Edmundo used a number line to show the solution for the inequality 12x-61 <4. Which number line shows the solution?
-6-5-4 2-1 0 1 2 3 4 5 6
-6-5-4-3-2-1 0 1 2 3 4 5 6
-6-5-4-3-2-1 0 1 2 3 4 5 6
-6-5-4-3-2-1 0 1 2 3 4 5 6
O

Answer:

B

Step-by-step explanation:

If you see two negatives next to each other, just think of them as adding. So add 8 and 7, you get 15.

To convert millimeters to centimeters, we divide by 10. 0.13 mm = 0.013 cm The given problem asks to convert the diameter of a bacterial cell, which is in millimeters, to centimeters.

This can be achieved by dividing the given value of 0.13 mm by 10, as there are 10 millimeters in a centimeter. So, the bacterial cell diameter in centimeters would be 0.013 cm. This conversion is necessary in order to express the diameter of the bacterial cell in a more common and convenient unit of length. It is important to note that conversions between different units of measurement are common in science and engineering fields, and being able to perform them accurately is a fundamental skill.

Learn more about bacterial cell here: brainly.com/question/2145627

#SPJ4

Yes , SAS (Side-Angle-Side) is a second Congruence postulate to prove triangle congruence by showing that two sides and their included angles are congruent.

Side-Angle-Side is the rule used to prove whether a given set of triangles are congruent. The SAS rule states: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle. An included angle is the angle formed by two given sides.. For example : let's us consider two triangles ∆SQR and ∆TSR ,

In above given figure, sides

RS = RS ( common side)

QS = ST ( S divides QT in two equal parts) and angle between QS and SR equal to angle between SR and ST i.e. ∠QSR = ∠RST = 90° (right angle ) and it is included angle . So, by SAS Congruence rule, both of triangles are congruent. Hence, Δ ABC ≅ Δ PQR.

To learn more about SAS Congruence rule, refer:

https://brainly.com/question/26157404

#SPJ4

\(f( - 4) = - 122\)

And

\(g(5) = - 21\)

Step-by-step explanation:

Greetings !

For the first expression

\(f(x) = 2x {}^{3} + 6\)

plug in -4 at the variable x and solve the expression.

\(f( - 4) = 2( - 4) {}^{3} + 6\)

Follow the PEMDAS order of operations

calculate the exponents

\(( - 4) {}^{3} = - 64\)

Apply exponent rule

\(( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd\)

Thus,

\(( - 4) {}^{3} = - 4 {}^{3} = - 64\)

Multiply and divide (left to right )

\(2( - 64) = - 128\)

\( = - 128 + 6 \\ = - 122\)

Fairly follow the same. process for the second function

Hope it helps !!

(a) The statement is true.

Proof: By definition, a rational number is any number that can be expressed as the quotient of two integers. Let's consider two rational numbers, a and b, where a = p/q and b = r/s, where p, q, r, and s are integers and q ≠ 0 and s ≠ 0.

Now, let's examine the sum of a and b: a + b = (p/q) + (r/s).

We can find a common denominator by multiplying the denominators: a + b = (ps)/(qs) + (rq)/(sq).

Combining the fractions with the common denominator, we have: a + b = (ps + rq)/(qs).

Since p, q, r, and s are all integers, their products and sums are also integers. Therefore, the numerator (ps + rq) and the denominator (qs) are both integers. This means that a + b is expressed as the quotient of two integers, making it a rational number.

Hence, the statement is true.

(b) The statement is true.

Proof: Let's consider an integer, n, and a rational number, a = p/q, where p and q are integers and q ≠ 0.

The sum of n and a can be expressed as: n + a = n + (p/q).

We can rewrite n as the fraction n/1: n + a = (n/1) + (p/q).

To find the common denominator, we multiply the denominators: n + a = (nq)/(1q) + (p1)/(q1).

Combining the fractions, we have: n + a = (nq + p)/(q1).

(c) The statement is false.

Counterexample: Consider the irrational numbers √2 and -√2.

Both √2 and -√2 are irrational because they cannot be expressed as the quotient of two integers, and they are distinct from each other.

However, the product of √2 and -√2 is (-√2) * (√2) = -2, which is a rational number since it can be expressed as the quotient of two integers (-2/1).

Therefore, the product of two distinct irrational numbers can be rational, which contradicts the statement. Hence, the statement is false.

Learn more about Rational Number here:

https://brainly.com/question/17450097

#SPJ11

Answer:

g=7

Step-by-step explanation:

5.1 times 7 is 35.7

Answer:

Step-by-step explanation:

5.1g = 35.7

g = 35.7 / 5.1

= 7.

The length of A'B' = 5 units

The line segment AB is of 5 units. AB is then transformed through translation of 3 units to the right.

The translation only means change through a straight line. This transformation does not change the length of a line segment.

So the length of A'B' will also be 5 units.

But the position of A'B' will be different from that of AB on the co-ordinate plane. To be exactly, A'B' would be 3 units right to the position of AB on the co-ordinate plane.

Also the co-ordinates of A'B' will be different. Still their lengths will be same.

Thus the length of A'B' = 5 units

Learn more about translation at https://brainly.com/question/28025572

#SPJ1

First you will get 4dz

The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given are three figures of triangles,

Figure 1)

5/x+5 = 8/10

50 = 40+8x

x = 5/4

y = 7/7+y = 8/10

70 = 56 +8y

y = 4/7

Figure 2)

12/12+y = 18/18+6

12/12+y = 18/24

48 = 36 +3y

y = 4

12/4 = x/5

x = 15

Figure 3)

y/4 = 1.5/3

y = 2

x/6 = 1.5/3

x = 3

Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

For more references on Thales theorem, click;

https://brainly.com/question/29626660

#SPJ1

Answer:

308

Step-by-step explanation:

Based on the given conditions, formulate: 7 x 572/13

Cross out the common factor: 7 x 44

Calculate the product or quotient: 308

Answer:

308

Step-by-step explanation:

572 divided by 13 is 44 which means there is 44 miles per gallon. So multiply 44 x 7 and you get 308 miles.

If the curve defined by F(t) = (e * cos(t), e sin(t)), then the unit tangent vector T(t) is T(t) = (-sin(t), cos(t)) and the tangential acceleration aT(t) is

aT(t) = (-cos(t), -sin(t)).

To find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration for the curve defined by F(t) = (e * cos(t), e * sin(t)), we need to compute the derivatives and evaluate them at t = 5π/4.

First, let's find the first derivative of F(t) with respect to t:

F'(t) = (-e * sin(t), e * cos(t))

Next, let's find the second derivative of F(t) with respect to t:

F''(t) = (-e * cos(t), -e * sin(t))

To find the unit tangent vector, we normalize the first derivative:

T(t) = F'(t) / ||F'(t)||

The magnitude of the first derivative can be found as follows:

||F'(t)|| = sqrt((-e * sin(t))^2 + (e * cos(t))^2)

= sqrt(e^2 * sin^2(t) + e^2 * cos^2(t))

= sqrt(e^2 * (sin^2(t) + cos^2(t)))

= sqrt(e^2)

= e

Therefore, the unit tangent vector T(t) is:

T(t) = (-sin(t), cos(t))

Now, let's find the unit normal vector N(t). The unit normal vector is perpendicular to the unit tangent vector and can be found by rotating the unit tangent vector by 90 degrees counterclockwise:

N(t) = (cos(t), sin(t))

To find the normal acceleration, we need to compute the magnitude of the second derivative and multiply it by the unit normal vector:

aN(t) = ||F''(t)|| * N(t)

The magnitude of the second derivative is:

||F''(t)|| = sqrt((-e * cos(t))^2 + (-e * sin(t))^2)

= sqrt(e^2 * cos^2(t) + e^2 * sin^2(t))

= sqrt(e^2 * (cos^2(t) + sin^2(t)))

= sqrt(e^2)

= e

Therefore, the normal acceleration aN(t) is:

aN(t) = e * N(t)

= e * (cos(t), sin(t))

Finally, to find the tangential acceleration, we can use the formula:

aT(t) = T'(t)

The derivative of the unit tangent vector is:

T'(t) = (-cos(t), -sin(t))

Therefore the tangential acceleration aT(t) is:

aT(t) = (-cos(t), -sin(t))

To evaluate these vectors and accelerations at t = 5π/4, substitute t = 5π/4 into the respective formulas:

T(5π/4) = (-sin(5π/4), cos(5π/4))

N(5π/4) = (cos(5π/4), sin(5π/4))

aN(5π/4) = e * (cos(5π/4), sin(5π/4))

aT(5π/4) = (-cos(5π/4), -sin(5π/4))

To learn more about “vector” refer to the https://brainly.com/question/3184914

#SPJ11

Answer: 6.2

Step-by-step explanation:

You take 0.62x10 and put it in your calculator which gives you 6.2.

Answer:6.2 I hope this you

Step-by-step explanation:

0.62 times 10

Multiply the numbers

you will get your answer

6.2

Answer:

16, 10

Step-by-step explanation:

There are 4 quarts in a gallon, so 4 gallons has 16 qt.

There are 2 pints in a quart, so 5 quarts has 10 pt.

All students in a class are divided into groups according to the rows that they are seated. One of the groups is randomly selected. The correct answer is C.

1. The continuous quantitative (numerical) variable is a. The number of gallons of milk sold at the local grocery store yesterday.
2. The discrete quantitative (numerical) variable is c.

The Dow Jones Industrial average.
How many gallons of milk were sold at your local grocery store yesterday – This is a continuous variable because it can take on any number within a certain range. For example, 2.5 gallons, 3.2 gallons, and so on.

Insurance Company Employees - This is an integer count of employees, so it is a discrete variable. It cannot take fractional or continuous values.

Amount of water released from the dam – This is a continuous quantitative variable that can take any number within a certain range. For example, 1000 cubic meters, 1500 cubic meters, and so on.

a. All students in the class are divided into groups of 15 students each.

One of her students is randomly selected from the first group, and then every 15 of her remaining observations are made.

This is an example of systematic sampling rather than cluster sampling.

b.Fifteen of her students who are the best in the class will be selected according to the instructor's opinion. This is an example evaluation sample, not a cluster sample.

c. All students in the class are divided into groups according to their seating rows.

One of hers in the group is randomly selected. This is an example of a cluster sample. A group is a cluster and one cluster is randomly selected.

d. None of these are true cluster samples.

This is not the correct answer, because option (c) talks about cluster sampling.

e. All students in the class are grouped by gender. 8 random samples of her are selected from males and another random sample of 7 from females. This is an example of a stratified sample, not a cluster sample.

The option that yields a cluster sample is c.

For more related questions on randomly selected:

https://brainly.com/question/27956311

#SPJ8

To ensure that a piece of popular media accurately represents the original research of a scientific study, (B) locate and read the relevant original scientific journal.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science (with notable practitioners in previous centuries; see the article history of the scientific method for additional detail.)

As one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

Find and read the original scientific publication to make sure that a popular media piece appropriately reflects the original research of a scientific study.

It entails developing hypotheses through induction based on these observations, testing the validity of those hypotheses through experimental and measurement-based statistical testing of the inferences made from them, and then fine-tuning (or discarding) those hypotheses in light of the experimental results.

Therefore, to ensure that a piece of popular media accurately represents the original research of a scientific study, (B) locate and read the relevant original scientific journal.

Know more about the scientific study here:

https://brainly.com/question/28145780

#SPJ1

Answer:

1.2, 3/5, 25%, 0.17, -12

Step-by-step explanation:

In order to put these from greatest to least, you must put these in like terms.

Since there are more decimals that other terms, we're going to convert them all to decimals.

25%= 0.25

0.17= 0.17

3/5= 0.60

1.2= 1.20

-12= -12.00

Now that we see which numbers are greater, we convert them back to their original terms and place them in order from greatest to least.

1.2, 3/5, 25%, 0.17, -12

the answer is A and D

when you differentiate the question you find that the maximum point is (0,0)i.e

\( \frac{dy}{dx} = - 8x\)

when dy/dx is 0 values of x are 0,0

and the function shows that valies of x are real numbers.

The domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

Given function as

f(x) = -4x²

The range is the set of values that correspond with the domain.

Range: (−∞,0], {y|y≤0}

Domain: (−∞,∞), {x|x∈R}

and the function shows that values of x are real numbers.

The maximum point is when differentiating the function, which is (0,0) i.e

dy/dx = -8x

Values of x are 0 when dy/dx is 0.

Hence, the domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

Learn more about the domain and the range here:

brainly.com/question/21027387

#SPJ5

Answer:

A. You need to draw a straight line that increases from left to right. Try and get the same amount of plots on the top and bottom of the line and go through one or two of the plots. Don't connect the dots, though.

B. This scatter plot demonstrates a positive association between a person's height and weight because the trendline increases from left to right. According to this data, as weight increases, so does height. The more someone weighs, the more likely they are to be tall.

Answer:

5

Step-by-step explanation:

By process of elimination, we can say for sure that C and D are not the right answers because as x- the numbers on the top- increases, y- the numbers on the bottom- increases. This means that the slope is not negative, because the slope is the rate of change and it does not have a negative rate of change.

The equation for slope is y2-y1 / x2-x1. Meaning, y is on top and x is on bottom. This creates a fraction. So let's take 0 and 1 for X, the first and second values, and 3 and 8 for y, the first and second values. We swap them, because the second y value comes first, so we have 8 - 3 for the top, the numerator. Then we have 1 - 0 for the bottom, the denominator. Solving 8 - 3 and 1 - 0, we have 5/1. 5/1 simplifies to 5, and thus 5 is your slope.

Answer

6th of the power of 1 would be 5th power

Step-by-step explanation:

20

Step-by-step explanation:

30-6=24-4=20 that how you find your a answer

Answer:

the annual rate of interest is 7.8%

Step-by-step explanation:

The computation of the annual rate of interest is as follows:

As we know that

Simple interest = Principal × rate × time

$195 = $6,000 × rate × 5 months ÷ 12 months

$195 = 25 × rate

Rate =  $195 ÷ 25

= 7.8%

Hence, the annual rate of interest is 7.8%

We simply applied the above formula so that the correct value could come

And, the same is to be considered

The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

To know more about differential equation refer here:

https://brainly.com/question/32524608#

#SPJ11

Answer:

19 feets

Step-by-step explanation:

Given the following:

Initial dive depth = 22 feet

Additional dive = 7 feets

Swims back up for 14 feets and dives down another 4 feets before finally finding the fish.

Hence, depth at which the fish was found :

22 feets + 7 feets - 14 feets + 4 feets

29 feets - 14 feets + 4 feets

15 feets + 4 feets

= 19 feets

Hence, the depth at which the fish was found is 19 feets.

Answer:

-19

Step-by-step explanation:

since the diver is going down under sea level that makes the number negative so then when you solve the equation and get 19 you have to put it as negative.

Answer: About 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.

Step-by-step explanation:

Complete question is attached below.

Given: The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 8 days.

i.e. \(\sigma= 8\)

let X denotes the random variable that represents the lengths of pregnancy.

The probability of births would be expected to occur within 24 days of the mean pregnancy​ length:

\(P(\mu-24<X<\mu+24)=P(\dfrac{\mu-24-\mu}{8}<\dfrac{X-\mu}{\sigma}<\dfrac{\mu+24-\mu}{8})\\\\=P(\dfrac{-24}{8}<Z<\dfrac{24}{8})\ \ \ [\because Z=\dfrac{X-\mu}{\sigma}]\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=P(Z<3)-(1-P(Z<3))\\\\=2P(Z<3)-1\)

\(= 2(0.9987)-1\ \ \ [\text{ By z-table}]\\\\=0.9974\)

=99.74%

Hence, about 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.

8 Guidelines for Critically Evaluating a Statistical Study

1. Identify the Goal, Population, and Type of Study

2. Consider the Source

3. Examine the Sampling Method

4. Look for Problems in Defining or Measuring the Variables of

Interest

5. Watch Out for Confounding Variables

6. Consider the Setting and Wording of Any Survey

7. Check That Results Are Fairly Represented in Graphics or

Concluding Statements

8. Stand Back and Consider the Conclusions

Learn more about Statistical Study here

https://brainly.com/question/16859876

#SPJ4

a. The number of people that enjoyed only skiing is 129

b. The number of people that enjoyed snow boarding and ice skating only is 13

c. The number of people that enjoyed snow board or ice skating is 221

d. The number of people that enjoyed none is 35

e. The number of people that enjoyed at least two is 62

sets is a collection of well-defined objects or elements.

The total number of visitors is 350

n(ski and snow board only) = 49-2 = 47

n( ski and skating) only= 2-2 = 0

n( snow board and skating) = 15-2 = 13

n( snow board only) = 154-(47+13+2) = 92

n( skating only) = 57-(13+2) = 32

a. The number of that that enjoyed skiing only = 178-(47+2) = 129

b. n( skating and snow board) only= 13

c. n ( ski or snow board) only = 129+92 = 221

d. the number of people that didn't enjoy any = 350-(129+47+92+13+32+2)

= 350-315 = 35

e. the number of people that enjoyed at least two = 13+2+47 = 62

learn more about set from

https://brainly.com/question/28365114

#SPJ1

Muscular strength can be measured based on the amount of weight lifted.

Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).

learn more about muscular strength from

https://brainly.com/question/4088369

#SPJ4