A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth

Answer:

6

Step-by-step explanation:

Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.

[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]

The length of AC is simply x, therefore 6

The characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

A linear equation is given as:

y = mx + b

Where m represents the slope of the linear equation.

When the value of  is 0

i.e. m = 0, the equation becomes

y = 0 *x + b

Evaluate

y= b

The above equation is a horizontal line that passes through the y-axis at y= b

Hence, the characteristics of a linear function that has a slope of 0 is a horizontal line that passes through the y-axis at y= b

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The probability that a randomly selected adult has an IQ less than 130 is 0.9332

For given question,

We have been given adults IQ scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 15.

We need to find the probability that a randomly selected adult has an IQ less than 130

Sketch the curve.

The probability that X < 130 is equal to the area under the curve which is less than X = 130

Since μ = 100 and σ = 15 we have:

⇒ P ( X < 130 ) = P ( X- μ < 130 - 100 )

⇒ P ( X < 130 ) = P((X− μ)/ σ < 130 - 100/20 )

Since (X-μ)/σ = Z and (130 - 100)/20 = 1.5 we have:

P (X < 130) = P (Z < 1.5)

Now, we use the standard normal table to conclude that:

P (Z < 1.5) = 0.9332

Therefore, the probability that a randomly selected adult has an IQ less than 130 is 0.9332

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The surface area of the rectangular prism shown in the figure is 512 in²

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Surface area = 2(8 * 8) + 2(12 * 8) + 2(8 * 12) = 512 in²

The surface area of the rectangular prism shown in the figure is 512 in²

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Answer:

False

Step-by-step explanation:

If two angles are right angles, then they are congruent.

Parabolas could Lauren be describing are:

c) y2 = x

d) y2 = 10x

F)  y2 = 5x

The intersection of a cone with a plane that is parallel to the side of the cone results in the formation of a parabola, which is a symmetrical open plane curve. Under the influence of gravity, the route taken by a projectile takes the form of a curve similar to this one.

In the question that is presented to her, Lauren gives an example of a parabola that has a positive non-zero coordinate value on focus

Generally, the equation for focus is  mathematically given as

y=a(x-h)^2+k

In conclusion

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Answer: 7 pigeons sitting on the branches,  5 pigeons under the tree

=12 in total

Step-by-step explanation:

Upper branch has x pigeons, lower has y.

Top branch said: "If one of you flies up to us our number will be double yours":

Well, if one of the bottom branch flies up, the top branch will have x+1 birds and the bottom will have (y−1). The top will have double the bottom, so:

x+1=2(y−1)

Top branch said: "If one of us flies down to you, our numbers will be equal":

Now, the top branch will have x−1 and the bottom y+1. The numbers should be equal:

x−1=y+1

The true and false statement about the mean salary is illustrated below.

The true false statement about the mean salary include:

When Tom's salary has a z-score of 0.5, the amount that he earns will be:

0.5 = (x - 29300)/5400

0.5 × 5400 = x - 29300

2700 = x - 29300

x = 29300 + 2700.

x = 32000

The amount he earns is 32000.

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1) a) The volume of the sphere is 100 cubic centimeters.

b) The volume of the cylinder is 200 cubic centimeters.

2) The volume of the cone is 175 cubic centimeters.

Herein we have two case of submerging solids into recipients full of liquid, the volume of the objects is equal to the volume of the displaced liquid. Now we proceed to calculate the volume of each object:

Point 1 - Part A:

0.8 L - 0.5 L = 3 · x

0.3 = 3 · x

x = 0.1 L

x = 100 cm³

The volume of the sphere is 100 cubic centimeters.

Point 1 - Part B:

0.8 L - 0.5 L = x + y

0.3 = x + y

0.3 = 0.1 + y

y = 0.2 L

y = 200 cm³

The volume of the cylinder is 200 cubic centimeters.

Point 2:

350 mL = 2 · z

z = 175 mL

z = 175 cm³

The volume of the cone is 175 cubic centimeters.

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Answer:

[tex]x^{2} +10x+24[/tex]

Step-by-step explanation:

Answer:

=(x+1)^2-25

Step-by-step explanation:

=x(x−4)+6(x−4)

=x^2−4x+6x−24

=x^2+2x−24

=x^2+2x+1−25

=(x+1)^2-25

Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,

(a) The sample means of the backpacks are: 6.375,6.375,6.625

(b) Range of sample means: 0.25

(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.

For the first sample, mean= 6.375

For the second sample, mean= 6.375

For the third sample, mean= 6.625

Range of sample means=Maximum Mean- Minimum Mean

                                        = 6.625 - 6.375

                                        = 0.25

The students will estimate the average backpack weight of their classmates using sample means, the true statement is:

The closer the range of the sample means is to 0, the more confident they can be in their estimate.

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Answer:

8.57.

Step-by-step explanation:

that would be 360/42

= 8.5714

The identity for addition for rational numbers is zero which is the option b.

Given addition of rational numbers.

We are required to find the identity for the addition of rational numbers.

Rational numbers are those numbers which can be written in the form of p/q and q cannot be equal to zero because if q is equal to zero the whole fraction will become infinity. The numbers whih cannot be written as p/q are known as irrational numbers.

From the all option zero is the identity for addition for rational numbers. This  means if a is a rational number. Then a+0=0+a=a.

Hence the identity for addition for rational numbers is zero which is the option b.

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80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.

Here in the question it is given that,

that is each day the athlete spends 80 min.

So we can write that,

400 min is the time spent by the athlete

400 min  = number of days × time spent by the athlete in one day

400 min  = d × 80

⇒ 80d = 400  

Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.

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Answer:

probability of the personal information on the direction of the personal information to my house

Answer: Mean = 23

Step-by-step explanation:

Given information:

35, 40, 12, 16, 25, 10

Given formula:

[tex]Mean~=~\frac{Sum~of~terms}{Number~of~terms}[/tex]

Substitute values into the formula

[tex]Mean~=~\frac{35~+~40~+~12~+~16~+~25~+~10}{6}[/tex]

Combine like terms

[tex]Mean~=~\frac{75~+~28~+~35}{6}[/tex]

[tex]Mean~=~\frac{103~+~35}{6}[/tex]

[tex]Mean~=~\frac{138}{6}[/tex]

Simplify the fraction

[tex]\Large\boxed{Mean=23}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The mistake that the researcher made is that; neither critical nor obtained Chi squares can have negative values

A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables.

The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.

Now, Chi square (χ²) is the sum of a set of squared values, and as such it can never be negative. The minimum chi - squared value would be obtained if each Z = 0 so that χ² would also be 0. There is no upper limit to the χ² value. Similarly, the critical chi square cannot also be negative.

Thus, we can conclude that the mistake that the researcher made is that neither critical nor obtained Chi squares can have negative values

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Considering the given box-and-whisker plot, it is found that the bookstore sold between 2 to 12 books in 20 days.

A box and whisker plot shows three things:

From the plot given in this problem, the have that:

This means that the percentage of days in which between 2 to 12 books were sold is:

P = 75 - 25 = 50%.

Hence, out of 40 days, the amount of days is:

0.5 x 40 = 20 days.

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The probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5 is 0.0494.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Probability of an event P(E) = Number of favourable outcomes/Total number of outcomes.

Calculation for the given condition;

Either 1 or 3 must be present if a given integer is odd and smaller than 5.

The likelihood that it was picked from a set of nine numbers is (2/9).

The probability that the first integer is 1 is 50/50.

If it is and their combined number is less to 5, the second number will either be 1, 2, or 3.

The likelihood that it was picked out of the nine numbers is (3/9).

Additionally, there is a 50/50 probability that the first digit will be 3.

A second number is 1 if it is and the sum would be less than 5.

It was selected with a 1 in 9 chance of being one of the other 8 numbers.

The total probability is;

= (2/9)  times  [ (0.5 x 3/9)  +  (0.5 x 1/9) ]

= (2/9)  times  [ (1.5/9)  +  (0.5/9) ]

= (2/9)  times  [ 2/9 ]  =  4/81

= 0.0494

Therefore,  the probability that the sum of the two numbers malik picks is less than 5 is 0.0494.

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Answer:

See image

Step-by-step explanation:

Plato

Answer:

(a) 22cm^2

Step-by-step explanation:

(a) 6*3=18

2*2=4

4+18=22

By the integral test, the series is convergent.

The sequence [tex]k^3/e^{k^4}[/tex] is clearly positive and decreasing for [tex]k\in\Bbb N[/tex]; then by the integral test,

[tex]\displaystyle \int_1^\infty \frac{x^3}{e^{x^4}} \, dx \le \sum_{k=1}^\infty \frac{k^3}{e^{k^4}}[/tex]

and

[tex]\displaystyle \int_1^\infty \frac{x^3}{e^{x^4}} \, dx = \frac14 \int_1^\infty e^{-u}\, du = \frac1{4e} < \infty[/tex]

By using the integral test, series converges

What is an integral test for convergence and divergence?

⇒ It is used to prove the divergence or convergence of series. This test is called the integral test, which compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

How to know if a series is converging or diverging?

If the limit exists and is a finite number (a number less than infinity), we say the integral converges. If the limit is ±∞ or does not exist, we say the integral diverges.

let aₓ= f (x) is any function

⇒ In order for the integral test to work The function must be positive it has to be continuous and it has to be decreasing when x≥1

If the integral converges it means the series is also converging

If the integral diverges it means the series is also diverging

The sequence [tex]k^{3} /{e^{k^{4} }[/tex] is clearly positive and decreases for k∈N then by the integral test,

[tex]\int\limits^\infty_1 {x^{3} /e^{x^4} dx[/tex] [tex]\leq\displaystyle \sum^{\infty}_{k = 1} {x^{3} /e^{x^{4}[/tex]

and

[tex]\int\limits^\infty_1 {x^{3} /e^{x^4} dx[/tex][tex]=1/4\int\limits^\infty_1 {x^{3} /e^{-u} du[/tex]

⇒ [tex]1/4 < \infty[/tex]

So it comes with a finite value hence the series converges

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The equation of the hyperbola on which the ship is positioned is x²/2025-y²/4375=1

Given that radio stations, A and B are 160 kilometers apart and the signal from B arrives 0.0003 seconds before the signal from A and the signal travels 300,000 kilometers per second.

The distance between radio station A and B are d=160 km.

The time is t=0.0003s.

The speed of the signal travel is v=300000 km/s.

Consider both radio stations A and B lie at foci on the x-axis.

The origin lies at the midpoint between the stations.

The distance of one of the stations from the origin is,

c=d/2

c=160km/2

c=80km

The centre of the hyperbola lies at (0,0), so both stations lie at coordinates points of (-80,0) and (80,0).

The expression for the difference in distance is,

I=vt

I=300000×0.0003

I=90km

The semi-major axis of the hyperbola is,

a=I/2

a=90km/2

a=45km

The expression for the semi-minor axis of the hyperbola is,

b²=c²-a²

b²=(80)²-(45)²

b²=6400-2025

b²=4375

The expression for the hyperbola on which the ship is positioned,

x²/a²-y²/b²=1

x²/(45)²-y²/4375=1

x²/2025-y²/4375=1

Hence, the equation of hyperbola on which the ship is positioned for radio stations, A and B are 160 kilometers apart and signal from B arrives 0.0003 seconds before the signal from A is x²/2025-y²/4375=1.

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Answer:

  $1876.31

Step-by-step explanation:

The present value can be found using the compound interest formula.

The formula for the future value of an investment of P earning annual interest rate r compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Filling in the known values gives ...

  4000 = P(1 +0.085/4)^(4·9) = P(1.02125^36)

Then the amount to be invested is ...

  P = 4000/1.02125^36 ≈ 1876.31

The present value is $1876.31.

The ball will take 1.15 seconds to hit the floor.

It is given that,

A juggler is performing her act using several balls. The height as a function of time is given by :

[tex]h(t) =-16t^{2} + vt +s[/tex].............(1)

where,

v is the speed of the ball

s is initial height

t is time taken

Putting h(t) = 0 and solving equation (1)

[tex]-16t^{2} + vt +s = 0[/tex]

[tex]-16t^{2} + 15t +4 = 0[/tex]

On solving above equation using graphing calculator and solving for t we get, t = 1.154 second.

Hence, the correct option is (b) " 1.15 seconds ".

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The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.

An equation is an expression that shows the relationship between two numbers and variables.

The fact family (number family) is a group of equations that derive from a set of numbers.

Fact Family Triangle are used for Addition, Subtraction, Multiplication and Division

The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.

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The mass of the sample should be reported as 3.54 g

The amount of matter in an object is expressed in terms of mass.

The most frequent way to determine mass is to weigh something.

The units of mass are grams, kilograms, tonnes (in metric units), or ounces and pounds (US units).

According to the question,

A label on an empty sample container reads 10.000 g

A sample of a compound is added and the mass of the sample container is found to be 13.54 g.

The mass of the sample should thus be reported as,

= 13.54 - 10.000

= 3.54 g

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The supplied lines' point of intersection has the x coordinate  is 6.

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.

The x coordinate of the location where the ensuing lines intersect must be chosen.

3x + 5y = 78 ...........................(1)

2x - y = 0 ...............................(2)

The given system of equations must be solved in order to determine the x coordinate of the site of intersection.

Equation (ii) provides us with

2x = y

y = 2x ........................(3)

Equation I yields the result when the value of y from equation (iii) is substituted.

3x + 5(2x) = 78

3x + 10x = 78

13x = 78

x = 78/13

x = 6.

As a result, the supplied lines' point of intersection has the x coordinate  6.

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I understand that the question you are looking is :

3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____.

A.  7

B.8

C. 6

D. -6

The given transformation is a reflection across the y-axis that changes the coordinates EFGH into E'F'G'H' as follows:

E(-4, -1) → E'(4, -1)

F(-2, -1) → F'(2, -1)

G(-1, -2) → G'(1, -2)

H(-1, -4) → H'(1, -4)

The transformation rules for reflection are:

Reflection at y-axis: y = f(-x);

Reflection at x-axis: y = -f(x);

The given polygon has four vertices EFGH.

Their coordinates are:

E(-4, -1), F(-2, -1), G(-1, -2), and H(-1, -4)

When the transformation rule: reflection across the y-axis is applied, the coordinates become:

y = f(-x); rule

For E(-4, -1), x-coordinate is -4. So, -(-4) = 4

⇒ E'(4, -1)

For F(-2, -1), x-coordinate is -2. So, -(-2) = 2

⇒ F'(2, -1)

For G(-1, -2), x-coordinate is -1. So, -(-1) = 1

⇒ G'(1, -2)

For H(-1, -4), x-coordinate is -1. So, -(-1) = 1

⇒ H'(1, -4)

Thus, the transformed coordinates are:

E(-4, -1) → E'(4, -1)

F(-2, -1) → F'(2, -1)

G(-1, -2) → G'(1, -2)

H(-1, -4) → H'(1, -4)

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Total value of all coins together is $2.7

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

1 Nickel = $0.05 and 1 quarter = $0.25.

Let number of nickels and number of quarter be x.

According to the situation

x.(0.25) = $1.80 + x.($0.05)

x(0.25 - 0.05) = $1.80

x (0.2) = $1.80

x = $1.80/0.2

x = 9 coins

Therefore total value of the currency is 9(0.05 + $0.25) = 9 (0.3) = $2.7

Thus total value of all coins together is $2.7.

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