Car A travels 221.5 km at a given time, while car B travels 1.2 times the distance car A travels at the same time. What is the distance car B travels during that time?

46. There are 9 complete doses available from the bottle. 47. There are 8 full doses available in the 120 mL bottle.

Although weight and mass are frequently used interchangeably, they have distinct meanings in the study of physics. Weight is a measurement of the force of gravity acting on an item, whereas mass is a measure of the amount of matter that makes up an object. Weight is typically expressed in newtons (N) or pounds, while mass is typically expressed in kilogrammes (kg) (lb). While an object's mass remains constant, its weight can change depending on how strongly gravity is pulling on it.

46. We know that,

1 fluid ounce = 29.5735 mL

4 fluid ounces = 4 x 29.5735 = 118.294 mL

Each dose is 12.5 mL:

118.294 / 12.5 = 9.46

So there are 9 complete doses available from the bottle.

47. Given, 1 tablespoon is equal to 15 mL.

Thus, doses of 15 mL are in a 120 mL bottle:

120 / 15 = 8

So there are 8 full doses available in the 120 mL bottle.

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A graph of the functions with the asymptotes is shown in the image below.

The pre-image of the function y = log₂(x + 1) was horizontally shifted to the left by 1 unit.

The pre-image of the function y = log₂(x) + 4 was vertically shifted up by 4 units.

In Mathematics, the translation a geometric figure or graph to the left means subtracting a numerical value to the point on the x-coordinate of the pre-image;

g(x) = f(x + N)

In Mathematics and Geometry, the translation a geometric figure upward means adding a numerical value to the point on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function f(x) was horizontally translated 1 unit left, we have the following transformed function;

y = log₂(x + 1)

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Answer:

I'm pretty much confused abt this one bc I didn't get an exact answer. Anyway I think it's 13.1

Step-by-step explanation:

The pic

Therefore, the usefulness of stigma in society depends on how it is applied and the context in which it is used.

Durkheim, one of the founding fathers of sociology, saw deviance as a normal and necessary aspect of society. According to Durkheim, deviance serves several important functions. Firstly, it reinforces social norms by defining what is acceptable and unacceptable behavior. Deviance also provides a sense of unity and reinforces social solidarity within a society by creating a common enemy for people to rally against. Additionally, deviance can facilitate social change by highlighting areas where social norms may be outdated or ineffective.

The labeling theory of deviance suggests that deviance is not a characteristic of the individual but rather a product of the social reaction to their behavior. The process of labeling a person as deviant can have a significant impact on their self-identity and can lead to further deviant behavior. Primary deviance refers to the initial act of deviance, whereas secondary deviance refers to the subsequent behavior that occurs after a person has been labeled as deviant.

Stigma, or the negative social label attached to deviant behavior, can have both positive and negative consequences for society. On the one hand, stigma can help to reinforce social norms and discourage deviant behavior. However, it can also lead to discrimination and marginalization of individuals who are labeled as deviant, which can have negative impacts on their life chances and well-being. Therefore, the usefulness of stigma in society depends on how it is applied and the context in which it is used.

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Answer:

21 and 42

Step-by-step explanation:

Lets say x and y are our numbers. x is the smaller number, y is the larger.

We can construct the equations:

x = 0.5y

x + y = 63

Substitute 0.5y for x in the second equation.

0.5y + y = 63

1.5y = 63

y = 42.

Plug y into the first equation.

x = 0.5 * 42

x = 21.

Your numbers are 21 and 42.

The number of roof trusses that would be needed for the longest length is 2

The longest lengths from the question are given

Longest lengths = 28 and 22

Next, we expand the lengths of the roof trusses

This is to calculate the greatest common factor (GCF) of the lengths

So, we have

28 = 2 * 2 * 7

22 = 2 * 11

Multiplying the common factors gives the GCF

So, we have

GCF = 2

This means that the number of roof trusses that would be needed for the longest length is 2

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Answer:

Triangle P has been rotated clockwise by 90° about the point (0,0).

PLEASE MARK IT THE BRAINLIEST!!!!

Answer:

d=23,000-500u

Step-by-step explanation:

im doing the test

Answer:

To write the Hindu-Arabic numeral 872 as a Babylonian numeral using the symbols I and <, we need to break it down into its place values:

The digit 8 is in the hundreds place.

The digit 7 is in the tens place.

The digit 2 is in the ones place.

To represent 800 in the hundreds place, we use 8 symbols <. To represent 70 in the tens place, we use 7 symbols < followed by 1 symbol I. To represent 2 in the ones place, we use 2 symbols I.

Putting these symbols together, we get the Babylonian numeral:

<<<<< <<<< <<<< <<<< IIII

So, the Babylonian numeral equivalent of the Hindu-Arabic numeral 872 is <<<<< <<<< <<<< <<<< IIII.

Step-by-step explanation:

To solve the inequality:

-3 > 5 - b

We can start by isolating the variable b on one side of the inequality. We can do this by subtracting 5 from both sides of the inequality:

-3 - 5 > -b

Simplifying the left-hand side of the inequality, we get:

-8 > -b

To isolate b, we can multiply both sides of the inequality by -1. When we do this, we need to reverse the inequality sign:

8 < b

So the solution to the inequality is:

b > 8

This means that b must be greater than 8 for the inequality to be true.

The value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.

Let the first term of the arithmetic series be a, and the common difference be d = 3. Then, we have:

a = 2t + 1

n-th term = a + (n-1)d = 2t + 1 + 3(n-1) = 3n + (2t - 2)

(Notice that the second equation can be found by substituting the expression for a into the formula for the n-th term and simplifying.)

We also know that the n-th term is given by (14t - 5), so we can equate the two expressions:

3n + (2t - 2) = 14t - 5

Simplifying and solving for n, we get:

n = (12t + 3)/3 = 4t + 1

So, the n-th term can also be expressed as:

3n + (2t - 2) = 3(4t + 1) + (2t - 2) = 14t - 5

Simplifying, we get:

14t - 5 = 14t - 5

This confirms that our expressions for the first term, common difference, and n-th term are all consistent with each other.

Now, we can use the formula for the sum of an arithmetic series to find the sum of the first n terms:

S_n = (n/2)(2a + (n-1)d) = (n/2)(4t + 4t + 1 + 3n - 3) = (3/2)n^2 + (5/2)t - 3n/2 + 1/2

We want to rewrite this expression in the form p(qt - 1)^r. To do this, we can try to complete the square in the n term, like this:

S_n = (3/2)[n^2 - 2n(t+1) + (t+1)^2] + (5/2)t - (3/2)(t+1)^2 + 1/2

S_n = (3/2)[n - (t+1)]^2 - (1/2)(t+1)^2 + (5/2)t + 1/2

Let u = n - (t+1), so that:

S_n = (3/2)u^2 - (1/2)(t+1)^2 + (5/2)t + 1/2

We want to rewrite this in the form p(qt - 1)^r, so let's try to match the terms:

p = -3/2

q = -1/(t+1)

r = 2

Therefore, the value of p is -3/2, the value of q is -1/(t+1), and the value of r is 2.

Note that the assumption that t is greater than 0 was not necessary for the derivation of the sum formula, but it is necessary for the existence of the arithmetic series (since otherwise the first term would be negative).

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The text format of the question in the picture:

22. The first term of an arithmetic series is (2t + 1) where t is > 0 The nth term of this arithmetic series is (14t - 5)

The common difference of the series is 3

The sum of the first n terms of the series can be written as p(qt - 1)^r where p, q and r are integers.

Find the value of p, the value of q and the value of r Show clear algebraic working.

The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex and other points, we can determine the value of a as follows:

g(x) = a(x - h)² + k

-13 = a(-7 + 4)² - 4

-13 = a(-3)² - 4

-13 + 4 = 9a

-9 = 9a

a = -1.

Therefore, the required quadratic function is given by:

g(x) = a(x - h)² + k

g(x) = y = -(x + 4)² - 4

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Answer:

  x < -1 or x ≥ 5

Step-by-step explanation:

You want the solution and its graph for the compound inequality ...

Adding 2 to the first inequality gives ...

  3x < -3

  x < -1 . . . . . divide by 3

Multiplying the second inequality by -1/2 gives ...

  x ≥ 5

The solution is x < -1 or x ≥ 5.

As per the given variables, Victor jumped a total of 4 yards.

Total yards jumped = 6 feet high

Additional yards = 2

A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.

Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.

There are 3 feet in a yard, therefore -

6 feet = 6/3  

= 2

Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.

Calculating, the total distance Victor jumped in yards -

= 2 + 2

= 4

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Answer:

Step-by-step explanation:

There are 2 parts for your function.    (see image)

y=4x, which is a line with a slope of 4 but x≠0, so there is a hole there

y=1 only at x=0  so the point is above the line

(a)  Domain: All real numbers.  There is a value for all x's

(b)  There is no x-intercept because the graph never touches x

y-intercept (1,0)  That's where the graph touch y

(c) see image

(d) range:  (-∞, 0) U (0, +∞)   there is a stop at 0 for y values

can also be written   -∞<x<1  and 1<x<+∞

(e) yes it's continuous for domain but not range.   because even though there is a jump at that point, i still have an x value.  The jump causes me to not have a y value at y=0, that's why range is discontinuous

The possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].

Since [tex]$a_1, a_2, a_3,\dots$[/tex] is an arithmetic sequence, we can write[tex]$a_3 = a_1 + d$[/tex] and [tex]$a_5 = a_1 + 2d$[/tex] where [tex]$d$[/tex] is the common difference between consecutive terms. Then the given equations become[tex]$3a_1 + 4d = -12$ and $a_1(a_1 + d)(a_1 + 2d) = 80$.[/tex] Simplifying the second equation gives $a_[tex]1^3 + 3da_1^2 + 2d^2a_1 - 80 = 0$.[/tex]

We can solve for [tex]$d$[/tex] in the first equation: [tex]$d = \frac{-3a_1-12}{4} = -\frac{3}{4}a_1 - 3$[/tex]. Substituting this into the second equation yields a cubic equation in terms of[tex]$a_1$[/tex]:

[tex]a\frac{3}{1}-[/tex] [tex]\frac{9}{4} a\frac{2}{1} -[/tex] [tex]\frac{15}{4} a_{1}- 80=0[/tex]

Using synthetic division or another method, we can find that [tex]$a_1 = -5$[/tex] is a root of this equation. Dividing by [tex]$a_1 + 5$[/tex] yields the quadratic [tex]$a_1^2 - \frac{1}{4}a_1 - 16 = 0$[/tex], which has roots [tex]$a_1 = -4$[/tex] and [tex]$a_1 = 4/5$[/tex].Therefore, the possible values of the common difference [tex]$d$[/tex] are [tex]$-\frac{27}{4}$[/tex] and [tex]\frac{4}{5}$[/tex]

Using [tex]$a_1 = -5$[/tex] and [tex]$d = -\frac{27}{4}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 - \frac{243}{4} = -\frac{263}{4}$.[/tex]

Using [tex]$a_1 = -5$[/tex] and [tex]$d = \frac{4}{5}$[/tex], we find that [tex]$a_{10} = a_1 + 9d = -5 + \frac{36}{5} = -\frac{13}{5}$.[/tex]

Therefore, the possible values of [tex]$a_{10}$[/tex] are [tex]$-\frac{263}{4}$[/tex]and [tex]$-\frac{13}{5}$[/tex].

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Answer:

Step-by-step explanation:

The percentage increase in the number of water bottles from February to April is 19%.

A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.

Therefore,

Therefore,

Number of water bottles in march = 4100 + 7% of 4100

Number of water bottles in march =4100 + 7 / 100 × 4100

Number of water bottles in march = 4100 + 287

Number of water bottles in march =  4387

Hence,

Number of water bottles manufactured in April = 4387 + 500 = 4887

Therefore,

percentage increase from February to April = 4887 - 4100 / 4100 × 100

percentage increase from February to April = 787 / 4100 × 100

percentage increase from February to April = 78700 / 4100

percentage increase from February to April = 19.1951219512

percentage increase from February to April = 19%

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ans. 1400000

we know that

work done by gravity =  mgh

just putting values we get

= 1400x 100 x 10

= 1400000

hence,work done an elevator motor need to do to lift a 1400kg elevator a height of 100m is 1400000

An equation that models the trigonometric graph is:

y = 4 sin 4x

The general form for an equation that models a wave is this:

±a (sin/cos) (2π(x - p)/T)

where:

a is the amplitude

p is the phase shift

T is the period.

The ±ve will turn into +ve if the graph tends to start from the positive direction, and then turns -ve if it the graph tends to start from the negative direction.

The (sin/cos) will definitely become sine if the graph starts at 0 before it is being shifted. Then, it becomes cosine if the graph begins at the amplitude.

In this problem, we see that the graph begins as positive, and then at the amplitude with no phase shift, we see that the ±ve becomes +ve, (sin/cos) becomes sin, and p becomes zero. Plugging in the given values  in the problem, we see that a = 4 and T = π/2.

We see that this equation becomes:

y = 4sin(2πx/(π/2)).

y = 4 sin 4x

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The expression 0 + 10 = 10 is an examle of the identity property of 0

From the question, we have the following parameters that can be used in our computation:

The list of options

The identity property of 0 states that

A number added to 0 equals to the number

Mathematically, we have

a + 0 = 0

The options are not clear

So, I will give another example of this property

The expression 0 + 10 = 10 is an examle of the identity property of 0

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Answer:

12

1,2,3,4,5,6,7,8,9,20,11,12

According to the information, Sandra charges $2.25 for each necklace. So the correct option would be A.

To find the answer to this problem we must identify the information that the function raises. In this case we must replace the n by a number (in this case it will be 5) to find the value of P as shown below:

Once we identify how much 5 necklaces are worth, we divide that value by 5 to find the unit value.

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Answer:

B. AB = CD = sqrt(13); DA = BC = sqrt(17)

This is because in a parallelogram, opposite sides are equal in length. In this statement, AB is equal to CD and DA is equal to BC, so opposite sides are equal. The values of AB, CD, DA, and BC are given as the square root of 13 and the square root of 17, which matches the condition of the statement.

In statement A, all sides are equal in length, which means the shape is a rhombus, not necessarily a parallelogram.

By using the corresponding angles, vertically opposite angles, alternate interior angles, and linear pair theorems, the measure of the angles are:

m ∠1 = 39°

m ∠2 = 141°

m ∠3 = 141°

m ∠4 = 39°

m ∠5 = 39°

m ∠6 = 141°

m ∠7 = 39°

From the question, we are to calculate the measure of the unknown angles in the given diagram

By the Linear pair theorem,

We can write that

m ∠5 + 141° = 180°

Thus,

m ∠5 = 180° - 141°

m ∠5 = 39°

Likewise

m ∠7 + 141° = 180°

m ∠7 = 180° - 141°

m ∠7 = 39°

By the vertical angles theorem,

We can write that

m ∠6 = 141° (Vertically opposite angles)

By the corresponding angles theorem,

We can write that

m ∠2 = 141° (Corresponding angles)

m ∠2 = m ∠3 (Vertically opposite angles)

Therefore,

m ∠3 = 141°

m ∠4 = m ∠5 (Alternate interior angles)

m ∠4 = 39°

m ∠1 = m ∠4 (Vertically opposite angles)

Therefore,

m ∠1 = 39°

Hence,

The measure of angle 1 is 39°

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a) Approximately 84% of the people are at least 26.5 years old. So, about 3528 people (0.84 * 4200).

b) Approximately 16% of the people are less than 26.5 years old. So, about 672 people (0.16 * 4200).

a) 26.5 years is 1.5 years (18 months) less than the mean (28 years). This is 1 standard deviation (18 months) below the mean.

The 68-95-99.7 Rule states that 68% of the data falls within 1 standard deviation of the mean. So, 100% - 68% = 32% is outside 1 standard deviation.

Since it's symmetrical, one-half of that 32% (16%) is less than 26.5 years, and the other half (16%) is older than 29.5 years.

Consequently, 100% - 16% = 84% is over 26.5 years old. If you multiply 0.84 by 4200, you get 3528 people.

b) As calculated earlier, 16% of the people are less than 26.5 years old. 0.16 * 4200 = 672 people.

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Answer: The Answer is NONE

Step-by-step explanation:

The test for polar symmetry is to replace θ with −θ and check if the equation remains the same. If it does, then the polar equation is symmetric about the polar axis. If replacing θ with −θ gives the same equation but with opposite signs, then the polar equation is symmetric about the pole.

Let's apply this test to the given equation:

r = 4cos^2 θ − 3sinθ + 5θ

Replacing θ with −θ, we get:

r = 4cos^2(−θ) − 3sin(−θ) + 5(−θ)

r = 4cos^2 θ + 3sinθ − 5θ

Since the two equations are not the same, we can conclude that the polar equation does not have polar symmetry about the pole or the polar axis.

Therefore, the answer is "none".

Answer: y = 3/5x - 2/5

Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.

Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.

Answer:

The p-value is the probability of observing a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. In this case, since it is a right-tailed test, the p-value is the area to the right of the observed test statistic Z=1.74 under the standard normal distribution curve.