Is the ordered pair (5, 24) a solution of y = 4x + 4? *​

The systems of equations A. x – y = 1, –3x + 3y = 3 and E. x + y = 1, –4x + 2y = 7 have no solutions because the equations lead to contradictory statements.

The systems of equations that have no solutions are A. x – y = 1, –3x + 3y = 3 and E. x + y = 1, –4x + 2y = 7.
Let's analyze each system of equations to understand why they have no solutions:
A. x – y = 1, –3x + 3y = 3
To determine if this system has a solution, we can rearrange the first equation to solve for x:
x = y + 1
Then we substitute this expression for x into the second equation:
-3(y + 1) + 3y = 3
Simplifying, we get:
-3y - 3 + 3y = 3
-3 = 3
Since -3 does not equal 3, the system has no solution.
E. x + y = 1, –4x + 2y = 7
Again, we can rearrange the first equation to solve for x:
x = 1 - y
Substituting this expression for x into the second equation:
-4(1 - y) + 2y = 7
Simplifying, we get:
-4 + 4y + 2y = 7
6y - 4 = 7
6y = 11
y = 11/6
However, if we substitute this value of y back into the first equation, we get:
x + 11/6 = 1
x = 1 - 11/6
x = -5/6
Therefore, this system of equations does not have a solution.
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The set containing all the colors of the marbles is given as follows:

{blue, yellow, purple, green, pink}.

A set of elements is composed by elements that respect a given characteristic, or are present in an experiment.

In this problem, we need to find the colors present in each marble, which are given as follows:

Then we have to list all these colors in a set, which are opened and closed by the brackets {}.

The color blue appears in both sets, however, it will appear only once in the set of the colors, as the elements are not repeated.

Thus, the set containing all the colors of the marbles is given by the set presented as follows:

{blue, yellow, purple, green, pink}.

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Answer:

10 shirts, 6 pants

Step-by-step explanation:

Let y = the number of shirts

Let x = the number of pants

y + 2 = 2x

x + y = 16

y = 2x - 2

x + (2x - 2) = 16

3x = 18

x = 6

y + 6 = 16

y =  10

Answer:

\(\textsf{A.} \quad \begin{cases}y=2x-2\\x+y=16\end{cases}\)

\(\textsf{B. \quad 6 pants and 10 shirts}\)

Step-by-step explanation:

Given variables:

If the number of shirts Sylvia packed was 2 fewer than twice the number of pants she packed:

\(\implies y=2x-2\)

If the total number of pairs of pants and shirts was 16:

\(\implies x+y=16\)

Therefore, the system of equations that represents the problem is:

\(\begin{cases}y=2x-2\\x+y=16\end{cases}\)

System of equations:

\(\begin{cases}y=2x-2\\x+y=16\end{cases}\)

Substitute the first equation into the second equation and solve for x:

\(\implies x+2x-2=16\)

\(\implies 3x-2=16\)

\(\implies 3x=18\)

\(\implies x=6\)

Substitute the found value of x into the first equation and solve for y:

\(\implies y=2(6)-2\)

\(\implies y=12-2\)

\(\implies y=10\)

Therefore, Sylvia packed:

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

Answer:

20

Step-by-step explanation:

fist you convert 6l to ml=6×1000

then,300/300:6000/300

gives you 1:20

The five key points of the parent function are:

The function is given as:

y = -2 sin[2(x - 45)] + 1

The above function is a sine function, and the parent function of a sine function is

y = sin(x)

The properties of the above function are:

The transformed function is given as:

y = -2 sin[2(x - 45)] + 1

A sine function is represented as:

y = A sin[Bx + C] + D

Where:

Using the above representations, we have:

See attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1

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As a result, the range of the population's mean height for male Swedes is between 70.331 and 73.669 inches.

The range of a function or relation in mathematics is the collection of all feasible output values (also known as the dependent variable). It is the collection of all possible values that such a function can have. For instance, since its function can output anything non-negative real integer, f(x) = x2 would have a range of all non-negative real numbers. The range is frequently stated as a collection of numbers or as a circle, and it may be either finite or infinite.

given

For the population mean height of male Swedes, the following formula provides a 95% confidence interval:

where n is the sample size, x is the sample mean, y is the standard deviation of height, n* is the z-score corresponding to a 95% confidence level, which is 1.96, and z* is the z-score.

By entering the specified values, we obtain:

CI = 72 ± 1.96 * (3/√48)

CI = (70.331, 73.669) (70.331, 73.669)

As a result, the range of the population's mean height for male Swedes is between 70.331 and 73.669 inches.

By multiplying the critical value (1.96), by the standard error, one may determine the error bound:

EBM = 1.96 * (3/√48) ≈ 1.382

The error bound is therefore roughly 1.382 inches.

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Answer:

34.8 N at 2.5 degrees from the positive x-axis

Step-by-step explanation:

From the given information:

The force F makes an angle A with the positive x axis can be expressed in terms horizontal and vertical components.

\(F_x = F cos A\\\\ F_y = Fsin A\)

Given that

\(F_1 = 50 \ N\)

\(\theta_1 = 30 ^0 \ \ \ (x-axis)\)

\(F_{1x} = F_1 \times Cos A_1\)

=  50 × cos 30

= 43.3 N

\(F_{1y} = F_1 \times Sin \ A_1\)

= 50 × sin 30

= 25 N

Similarly;

\(F_2 = 25 \ N\)

\(\theta_2 = 250 ^0 \ \ \ ( x-axis)\)

\(F_{2x} = F_2 \times cos \ A_2\)

= 25 × cos 250

= - 8.55 N

\(F_{2y} = F_2 \times A_2\)

= 25 × sin 250

= -23.5 N

The total net force;

\(F_{net} = F_{(net)}_x + F_{(net)}_y\)

\(F_{net} = (F_{1x} + F_{2x} ) i + (F_{1y} + F_{2y} )j\)

\(F_{net} = (43.3 - 8.55) i + (25-23.5 ) j\)

\(F_{net} =34.75 i + 1.5 j\)

\(|F_{net} | = \sqrt{F_{net}_x^2 + F_{net}_y^2}\)

\(|F_{net} | = \sqrt{34.75^2 + 1.5^2}\)

\(|F_{net} | = 34.8 \ N\)

Finally, the direction of the angle for the net force is:

\(tan \theta = \dfrac{F_{net_y}}{F_{net_x}}\)

\(\theta = tan^{-1} \Big (\dfrac{F_{net_y}}{F_{net_x}} \Big)\)

\(\theta = tan^{-1} \Big (\dfrac{1.5}{34.75}} \Big)\)

\(\theta = tan^{-1}( 0.043165)\)

\(\theta \simeq 2.5^0\ with \ positive \ x-axis\)

Answer:

7 5/6

Step-by-step explanation:

1 1/2= 1 3/6

6 1/3= 6 2/6

 1 3/6

+6 2/6

————-

7 5/6

The value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5. 

Two lines are parallel only if their slopes are the same. The slope of a line of the form y = mx + b (where m is the slope and b is the y-intercept) is m. The slope of a straight line of the form ax + by + c = 0 can be found using the formula: The calculation formula for the slope cutting shape will change.

So to find the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0, we need to find the slope of the line 5x - 3y + 44 = 0. To do this, we rearrange the equation into slope-intercept form.

5x - 3y + 44 = 0

-3y = -5x + 44

y = (5/3)x - 14.67

The straight line 5x - 3y + 44 = 0 has a slope of 5/3. In order for the 7x + ky = 35 line to be parallel to this line, the slope of 7x + ky = 35 must also be 5/3. To find the slope of 7x + ky = 35, rearrange the formula into slope-intercept form.

7x+ky=35

y = -(7/k)x + 35/k

Setting the slope of the line 7x + ky = 35 equal to the slope of the line 5x - 3y + 44 = 0 gives:

-(7/k) = 5/3

-7/k = 5/3

-7 * 3 = 5 * k

-21 = 5k

k = -21/5

Therefore, the value of k that makes the line 7x + ky = 35 parallel to the line 5x - 3y + 44 = 0 is k = -21/5. 

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The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

Answer:

5.4 = 7.56

1.5 = 2.1

Step-by-step explanation:

Just find the answer for 40% of the given meters.

Answer:

Angle bisector

Step-by-step explanation:

an angle bisector cuts an angle in half. COA goes from point c to point o to point a to make an angle. and OB is the exact middle of the angle. hope this helps :)

Knowing how to recognize congruent lines, we have Angles A&H are congruent.

Two line segments are collinear if they lie on a line. Two line segments are congruent when they have equal measures.

Parallel lines are lines in a plane that are always the same distance from each other. Parallel lines never intersect, while perpendicular lines are those that intersect at a right angle (90 degrees).

In this way, we can identify that the only lines that represent a congruent line are lines A and H.

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Answer:

Step-by-step explanation:

Answer:1. 12:6         equivalant ratio:24:12

Step-by-step explanation:

12:6 means twelve to 6 and to find a equivalant ratio means to find a number that 12 and 6 can equal so it would be 24:12 which i multiplied by 2.

Domain: 8, 9, 10, 11.Range: -7, 7 This relation does not represent a function because the same x-value (8, 10, 11) is associated with more than one y-value (-7, 7).

Domain: 8, 9, 10, 11

Range: -7, 7

A function is a relation between a set of inputs and a set of outputs such that each input is associated with exactly one output. This particular relation fails to meet this condition because the domain value 8 is associated with two different range values (-7 and 7). In other words, the same input (8) is associated with two different outputs, which means the relation does not represent a function. The domain of the relation is 8, 9, 10, 11 and the range is -7 and 7. Therefore, this relation does not represent a function because it violates the condition that each input must have one and only one associated output.

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There are no sufficient evidence using hypothesis to conclude percentage of commercial truck drivers those who suffer from sleep apnea is different from population's percentage of 5.2%.

To test the claim that the percentage of commercial truck drivers who suffer from sleep apnea is not 5.2%,

Use a hypothesis test.

Let p be the true proportion of commercial truck drivers who suffer from sleep apnea.

The null hypothesis is that the proportion of commercial truck drivers who suffer from sleep apnea is equal to 5.2%, or p = 0.052.

The alternative hypothesis is that the proportion is not equal to 5.2%, or p ≠ 0.052.

Use a z-test for the proportion to test this hypothesis.

The test statistic is,

z = (p₁ - p) / √(p(1-p) / n)

where p₁ is the sample proportion, n is the sample size, and p is the hypothesized population proportion.

In this case, we have,

p₁ = 30/397

   = 0.0756

n = 397

p = 0.052

Plugging these values into the formula, we get,

z = (0.0756 - 0.052) / √(0.052(1-0.052) / 397)

 = 2.11

The critical value for a two-tailed test at a 0.02 level of significance is ±2.33.

Since our test statistic, 2.11, is less than the critical value of 2.33, we fail to reject the null hypothesis.

Therefore, as per hypothesis we do not have sufficient evidence to conclude percentage of commercial truck drivers who suffer from sleep apnea is different from population's percentage of 5.2%.

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Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

Solving the proportion 22 miles/ 55 hours :: 12 miles/ k hours using cross products, value of h is 30.

Comparing two integers that each stand for a component of a whole results in a proportion. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10. When determining if two ratios or fractions are equivalent, the proportion formula is utilized. By dividing the supplied values, we may determine the missing value. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, b::c: d = a/b = c/d.

Given,

22 miles/ 55 hours = 12 miles/ k hours

Solving the proportion using cross products,

22 × h = 12 × 55

22 × h = 660

h = 660 ÷ 22

h = 30

Solving the proportion 22 miles/ 55 hours :: 12 miles/ k hours using cross products, value of h is 30.

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The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.

The ratio refers to the relative size of one quantity compared to another.

The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction.  We can also express the ratio in its standard form (:).

Given   Sum of     Equivalent

Ratio     Ratios          Ratios

5/36        36         13.89% or 0.1389

2:9           11          18.18% or 0.1818

3 to 18     21          14.28% or 0.14.28

1:3            4           25% or 0.25

Thus, we can conclude that 1:3 is the largest ratio amont the others.

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Answer:

#2

Even though the graph dips down, x is still increasing, and y will increase as will .

As x is decreasing, y is also decreasing.

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

In the provided text is a questionnaire or form related to a research tool for assessing a campaign in the community.

The first question asks whether the campaign pursues its aims, with the options of answering "YES" or "NO." The respondent is then instructed to elaborate on their answer.

A questionnaire is a research tool   used to collect data by presenting a series of questions to respondents,typically in a written format.

Questionnaires are an important research tool as they allow researchers to gather   large amounts of data from a large number of participants in   a standardized and efficient manner.

They provide a structured approach to collecting information,allowing for easy analysis and comparison   of responses.

Questionnaires can be used in various   research settings and are particularly useful for collecting quantitative data,measuring attitudes, opinions, behaviors, and gathering demographic information.

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Check the picture below.

\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

Make sure your calculator is in Degree mode.

Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

The probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins is 0.000045.

From the information illustrated,

Let A = event that one friend is pregnant with identical twins, and note that P(A)=0.0045.

Let B = event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.

Therefore, the probability will be gotten by using the multiplication for two independent events. This will be:

= P(A) × P(B)

= 0.0045 × 0.01

= 0.000045

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Answer:

Step-by-step explanation:

*a is 6:55

*b is 37

*c is 15:12

Answer:

Step-by-step explanation: