The table shows the ratio of tables to chairs in a classroom.
A 2-column table with 4 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4. Column 2 is labeled Chairs with entries 4, 8, question mark, 16.
Find the missing value in the table.

For 3 tables, there are chairs.

Answer:

assume \(13 = z \\ 8 =x \\ bc = y\)

by phytagorean theorem

\({y}^{2} + {x}^{2} = z^{2} \)

so

\(bc = y = \sqrt{ {z}^{2} - {x}^{2} } = \sqrt{169 - 64} = \sqrt{105} \)

\( \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }\)

\( \large\underline{ \boxed{ \sf{✰\:Note }}}\)

★ 1st let's know what is the given figure is and it's related concepts for solving !

\( \rule{70mm}{2.9pt}\)

★ Writing this theorem mathematically ★

\( { \boxed{✫\underline{ \boxed{ \sf{Pythagorean \: theorem \: ⇒ {Hypotenuse }^2={ Base }^2+ {Height }^2}}}✫}}\)

★ Here ★

\( \rule{70mm}{2.9pt}\)

\( \boxed{ \rm{ \pink ➛BA^2= AC^2+BC^2}}\)

\( \rule{70mm}{2.9pt}\)

\(\rm{ \pink ➛13^2= 8^2+x^2} \\ \rm{ \pink ➛169 = 64 + {x}^{2} } \\ \rm{ \pink ➛169 - 64 = {x}^{2} } \\ \rm{ \pink ➛105 = {x}^{2}} \\ \rm{ \pink ➛ \sqrt{105} \: or \: 10.2469 = x} \\ \)

\( \rule{70mm}{2.9pt}\)

Hence length (BC) in the given triangle is of

\( { \boxed{✛\underline{ \boxed{ \sf{\sqrt{105} cm\: or \: 10.2469cm\green✓}}}✛}}\)

\( \rule{70mm}{2.9pt}\)

Hope it helps !

Answer:

It is easier to stay balanced

Step-by-step explanation:

The rejection region for a left-tail hypothesis test with a significance level of 0.05 is z < -1.96

The rejection region for a left-tail hypothesis test with a significance level of 0.05 is z < -1.96. Since the calculated test statistic of -1.95 falls just outside of the rejection region, but still within the non-rejection region, the correct conclusion would be to ""Fail to reject the null hypothesis"" (option b). This means that there is not enough evidence to reject the null hypothesis at the chosen level of significance.

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Answer:

x=68º

Step-by-step explanation:

The dashes on the lines show they are equal in length making it an isosceles triangle. this makes the degrees equal as well so:

68º=x and vise versa

Answer:

x = 68°

Step-by-step explanation:

68° = x° [ being Isosceles triangle ]

The regression equation for predicting the height of girls at age 18 based on their height at age 2 is:

y ≈ 68.953 + 1.210x

The correlation coefficient illustrates how closely two variables are related to one another. This coefficient's range is from -1 to +1. This coefficient demonstrates the degree to which the observed data for two variables are significantly associated.

Based on the given information, we can use the linear regression model to predict the height of girls at age 18 based on their height at age 2. Here are the summary statistics:

n = 70 (sample size)

x = 87.25 (mean height at age 2 in cm)

y = 166.54 (mean height at age 18 in cm)

R = 0.664 (correlation coefficient)

S = 3.33 (standard deviation of height at age 2 in cm)

\(S_y\) = 6.07 (standard deviation of height at age 18 in cm)

To predict the height of girls at age 18 (y) based on their height at age 2 (x), we can use the regression equation:

y = a + bx

where a is the y-intercept (predicted height at age 18 when x = 0) and b is the slope of the regression line.

From the given information, we have the following values:

x = 87.25

y = 166.54

R = 0.664

Using these values, we can calculate the slope (b) of the regression line:

b = R * (\(S_y\) / S)

 = 0.664 * (6.07 / 3.33)

 ≈ 1.210

Next, we can calculate the y-intercept (a) using the formula:

a = y - b * x

 = 166.54 - 1.210 * 87.25

 ≈ 68.953

Therefore, the regression equation for predicting the height of girls at age 18 based on their height at age 2 is:

y ≈ 68.953 + 1.210x

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Answer:

\( P = \frac{3}{4}k \)

Step-by-step explanation:

\( y=xk \)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Since the two quantities are named P and V, then we will replace x and y with P and V:

P = Vk

P=18 when V=24:

\( 18 = 24k \)

\( \frac{18}{24} = k \)

\( k = \frac{3}{4} \)

Now we have the value of k, we can now express P in terms of V:

\( P = \frac{3}{4}V \)

Answer:

P = \(\frac{432}{V}\)

Step-by-step explanation:

Given that P is inversely proportional to V then the equation relating them is

P = \(\frac{k}{V}\) ← k is the constant of variation

To find k use the condition P = 18 when V = 24, that is

18 = \(\frac{k}{24}\) ( multiply both sides by 24 )

432 = k

P = \(\frac{432}{V}\) ← equation of variation

Answer:

96

Step-by-step explanation:

Based on the given conditions, formulate:

\(2\times8\times6\)

Calculate the product or quotient:

\(16\times6\)

96

Answer:

x=25 y=30

Step-by-step explanation:

same side interior:

6x-19+2x-1=180

once you do that substitute the variable on the bottom of the same side interior. 2x-1 you should get 50-1

once once do that put y+19=49

f(5) = 1/4(2)^5

f(5) = 1/4 (32)

f(5) = 8

answer

A. 8

The reasonable way to test this one is to identify the validity of the hypothesis can be tested.

The hypothesis suggests that when an electric current passes through a wire, it generates a magnetic field. If this magnetic field is strong enough, it could magnetize a non-magnetic nail that is placed nearby. To test this hypothesis, an experiment can be conducted as follows:

A non-magnetic nail, a battery, a wire, and a switch.

Connect the wire to the battery and switch in series. The other end of the wire should be wrapped around the nail multiple times. Once the apparatus is set up, turn on the switch to pass an electric current through the wire.

Before running the current through the wire, test the nail for its magnetic properties by holding it close to some iron filings or other small magnetic objects. If it does not attract any of these objects, then it is non-magnetic.

Turn on the switch and run the electric current through the wire wrapped around the nail for a few minutes.

After running the current through the wire, test the nail again for its magnetic properties. Hold it close to the iron filings or other small magnetic objects and observe if it attracts them.

Compare the results obtained before and after running the current through the wire. If the nail exhibits magnetic properties after running the current, then the hypothesis that passing an electric current through a wire can magnetize a non-magnetic nail can be considered valid.

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The correct answer is option (e) (-10,12,3).

To find DA(AUC), we first need to find AUC, which is the union of sets A and C. The union of two sets contains all elements that are in either set, so:

AUC = {-10, 12, 34, 5} ∪ {2, 3, 4, 5, 6, 7, 8}

= {-10, 2, 3, 4, 5, 6, 7, 8, 12, 34}

Now, we need to find DA(AUC), which is the set difference between AUC and D. The set difference between two sets contains all elements that are in the first set but not in the second set, so:

DA(AUC) = AUC - D

= {-10, 2, 3, 4, 5, 6, 7, 8, 12, 34} - {-11, 3, 5}

= {-10, 2, 4, 6, 7, 8, 12, 34}

Therefore, DA(AUC) = {-10, 2, 4, 6, 7, 8, 12, 34}. Option (c) (0.12, 3,4.5) is not a valid answer because it contains decimal values, whereas the given sets only contain integers. Option (a) (-1135) is not a valid answer because it only contains a single integer, whereas the given set differences should be sets themselves. Option (b) (3,5) and option (d) (empty set) are also not valid answers as they do not contain all the elements in DA(AUC). Therefore, the correct answer is option (e) (-10,12,3).

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Answer:

Step-by-step explanation:

21

Answer:

Sam bikes at a faster rate.  He can go 42.6 km in one hour while Alex is only able to go 39.6 km in the same amount of time.

Step-by-step explanation:

Alex's unit rate:

198/5 = 39.6 km per hour

Sam's unit rate:

298/7 = 42.6 km per hour rounded to the nearest tenths'

If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to widen.

This is because the standard deviation is a measure of the spread of the data, so if it increases, the data points are more spread out from the mean. As a result, the range of values that could reasonably contain the true population parameter (i.e., the confidence interval) needs to be wider to account for the increased variability in the sample.
If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to become wider.
When standard deviation increases, it indicates more variability in the data. As a result, the confidence interval, which is a range of values that estimates the true population parameter with a certain level of confidence, needs to be wider to account for the increased variability. This ensures that the true population parameter is still captured within the interval with the same level of confidence.

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Answer:

Step-by-step explanation:

Rationalization.  

                                                                              2 + i

For example:  " rationalize the denominator of ---------  "

                                                                               -3 + i

The time Sonto spent doing housework to the time she spent visiting friends to the time she spent watching television can be expressed as 2 : 3 : 4 : 6 .

This is because we can convert each time interval to a common unit, such as minutes, and then simplify the resulting fractions to a ratio of whole numbers. Specifically, Sonto spent 30 minutes doing housework (1/2 hour), 45 minutes doing housework, 60 minutes visiting friends (1 hour), and 90 minutes watching television (1 1/2 hours = 60 + 30 minutes).

Simplifying these fractions gives us the ratio

30 : 45 : 60 : 90

Dividing by GCF 15

2 : 3 : 4 : 6

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Answer:

D. 3x + 3 + 6 = 33

Step-by-step explanation:

3(x +1) + 6 = 3

multiply 3 by everything in the parenthesis

3(x) + 3(1) + 6 = 33

3x + 3 + 6 = 33

I hope this helps!

Answer:

153.94 in²

Step-by-step explanation:

The equation for Area is

Area = πr²

Plugging in the value for the radius into r, it will be

(note, r means radius)

Area = π(7)²= 49π ≈ 153.94

The units is -> in² so add that in the end

This means that the expressions can be simplified in such a way that they have the same final form.Expression 1:4(3x + 4x) = 12x + 16x = 28xExpression 2:12x + 16x = 28xThus, the two expressions are equivalent since they both have the same value of 28x, and they have the same simplified form.

Two expressions are considered equivalent if they have the same value for every possible value of the variable(s) involved. In this case, we have expression 1: 4(3x + 4x) and expression 2: 12x + 16x.

To demonstrate their equivalence, we can simplify expression 1 by distributing the 4: 4(3x + 4x) becomes 12x + 16x, which is equal to expression 2.

Therefore, both expressions are equivalent because they simplify to the same form, namely 28x. This means that regardless of the value of x, the two expressions will yield the same result, confirming their equivalence.

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Therefore, the figure's volume is 32 times Prism A's length less 40 cubic feet.

In three dimensions, each object takes up some space. What is being assessed is the size of this region. The volume of an item is the region that fills its three-dimensional boundaries. It is additionally known as an object's potential.

To determine the volume of the figure, we need to find the dimensions of both prisms and then add their volumes together.

Let's start by finding the width of Prism A. Since Prism A and Prism B are attached to each other, they must share a common width. We know the width of Prism B is 4 feet, so the width of Prism A must also be 4 feet.

Now we can calculate the volume of Prism A:

Volume of Prism A = length x width x height

Volume of Prism A = unknown x 4 feet x 8 feet (since we don't know the length of Prism A)

We don't know the length of Prism A, but we do know that it is connected to Prism B, which has a length of 2 feet. Therefore, the length of Prism A must be the remaining distance between the two prisms, which is:

Length of Prism A = total length - length of Prism B

Length of Prism A = unknown - 2 feet

Now we can substitute this value into the volume equation for Prism A:

Volume of Prism A = (unknown - 2 feet) x 4 feet x 8 feet

Next, we can calculate the volume of Prism B:

Volume of Prism B = length x width x height

Volume of Prism B = 2 feet x 4 feet x 3 feet

Volume of Prism B = 24 cubic feet

Finally, we can add the volumes of the two prisms together to get the total volume of the figure:

Total volume = Volume of Prism A + Volume of Prism B

Total volume = (unknown - 2 feet) x 4 feet x 8 feet + 24 cubic feet

Without knowing the value of "unknown", we cannot calculate the exact volume of the figure. However, we can simplify the equation by multiplying out the terms:

Total volume = (32 x unknown - 64) cubic feet + 24 cubic feet

Total volume = 32 x unknown - 40 cubic feet

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Answer:

vfedddyujnyuki4yutnrbqfv

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

..

Answer:

D

Step-by-step explanation:

Answer:

\(w=-4\)

Step-by-step explanation:

So we have the equation:

\(-79=7w+3(4w-1)\)

Distribute the right:

\(-79=7w+12w-3\)

Combine like terms:

\(-79=19w-3\)

Add 3 to both sides:

\(-76=19w\)

Divide both sides by 19:

\(w=-4\)

So, the value of w is -4.

And we're done!

Answer:

w = -4

Step-by-step explanation:

-79 = 7w + 3(4w - 1)

\(-79 = 7w + 3(4w - 1)\\\\-79=7w+12w-3\\\\-79=19w-3\\\\-79+3=19w-3+3\\\\-76=19w\\\\\frac{-76=19w}{19}\\\\ -4=w\\\\\boxed{w=-4}\)

Hope this helps.

Answer:

Step-by-step explanation:

Given system of equations

Express the first equation as

Substitute the value of y into second equation

Solve for x

Find the value of y

Answer:

(-5, 9)

Step-by-step explanation:

Given system of linear equations:

\(\begin{cases}-2x-y=1\\-4x-y=11\end{cases}\)

To solve by substitution, use arithmetic operations to isolate y in Equation 1:

\(\implies -2x-y=1\)

\(\implies -2x-y+y=1+y\)

\(\implies -2x=1+y\)

\(\implies -2x-1=1+y-1\)

\(\implies y=-2x-1\)

Substitute the expression for y into Equation 2 and solve for x:

\(\implies -4x-(-2x-1)=11\)

\(\implies -4x+2x+1=11\)

\(\implies -2x+1=11\)

\(\implies -2x+1-1=11-1\)

\(\implies -2x=10\)

\(\implies -2x \div -2=10 \div -2\)

\(\implies x=-5\)

Substitute the found value of x into one of the equations and solve for y:

\(\implies -2(-5)-y=1\)

\(\implies 10-y=1\)

\(\implies 10-y+y=1+y\)

\(\implies 10=1+y\)

\(\implies 10-1=1+y-1\)

\(\implies y=9\)

Therefore, the solution to the given system of linear equations is (-5, 9).

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282.040 cm³ of helium will be left in the balloon at the start of the tenth day. The sequence in this problem is neither arithmetic nor geometric.

To find out how much helium will be left in the balloon at the start of the tenth day, we need to calculate the remaining volume of helium after each day.

Let's denote the initial volume of helium as V₀ = 5000 cm³.

Since the balloon loses one fourth of its helium each day, the remaining volume after each day can be calculated as follows:

Day 1: V₁ = V₀ - (1/4) * V₀

Day 2: V₂ = V₁ - (1/4) * V₁

Day 3: V₃ = V₂ - (1/4) * V₂

...

Day n: Vₙ = Vₙ₋₁ - (1/4) * Vₙ₋₁

We can continue this calculation up to the tenth day:

V₁ = (3/4) * V₀

V₂ = (3/4) * V₁

V₃ = (3/4) * V₂

...

V₁₀ = (3/4) * V₉

Now, let's substitute the initial volume V₀ = 5000 cm³ into the equation to calculate the volume at the start of the tenth day:

V₁₀ = (3/4) * V₉

V₁₀ = (3/4) * ((3/4) * ((3/4) * ... * ((3/4) * V₀)))

Expanding this expression, we have:

V₁₀ = (3/4) * (3/4) * (3/4) * ... * (3/4) * V₀

Since we are multiplying (3/4) ten times, the expression becomes:

V₁₀ = \((3/4)^{10\) * V₀

Calculating this expression, we have:

V₁₀ = (59049/1048576) * 5000

V₁₀ ≈ 282.040 cm³

Therefore, approximately 282.040 cm³ of helium will be left in the balloon at the start of the tenth day.

Regarding the second part of the question, the sequence in this problem is neither arithmetic nor geometric. It involves a specific rule for each term that is not based on a consistent common difference or ratio.

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The area of the right triangle with one end at the origin and one end on the curve can be expressed as (1/2) * x * f(x), where x represents the x-coordinate of the end on the curve, and f(x) represents the y-coordinate of the end on the curve as a function of x.

The hypotenuse of a right triangle with one end at the origin and one end on the curve can be expressed as the square root of the sum of the squares of the x and y coordinates. In this case, the x-coordinate of the end on the curve is given as x, and the y-coordinate can be expressed as a function of x.

To find the area of the right triangle, we need to determine the lengths of its base and height. The base is the x-coordinate of the end on the curve, which is given as x. The height can be found by subtracting the y-coordinate of the end on the curve from the y-coordinate of the origin, which is 0. Since the y-coordinate can be expressed as a function of x, we can write the height as f(x) - 0, or simply f(x).

Therefore, the area of the right triangle can be calculated using the formula for the area of a triangle, which is (1/2) * base * height. Substituting the values we found, the area can be expressed as:

(1/2) * x * f(x)

This equation represents the area of the right triangle as a function of x. To calculate the actual area, you would need to know the specific function f(x) that represents the curve.

In summary, the area of the right triangle with one end at the origin and one end on the curve can be expressed as (1/2) * x * f(x), where x represents the x-coordinate of the end on the curve, and f(x) represents the y-coordinate of the end on the curve as a function of x.

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Answer:

many

a = 0.2

b = 0.7

Step-by-step explanation:

if a÷b is less than 1, then a must be smaller than b, so you can use any two decimals as long as a is the smaller of the two.