Which expression is represented by the model shown?
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Given below is the table that shows the equation and the surface it defines:S.NoEquationSurfaceType1x^2/a^2 + y^2/b^2 - z^2/c^2=1Ellipsoid2(x^2)/a^2 - (y^2)/b^2 + z^2/c^2=1Elliptical Paraboloid3-(x^2/a^2)-(y^2/b^2)+(z^2/c^2)=1Hyperboloid of Two Sheets4(x^2/a^2)-(y^2/b^2)-(z^2/c^2)=1Hyperboloid of One SheetOn comparing the given equation to the table, the surface is Hyperboloid of one sheet. The equation of the Hyperboloid of One Sheet is given by (x^2/a^2)-(y^2/b^2)-(z^2/c^2)=1. Therefore, the type of surface is the hyperboloid of one sheet.The given surface can be identified from the figure below:As per the given figure, the surface is the hyperboloid of one sheet as the shape of the surface is like an open saddle in which the curves are placed like a hyperbola.

The equation 18x = z² - y² represents a surface known as a Hyperboloid of one sheet (option c).

Therefore, the correct match is:

Equation: 18x = z² - y²

Surface: C - Hyperboloid of one sheet

A Hyperboloid of one sheet is characterized by the difference of squares in its equation. It has two distinct sheets that curve away from each other. The equation's form indicates that the surface will have different signs for the terms involving z² and y², resulting in a hyperbolic shape.

So, the correct type of surface for the given equation is a Hyperboloid of one sheet (Option C).

The complete question is:

Match the equation with the surface it defines. Also, Identify the surface by type (paraboloid, ellipsoid, etc.)

18x=z²-y²

What type of surface is this?

A: Elliptical Paraboloid

B: Ellipsoid

C: Hyperboloid of one sheet

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Answer:

\(0.03\)

Step-by-step explanation:

\(--------------------------------------------\)

\(-0.8+\frac{54}{50}-0.25\) = \(?\)

\(0.28-0.25\) = \(?\)

\(0.03\)

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

Therefore , the solution to the given problem of speed comes out to be v=21.12m/s.

How quickly something is moving is measured by its speed at a distance. How far an object moves in one unit of time is determined by its speed. Speed is calculated as follows: speed = distance * time. The most widely used speed measurement units are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :  A 2.0 m long cord is supporting a 3.3 kg lump of clay.

Two swing up to an absolute maximum of 0.080 meters

Ball and clay's subsequent impact velocity

=>√(2*10*0.08)=1.264m/s

To find the velocity of the ball before collision

0.21*v=(3.3+0.21)*1.264

v=21.12m/s

Therefore , the solution to the given problem of speed comes out to be v=21.12m/s.

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True. Birth statistics typically include data on both live births and fetal deaths.

Fetal deaths refer to the loss of a pregnancy before the fetus is delivered and can be classified as either early or late fetal deaths, depending on the gestational age at the time of the loss. While the focus of birth statistics is often on live births, tracking fetal deaths is important for monitoring the health of pregnant women and identifying potential risks or problems with pregnancy. In the United States, fetal death statistics are typically collected by state health departments and reported to the National Vital Statistics System. These statistics provide important information for researchers, healthcare providers, and policymakers working to improve maternal and fetal health outcomes.

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Answer: No, it is not.

Step-by-step explanation:

If you solve and graph the equation, the point (4,10) falls below the line, not satisfying the equation.

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

Option B.

Step-by-step explanation:

The general equation of best fit line is

\(y=ax+b\)

where, a is the slope of best fit line and b is y-intercept.

Using graphing calculator a=-4.54762 and b=43.7143. So equation of best fit line is

\(y=-4.54762x+43.7143\)

Here,

\(Slope=-4.54762\)

\(Slope\approx -4.5\)

Note: In alternate method, you can use the below formula to find slope.

\(m=\dfrac{\overline{x}\cdot \overline{y}-\overline{xy}}{(\overline{x})^2-\overline{x^2}}\)

Therefore, the correct option is B.

Answer:

B: -4.5

Step-by-step explanation:

edg2021

y ≈ -4.548x + 43.714 is the entire equation. So -4.548 or -4.5 is the slope.

Answer:

The y-intercept is (0,-12)

Step-by-step explanation:

Graph the equation

Scores on one variable plotted against scores on a second variable.

The correct answer is (b)

Now, According to the question:

Let's know:

A scatterplot shows:

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

Hence, The correct answer is (b) i.e.,

Scores on one variable plotted against scores on a second variable.

Given,

In the question:

A scatterplot shows:

a. the average value of groups of data.

b. scores on one variable plotted against scores on a second variable.

c. the frequency with which values appear in the data

d. the proportion of data falling into different categories.

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Based on my intuition, I believe that the two events, drawing a club and drawing a card with a black symbol, are likely to be associated. This can be answered by the concept of Probability.

This is because clubs are always black symbols, and therefore the probability of drawing a club and the probability of drawing a black symbol are not independent of each other. In other words, if we know that a card is a club, then we also know that it is a black symbol.

Therefore, these two events are associated.

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Answer:

Step-by-step explanation:

f^-1(x)=x/2+3

There were 110 children and 237 adults whο swam at the public pοοl that day.

Let's assume that the number οf children whο used the swimming pοοl is x, and the number οf adults is y.

Accοrding tο the prοblem, the tοtal number οf peοple whο used the swimming pοοl is 347. Therefοre, we have:

x + y = 347 ....(1)

Alsο, the tοtal amοunt cοllected in admissiοn fees is $785.00. We knοw that the admissiοn fee fοr children is $1.75 and fοr adults is $2.50. Therefοre, we can write anοther equatiοn as:

1.75x + 2.5y = 785 ....(2)

We nοw have twο equatiοns with twο unknοwns. We can sοlve fοr x and y by using any suitable methοd. Here, we will use the substitutiοn methοd.

Frοm equatiοn (1), we can express y in terms οf x as:

y = 347 - x

We can substitute this expressiοn fοr y in equatiοn (2), and sοlve fοr x:

1.75x + 2.5(347 - x) = 785

1.75x + 867.5 - 2.5x = 785

-0.75x = -82.5

x = 110

Therefοre, the number οf children whο used the swimming pοοl is 110. We can use equatiοn (1) tο find the number οf adults:

110 + y = 347

y = 237

Therefοre, the number οf adults whο used the swimming pοοl is 237.

Therefοre, there were 110 children and 237 adults whο swam at the public pοοl that day.

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Answer: -11.8  =  11.8 feet below the water's surface

Step-by-step explanation:

-15 + (0.5)(4) + 3(0.4)

-15 + 2 + 1.2

-11.8

Answer:

the hypotenuse is 6 and the other leg is 3\(\sqrt{2\)

Step-by-step explanation:

Answer:

\(x > -5\)

Step-by-step explanation:

Flip the equation over- \(10x+16 > 9x+11\)

Now do \(10x-9x=x\)

So the equation now looks like this \(x+16 > 11\)

Now subtract 16 from both sides to give you the answer \(x > -5\)

Answer: \(x > \Large\boxed{-5}\)

Step-by-step explanation:

Given inequality

\(9x+11 < 10x+16\)

Subtract 9x on both sides

\(9x+11-9x < 10x+16-9x\)

\(11 < x+16\)

Subtract 16 on both sides

\(11 -16 < x+16-16\)

\(-5 < x\)

\(x > \Large\boxed{-5}\)

Answer:

1111111111111111

Step-by-step explanation:

222222222222

The study outlined above is an experiment. In the study, two firefly colonies are set up in a laboratory environment and are subjected to different conditions. Therefore, it is an experimental design as the researcher is actively manipulating the independent variable which is the exposure of fireflies to light.

An observational study would involve recording data on a subject without manipulating their environment or situation. An observational study would have a less controlled environment in which the researcher does not interfere with the study subjects. There is a control group and a treatment group. The control group is the colony that is exposed to normal daylight/darkness conditions. The treatment group is the colony that is exposed to continuous light. The control group is used to provide a baseline measure or standard of comparison for the experiment.

It provides a way to compare the difference between the treatment group and the control group. Thus, the control group is the normal light/darkness colony, and the treatment group is the continuous light colony.

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Answer:

abc- 130

ebd-130

abe-50

Step-by-step explanation:

\(y = \cfrac{2}{5}x + 0\implies y=\cfrac{2}{5}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

Answer:

7 po ang tamang sagot welcome

The point (-2,2), we need to evaluate each case

In this case, for the real part we need to obtain -2

For the imaginary part, we need to obtain 2

As we can see the complex number that is shown in the graph is

ANSWER

A.

Answer:

≈20.56

Step-by-step explanation:

Since the total length of a side is 6 and the small bit is 2, the radius of the curve is 2. The curves are all 90° meaning they add up to one full circle, so you could just find the circumference of the circle with a radius of 2 plus the lengths between the curves.

Circumference = 2π(2) ≈ 12.57

Perimeter = 12.57 + 4(2) = 20.56

\( \bigstar \: {\large{\textsf{\textbf{\underline{\underline{Concept :}}}}}}\)

• Some of the properties of the log are as follows :

1) Product law -

\( \star \: \sf log(mnp) = \underline{{\boxed{{\sf logm +logn + logp}}}}\)

2) Division law -

\( \star \: \sf log( \dfrac{m}{n} ) = \underline{{\boxed{{\sf logm - logn }}}}\)

3) Power law -

\( \star \: \sf log \: {m}^{n} = \underline{{\boxed{{\sf n \: log m }}}}\)

4) We should also know that -

\( \star \: \sf log 10 = \underline{{\boxed{{\sf 1 }}}}\)

• To prove R.H.S equals to L.H.S, there exists three conditions :

1) To make R.H.S equals to L.H.S

2) To make L.H.S equals to R.H.S

3) To simplify both side equations and make them equal to a single value

In proving these questions, we're going to apply 2nd condition though all the three conditions described above are convertible to each other.

Now, let's start!

\( \: {\large{\textsf{\textbf{\underline{\underline{Solution:}}}}}}\)

\( \sf \red{ Question\: 1}\)

Taking L.H.S

\( \sf log630\)

✦ Prime factors of 630 -

\(\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&630 \\ \hline 3&315 \\ \hline 3&105\\ \hline5&35 \\ \hline 7&7\\ \hline &1\end{array}}\end{gathered}\end{gathered}\)

\( \implies \sf log(2 \times {3}^{2} \times 5 \times 7)\)

• Using first property

\( \implies \sf log2 + \underline{log {3}^{2} }+ log5 + log 7\)

• Using third property

\( \implies \sf log2 +2 \: log3 + log5 + log 7\)

\( \therefore \: \sf log630 = \underline{{\boxed{ \red{{\sf log2+2 \: log3 + log5 + log7}}}}}\)

\(\sf \green{ Question\: 2}\)

Taking L.H.S

\( \sf log10 + log100 + log1000 + log10000\)

\( \implies \sf log10 + log {10}^{2} + log {10}^{3} + log {10}^{4} \)

• Using third property

\( \implies \sf log10 +2 \: log 10 + 3 \: log 10 + 4 \: log 10\)

• As we know log10 = 1

\(\implies \sf 1+2 (1) + 3 (1)+ 4 (1)\)

\(\implies \sf 1+2 + 3 + 4 \)

\(\implies \sf \green{10}\)

\( \therefore \: \sf log10 + log100 + log1000 + log10000= \underline{{\boxed{ \green{{\sf 10}}}}}\)

\(\rule{280pt}{2pt}\)

Number 1

log 630

=log (2×3×3×5×7)

=log2+log 3^2-log 5+log7

= log 2+2 log 3 + log 5 + log 7

Number 2

log 10+ log 100+ log 1000+ log 10000

= log 10+2 log 10+ 3 log 10+ 4 log 10

= 10 log 10

= 10

Answer:

The right answer is ZP = 43

Step-by-step explanation:

I just took the quick check

Answer:

49.9

Step-by-step explanation:

335.5 minus 105.6 minus 180 = 49.9

Denise puts $67.50 in the savings account every week.

What is a percentage?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

To find out how much money Denise puts in the savings account each week, you need to multiply her weekly earnings by the percentage she puts into the savings account.

First, convert the percentage to a decimal by dividing by 100: 30% = 0.30

Then, multiply Denise's weekly earnings by this decimal to find the amount she puts into the savings account each week:

=$225 * 0.30

=67.50.

Hence, Denise puts $67.50 in the savings account each week.

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