line segment, either point A or point B.

Step 3 : Now mark an arc on the right side of the point if the compass is on point B or mark the arc on the left side if the compass is on point A.

Step 4 : Mark that arc as point C and join the line AC or BC.

Hence AC or BC will be the new line segment which will as twice as the given line segment.

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Answer:

48 because of the vowels it became 48 .

Step-by-step explanation:

I Quesliod. Make sure you start new workings. In the word grapefruit, the ratio of vowels to consonants is . Find the ratios of vowels to consonants in the words pineapple and strawberry. Give each ratio in its simplest form. grapefruit Vowels :Consonants  Remember: vowels are a, e, i, o, u

Answer:

The answer is 2.72 * 10^8 sec.

Step-by-step explanation:

Distance between Earth and Sirius is 5.062 * 10^13 miles.

Time taken = Distance travelled/speed

5.062*10^13 miles/sec/1.86*10^5 miles.

=2.72 * 10^8 sec.

So this means that the time taken to travel light from Sirius to Earth is 2.72*10^8.

Answer:

fdsjfgdndgnxhñgjxgjxgjx

Using a linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

For this problem, when x increases by 10, the profit increases by 5, hence the slope is:

m = 5/10 = 0.5.

Then:

P(x) = 0.5x + b.

When x = 10, P(x) = -70, hence:

-70 = 0.5(10) + b

b = -75.

Hence:

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Answer:

182.5

Step-by-step explanation:

182.5

steps

623420÷3416=

182.5