Write the hypothesis and the conclusion of each conditional.
1. If 3x-7 = 32, then x = 13.

Answer:

\(\sf \sqrt{218}=14.76\:\:(2\:d.p.)\)

Step-by-step explanation:

Distance between two points

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}\)

Define the given points:

Substitute the defined points into the formula and solve for d:

\(\implies d=\sqrt{(3-(-4))^2+(-7-6)^2}\)

\(\implies d=\sqrt{(7)^2+(-13)^2}\)

\(\implies d=\sqrt{49+169}\)

\(\implies d=\sqrt{218}\)

\(\implies d=14.76\:\: \sf (2 \:d.p.)\)

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\(\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}\)

Given:

▪ \(\longrightarrow \sf{- (-4, 6) }\)

▪ \(\longrightarrow \sf{(3, -7)}\)

\(\leadsto\) The rule of distance between the two points (x 1, y 1) and (x 2, y 2) is:

\(\longrightarrow \sf{d= \sqrt{ (x_2 - x_1 ) {}^{2} + (y_2 - y_1) {}^{2} } }\)

▪ \(\longrightarrow \sf{ (x1, y1) = (-4, 6)}\)

▪ \(\longrightarrow \sf{(x2, y2) = (3, -7)}\)

\(\leadsto\) Substitute them in the rule above:

\(\small\longrightarrow \sf{ d = \sqrt{(3 - 4) {}^{2} + ( - 7 - 6) {}^{2} } }\)

\(\small\longrightarrow \sf{d= \sqrt{7 {}^{2} + ( - 13) {}^{2} } }\)

\(\small\longrightarrow \sf{d= \sqrt{49 + 169} }\)

\(\small\longrightarrow \sf{d= \sqrt{218} }\)

\(\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}\)

\(\small\bm{ \small \bm{The \: \: distance \: \: between \: \: the \: \: 2 \: \: points \: \: is \: }} \) \(\small\bm{ \: \: \sqrt{218} \: \: or \: \: 14.76.}\)

Applying the knowledge of quotient and fractions, we have:

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

Problem 1:

The expression that matches the situation is: 7 ÷ 3 (quotient of 7 and 3)

7/3 = \(1\frac{2}{3} \)

The number of soda each person will drink is: \(1\frac{2}{3} \) glasses.

Problem 2:

The expression that matches the situation is: 8 ÷ 5 (quotient of 8 and 5)

8/5 = \(1\frac{3}{5} \)

The fraction of sugar to be used per cupcake is: \(1\frac{3}{5} \)

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When examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

What is statistical validity?

Statistical validity is defined as a procedure or an extent of drawing conclusions to which research works or studies can be considered precise and accurate which are derived from the already existing or reliable statistical tests.

It can also be the statistics which are derived from the research works or studies.

What is frequency in statistics?

Frequency in statistics can be defined as the number of times an observation or a record or a value occurred in the duration of the research work. The frequencies of different records are represented in a tabular form.

For a given set of data the frequency can either be 0 or more than that.

Frequency of a given record or an observation cannot be negative as the least number of times the instance of an object can appear is zero.

What is margin of error estimate?

The margin of error estimate is a percentage figure which can be some percentage more or less than the actual or ideal value.

The margin of error is the range of values greater or lesser than the sample outcome statistic in the accuracy or confidence region or the  interval.

Hence, when examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

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Answer:

x=1/2

Step-by-step explanation:

98+29x=96+33x

Step 1: Simplify both sides of the equation.

29x+98=33x+96

Step 2: Subtract 33x from both sides.

29x+98−33x=33x+96−33x

−4x+98=96

Step 3: Subtract 98 from both sides.

−4x+98−98=96−98

−4x=−2

Step 4: Divide both sides by -4.

−4x

−4

=

−2/−4

x=1/2

Step-by-step explanation:

Let the number be \(\overline{abc}=100a+10b+c\).

\(100a+10b+c=34a+34b+34c \\ \\ 66a-24b-33c=0 \\ \\ 22a-8b-11c=0\)

Taking the equation mod \(11\) yields \(-8b \equiv \pmod{11}\), meaning \(b=0\).

So, \(22a-11c=0 \implies c=2a\).

So, the only possibilites are \((a,c)=(1,2), (2,4),(3,6), (4,8)\).

Therefore, there are \(4\) such numbers.

The rate at which the top of the ladder is sliding down the wall when the top of the ladder is 7 feet from the ground is 105 ft/sec.

A 25 foot long ladder is leaning against a wall and sliding away at a rate of 15 ft/sec. We need to find how fast is the top of the ladder sliding down the wall when the top of the ladder is 7 feet from the ground.Let's assume the length of the ladder be 'L'.Therefore, L = 25 feet. The rate at which the ladder is sliding away from the wall is given by dL/dt. dL/dt = 15 ft/sec. Let the height of the wall be 'h'.

Therefore, h = 7 feet.We need to find the rate at which the top of the ladder is sliding down the wall. Let's assume this rate be 'x'.We know that, the ladder, wall, and the ground form a right-angled triangle.Let's assume that the distance between the base of the ladder and the wall be 'y'. Therefore, we have:x^2 + y^2 = L^2Differentiating with respect to time t, we get:2x(dx/dt)+2y(dy/dt)=0dx/dt=−y(dy/dt),Since the ladder is sliding down the wall, dy/dt is negative.dy/dt = -15 ft/sec.We need to find x when y = 7. y = 7.

Therefore, \(x=√(L2−y2)=√(252−72)=√(625−49)=√576=24\)ft.

Now, we can substitute the values in the equation we obtained for dx/dt.dx/dt = -y (dy/dt)= -7 × (-15) = 105 ft/sec.Hence, the rate at which the top of the ladder is sliding down the wall when the top of the ladder is 7 feet from the ground is 105 ft/sec.

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Las frecuencias son magnitudes que nos permiten representar valores de un fenómeno específico.

La frecuencia rotativa es un término que se refiere a la cantidad de ciclos completados en un período de tiempo por un elemento que gira en su propio eje. La magnitud con la que se puede asociar la frecuencia rotativa depende de distintos factores, no obstante los más comunes suelen ser: segundos, minutos y horas. Algunos ejemplos de frecuencia rotativa es:

La rueda de mi bicicleta tiene una frecuencia rotativa de 50 giros por minuto.

La frecuencia porcentual es un término que se refiere a la cantidad de elementos que tienen características similares por lo que pueden clasificarse en una categoría o clase similar. Por ejemplo, la frecuencia porcentual de personas con uniforme en mi escuela es del 90%.

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Answer:

Step-by-step explanation:

8,031,426,100

=8,000,000,000

=8×(10)^9

Answer: 1250

Step-by-step explanation:

1) The price of an article is marked 25% above the cost price.

SP = CP x 1.25

2) If it is sold at the profit of Rs 500 after allowing 15% discount

SP = CP x 0.85 + 500

SP = 0.85CP + 500

1.25CP = 0.85CP + 500

1.25CP - 0.85CP = 500

0.40CP = 500

CP = 500 / 0.4 = 1250

Answer:

solution,

Let C.P of article be X

\(mp = x + \frac{25}{100} \times x \\ \: \: \: \: = x + \frac{25x}{100} \\ = \frac{x \times 100 + 25x}{100} \\ = \frac{100x + 25x}{100} \\ = \frac{125x}{100} \\ sp = mp - \frac{15}{100} \times \frac{125x}{100} \\ \: \: \: \: = \frac{125x}{100} - \frac{15x}{80} \\ \: \: \: \: = \frac{125 x\times 4 - 15x \times 5}{400} \\ \: \: \: \: \: = \frac{500x - 75x}{400} \\ \: \: \: \: \: \: = \frac{425x}{400} \\ profit = sp - cp \\ or \: 500 = \frac{425x}{400} - x \\ or \: 500 = \frac{425x - x \times 400}{400} \\ or \: 500 = \frac{425x - 400x}{400} \\ or \: 500 = \frac{25x}{400} \\ or \: 25x = 200000 \\ or \: x = \frac{200000}{25} \\ x = 8000 \\ again \\ \: selling \: price = \frac{425x}{400} \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{425 \times 8000}{400} \\ \: \: \: \: \: \: = \frac{3400000}{400} \\ \: \: \: \: \: \: = 8500\)

hope this helps....

Good luck on your assignment...

Answer:

12.0 to 3 dig digs You must include the 0 to get 3 significant figures.

Step-by-step explanation:

Comment

This is a Pythagorean Problem. Use the formula

c ^2 = a^2 + b^2

Givens

a = 8 - 7 = 1 cm

b = 12 cm

c = ?

solution

c^2 = 1^2 + 12^2  

c^2 = 1 + 144

c^2 = 145                 Take the square root of both sides

√c^2 = √145  

c = 12.04

c = 12.0 to 3 sig digs.

the equation of the line that is parallel to the line and goes through the place where it intersects it at (8, -4)  is  mathematically given as

x - 4y = 12 is x - 4y = - 8.

If the slopes of two lines, m1 and m2, are equal, then the lines are parallel; if the slopes are not equal, then the lines are perpendicular.

In the question, we are asked for the equation of the line that is parallel to the line x - 4y = 12 and goes through the place where it is represented by the coordinates (8, -4).

The given line can be shown as:

x - 4y = 12,

We may determine the slope of the line by comparing it to its slope-intercept form, which is written as y = mx + b. The slope of the line is 1/4.

The slope, m = 1/4, will also be present on the line that is parallel to this one. The necessary line goes through the location in question (8, -4).

Considering the one-point formula, (y - y₁) = m(x - x₁), we can write the required equation as:

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

Therefore

x - 4y = - 8.

In conclusion, the equation of the line that is parallel to the line and goes through the place where it intersects it at (8, -4) x - 4y = 12 is x - 4y = - 8.

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Yes, there are different processes at work in statements about the world and arithmetical statements such as "2 + 2 = 4."

Statements about the world, also known as empirical statements or factual statements, involve making claims or assertions about the way the world is or the way things are in reality. These statements are based on observations, evidence, and empirical data. The process involved in evaluating and verifying the truth or falsity of such statements often relies on empirical evidence, experimentation, logical reasoning, and inference from available information.

On the other hand, arithmetical statements, such as "2 + 2 = 4," belong to the realm of mathematics and are considered analytical or logical statements. These statements are based on mathematical principles, definitions, and axioms. The process of evaluating the truth or falsity of arithmetical statements relies on the rules and properties of mathematics, such as addition, subtraction, multiplication, and division, as well as logical reasoning and deductive arguments.

In summary, statements about the world involve empirical processes that rely on observations and evidence from the real world, while arithmetical statements involve mathematical processes based on logical reasoning and mathematical principles.

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Complex numbers are represented on a cartesian coordinate system with a horizontal real axis and a vertical imaginary axis.

Any number that can be expressed as a+bi, where i is the imaginary unit and a and b are the real numbers, is a complex number. The number is made up of two parts: real part (a) and imaginary part (b).

Just like we can use the number line to visualize a set of real numbers, we can use the complex plane to visualize a set of complex numbers. The complex plane consists of two number lines intersecting at a right angle at the point (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.

The horizontal number line (what we know as the xxx-axis on a Cartesian plane) is the real axis. The imaginary axis is the vertical number line (the yyy-axis on a Cartesian plane).A point in the complex plane can represent every complex number.

For example, consider the number 3-5i3−5i3, minus 5, i. This number, also expressed as 3+(-5)i, has a real part of 3 and imaginary part of -5. The location of this number on the complex plane is the point that corresponds to 3 on the real axis and -5 on the imaginary axis.

So the number 3+(-5) corresponds with the point (3,-5). In the general complex number, a+bi corresponds to the complex plane's point(a,b).

Hence, complex numbers are represented on a cartesian coordinate system with a real horizontal axis and an imaginary vertical axis.

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Answer:

the answer is 5/12 !

because in figure , there is AC as perpendicular and BC as base

and by using formula of tan theta

p/b

it's AC/BC

that means 5/12

a) -43, -12, -1 1/2

b) 1 1/2. 12, 43

c) it is different

a) -1 1/2, -12, -43

from the least to the greatest:

The higher a negative number , the lesser the value of the number

-43, -12, -1 1/2

b) The absolute values of -1 1/2, -12, -43:

1 1/2, 12, 43

absolute values from least to greatest:

1 1/2. 12, 43

The order of the rational numbers in part (a) is different from the order of the numbers' absolute values in part (b)

c) Absolute values of a negative number gives a positive number. The higher a posititve number, the greater its value. While a higher negative number has a lower value. This makes the result in ordering the data different

Answer:

Volume = 112

Step-by-step explanation:

formula: V = (1/3) × L × W × h,

\(formula: V = ( \frac{1}{3} ) × L × W × h, \\ = \frac{1}{3} \times 8 \times 7 \times 6 \\ divide \: both \: 3 \: and \: 6 \\ = 1 \times 8 \times 7 \times 2 \\ = 56 \times 2 \\ = 112\)

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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The correct answer is option A. The assumption that is made so that the pooled variance estimate can be substituted for the population variances within the standard error of the differences formula is that the population variances are homogeneous.

This implies that the variances of the two populations under comparison should be comparable.

For many statistical tests, including the t-test and ANOVA, homogeneity of variance is a crucial presumption. The pooled variance estimate is not a reliable substitute for population variances if the variances of the two populations are not equal.

Consequently, in order to apply the pooled variance estimate in the standard error of the differences formula, the homogeneity of variance assumption is required.

Complete Question:

What  assumption is made so that the pooled variance estimate can be substituted for the population variances within the standard error of the differences formula?

A. The population variances are homogeneous

B. The population variances are heterogeneous

C. The sample sizes are equal

D. The sample sizes are large

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Answer:

Step-by-step explanation:

-2

Apply this particular rule of logs:

log a - log b = log a/b

Therefore, log2 (3) - log2 (12) = log2 (3/12) = log2 (1/4)

This last result simplifies to  log2 1 - log2 4 = 0 - 2 = -2

Answer:

-2

Step-by-step explanation:

\(log_2(3)-log_2(12)\)

~Simplify using log properties

\(log_2(\frac{3}{12})\)

\(log_2(\frac{1}{4})\)

~Apply log rules

\(-log_2(4)\)

~Rewrite

\(-log_2(2^2)\)

~Apply log rules

\(-2log_2(2)\)

~Apply log rules

-2 * 1

~Simplify

-2

Best of Luck!

Answer:

The correct answer is D. 3x² - x + 3

Step-by-step explanation:

4x² - x + 6 - (x² + 3)

= 4x² - x² - x + 6 - 3

= 3x² - x + 3

Answer:

the answer is approximately 8.2 units.

Let:

A = Annual income

M = Monthly income

N = Number of months in the year

So, the annual income will be given by the monthly income multiplied by the number of months:

Solve for M:

Divide both sides by 12:

Answer:

$2875

Answer:

2.2 times 10 exponent 4

Step-by-step explanation:

The current is therefore changing at such a rate of -0.6 amp/s. This indicates that current is dropping at a 0.6 amp/s rate.

Resistance is the amount that a substance obstructs or opposes an electric current. Electric current is the term used to describe the motion of electrons. To further comprehend resistance, imagine someone struggling to get from one shop to the next in a crowded market.

V = 12 volts and dR/dt = 0.8 ohms per second at R = 4 ohms are presented to us.

I = V/R calculates the current I via the resistance. With regard to time t, if we take the derivative, we get:

dI/dt = d(V/R)/dt

The quotient rule gives us:

dI/dt = (R dV/dt - V dR/dt) / R²

Inputting the values provided yields:

dI/dt = (4 d(12)/dt - 12 (0.8)) / 4²

Since dV/dt is zero because of voltage is constant, we can write:

dI/dt = (-9.6) / 16

If we simplify, we get:

dI/dt = -0.6 amp/s

Therefore, the current is changing at a rate of -0.6 amp/s. This means that the current is decreasing at a rate of 0.6 amp/s.

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The three median y-values that would form the summary points of the median dataset is:

Lower Median: 22

Middle Median: 26

Upper Median: 39

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

To find the three median y-values that would form the summary points of the median-median line, we first need to arrange the y-values in ascending order:

20, 21, 21, 22, 24, 25, 26, 35, 36, 38, 40, 44, 46

Next, we calculate the medians for the three partitions of the data:

Lower Median: The median of the lower half of the data

Median of: 20, 21, 21, 22, 24, 25 = 22

Middle Median: The median of the entire data

Median of: 20, 21, 21, 22, 24, 25, 26, 35, 36, 38, 40, 44, 46 = 26

Upper Median: The median of the upper half of the data

Median of: 35, 36, 38, 40, 44, 46 = 39

Therefore, the three median y-values that would form the summary points of the median-median line are:

Lower Median: 22

Middle Median: 26

Upper Median: 39

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Answer:

i dont know

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

since

\(\sqrt{5607} =74,879903...\\\\Let\ x\ the\ searched\ number\\\\5607-x=74^2\\\\x=5607-5476\\\\\boxed{x=131}\\\)

Answer:

D

Step-by-step explanation:

Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.

Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.

So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.

3/4 = 9/12

1/2 = 6/12

6/12 = 6/12

Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.

Therefore, Declan's reasoning is correct.

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Answer:

2.537 x 10¹⁵ miles

Step-by-step explanation:

We are given the following:

1 light year = 5.9 x 10¹² miles

Distance of the star = 4.3 x 10² light years

To get this we just convert the distance of the star in light years into miles.

We cancel out the light years and then we are left with:

In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.

Coefficients:

4.3 x 5.9 = 25.37

Exponents of 10:

10² x 10¹² = 10⁽²⁺¹²⁾=10¹⁴

Then we combine them again to form a scientific notation:

25.37 x 10¹⁴

But since the standard in writing a scientific notation, the coefficient needs to be a number from 1-9, we need to move the decimal. When we move the decimal to the right or left, we change the exponent of the power of 10. Since we will move it once to the left, we add 1.

The answer will then be:

2.537 x 10¹⁵ miles

Hope I helped! If you really thought I did a great job answering this question please rate, thanks, and award brainliest.

Yours,

Fellow Brainiac

Answer:    318,600

Step-by-step explanation:

This is what I got hope it helped:)

Answer:

A + B = 90° => A = 90 - B

So Tan A = Cot (90 - A) = Cot B

So Tan B = Cot (90 - B) = Cot A

SecB = Cosec (90 -B) = Cosec A

CosA = Sin (90 -A) = Sin B

The value of the angle given regarding the tangent will be tan²A.

From the information, TanA TanB + TanACot B/SinA SecB - Sin²B/Cos²A

= TanA CotA + TanATanA/AinA CosecA - Sin²B/Sin²B

= 1 + Tan²A - 1

= Tan²A

In conclusion, the correct option is Tan²A.

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