Pythagorean Theorem:a2 + b2 = c2 Re−write the formula solving for b2 .

Answer:

A. $54,550.84

Step-by-step explanation:

48,000(1.0325)^4

48,000(1.136475928)

54,550.84455

The critical t-value for a confidence level of 98% with a sample size of 30 is approximately 2.756.

To find the critical t-value for a confidence level of 98% with a sample size of 30, we'll use the t-distribution table or a statistical calculator. Here's how you can calculate it:

Determine the degrees of freedom (df) for the t-distribution. For a sample size of 30, the degrees of freedom will be df = n - 1 = 30 - 1 = 29.

Look up the critical t-value in the t-distribution table using the desired confidence level and the degrees of freedom. In this case, for a 98% confidence level, we're interested in the critical value that leaves 1% in the tails of the t-distribution. Since the distribution is symmetric, we divide the 1% by 2 to get 0.5% for each tail.

Locate the row in the t-distribution table corresponding to the degrees of freedom (29 in this case). Then, look for the column that corresponds to the desired significance level (0.005 or 0.5% in this case).

Using a statistical calculator or t-distribution table, we find that the critical t-value for a 98% confidence level and 29 degrees of freedom is approximately 2.756.

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The critical t-value for a confidence level of 98% is 2.756.

Given data:

To find the critical t-value for a confidence level of 98% with a sample size of 30,  use a t-distribution table or a calculator.

Since the sample size is small (less than 30) and the population standard deviation is unknown, we use the t-distribution instead of the standard normal distribution.

The critical t-value is determined based on the confidence level and the degrees of freedom (df), which is equal to the sample size minus 1.

For a 98% confidence level, the corresponding significance level (α) is 1 - 0.98 = 0.02. Since it's a two-tailed test, divide this significance level by 2 to find the area in each tail: 0.02 / 2 = 0.01.

With a sample size of 30, the degrees of freedom is 30 - 1 = 29.

Using a t-distribution table or a calculator, we find the critical t-value with a cumulative probability of 0.01 (in each tail) and 29 degrees of freedom.

The critical t-value for a confidence level of 98% with a sample size of 30 is approximately ±2.756.

Hence, the critical t-value is 2.756.

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Step-by-step explanation:

[tex]y = a {(x - h)}^{2} + k[/tex]

[tex]vertex = (h \: \: \: k)[/tex]

from the table

[tex]vertex = ( - 2 \: \: \: 4)[/tex]

therefore

[tex]h = - 2 \: \: and \: \: k = 4[/tex]

[tex]y = a {(x + 2)}^{2} + 4[/tex]

when x= 0, y = 3

[tex]3 = a {(2)}^{2} + 4[/tex]

[tex]3 = 4a + 4[/tex]

[tex]a = \frac{ - 1}{4} [/tex]

therefore equation of the function

[tex]y = - \frac{1}{4} {(x + 2)}^{2} + 4[/tex]

Answer:

Step-by-step explanation:

The statement that is true for the given figure will be AD/DC = AB/CB.

So the correct option is A.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

The triangle ABC is divided into two triangle by a median DB that are;

Triangle ADB and Triangle ADC

So here the proportion form as;

AD/DC = AB/CB.

Therefore, The statement that is true for the given figure will be AD/DC = AB/CB.

So the correct option is A.

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Answer: What is the question? You have not posted a inquiry...

The required value of the triple integral is (16/3)π.

To evaluate the triple integral ∫∫∫E z dV, where E lies above the paraboloid z = x² + y² and below the plane z = 2y, we can use cylindrical coordinates.

In cylindrical coordinates, we have:

x = r cosθ

y = r sinθ

z = z

To determine the limits of integration, we need to find the bounds for r, θ, and z.

The paraboloid z = x² + y² can be expressed in cylindrical coordinates as z = r².

The plane z = 2y can be expressed in cylindrical coordinates as z = 2r sinθ.

To find the bounds for r, we set the two equations equal to each other:

r^2 = 2r sinθ

Simplifying the equation, we have:

r = 2 sinθ

Since the paraboloid lies above the xy-plane, the lower bound for r is 0.

To find the bounds for θ, we need to determine the range of θ that corresponds to the region of interest. This can be done by plotting the two surfaces and visualizing the region. From the equations, we can see that the region lies within the range 0 ≤ θ ≤ π.

To find the bounds for z, we need to determine the range of z between the two surfaces. The paraboloid is below the plane, so the lower bound for z is the equation of the paraboloid, z = r^2. The upper bound for z is the equation of the plane, z = 2r sinθ.

Therefore, the limits of integration are as follows:

0 ≤ r ≤ 2 sinθ

0 ≤ θ ≤ π

r² ≤ z ≤ 2r sinθ

Now, we can evaluate the triple integral:

∫∫∫E z dV = ∫[0,2π] ∫[0,∞] ∫[r²,(2r sin θ)] (r cos(φ) sin(θ)) dz dr dθ
               = (16/3)π

Therefore, the value of the triple integral is (16/3)π.

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Answer:

B=4i+4j-2k

Step-by-step explanation:

Lets find the length of vector A

IAI= sqrt(2²+2²+1²)=sqrt(9)=3

So B=2*A  = 2(2i+2j-1k)=4i+4j-2k

Answer:

1 / 962598

Step-by-step explanation:

Let S be the sample space

total number of possible outcomes = n(S)

Let E be the event

total number of favorable outcomes = n(E)

Compute the number of ways to select 5 numbers from 0 through 42:

Total numbers to choose from = 43

So

Total number of ways to select 5 numbers from 43

= n(S) = 43C5                                                                        

= 43! / 5! ( 43-5)!                                                                      

=  43! / 5! 38!                                                                      

= 43*42*41*40*39*38! / (5*4*3*2*1)*38!

= 115511760/120

n(S) = 962598

Hence there are 962598 ways to select 5 numbers from 43

Compute the probability of being a Big Winner

In order to be a Big  Winner all 5 of the 5 winning balls are to be chosen and there is only one way you can for this event to occur. So

n(E) = 1

Here E is to be a Big Winner

So probability of being a Big Winner = P(E)

= n(E) / n(S)

= 1 / 962598

Hence

P(being a Big Winner) = P(E) = 1 / 962598

Answer:

Last option

Step-by-step explanation:

I think it would be the last option because when you reflect over the x-axis, the x-axis switched signs.

So, -8 would be 8 , -7 would be 7, and 3 would be negative 3.

Dont think the y-axis value would change..

Hope this helps!

(If this was good..please give brainly.)

Answer:

Option C

Step-by-step explanation:

They are the same coordinates but exchanged/reflected places

please gimme brainiest ;(

Answer:

I believe it would be TRUE but sorry if I'm wrong!

Step-by-step explanation:

Answer: True

Step-by-step explanation:

I got it right on my lesson.

Answer:

1 h with 20 min

Step-by-step explanation:

10-6 = 100-60

= 40, in percentages is 40%, 40% minus of 2 h is...

if 50% minus is 1 h, 40% is 1 h with 20 min or simply...

120 min - 40% = 120 - 40

120 - 40 = 80, 80 min are 1 h and 20 min

Hope this helps

Answer:

The probability is 0.0643 to 4 decimal places

Step-by-step explanation:

To calculate this probability, we find the z-score

Mathematically;

z-score = (x-mean)/SD

where in the question;

x = 46.3

mean = 55.1

SD = 5.8

Plugging these values, we have;

z-score = (46.3-55.1)/5.8 = -8.8/5.8 = -1.52

The probability we want to calculate is;

P(z < -1.52)

We can get this answer by using the standard normal distribution table;

Thus from the table, we have;

P(z < -1.52) = 0.064255 which is 0.0643 to 4 decimal places

Answer: 139

Step-by-step explanation:

(5^2+4)*5-2+(-4)

(25+4)*5-2+(-4)

29*5-2-4

145-2-4

139

The total miles run by four runners is 26.563 miles.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, Four runners are training for long races. Noah ran 5.123 miles, Andre ran 6.34 miles, Jada ran 7.1 miles, and Diego ran 8 miles.

Therefore, The total number of miles for the dour runners is the sum of the individual miles run by each player which is,

= (5.123 + 6.34 + 7.1 + 8) miles.

= 26.563 miles.

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Answer:

the tax on a $90,000 salary is: $5175

Step-by-step explanation:

Given that the person earns a $90,000 annual salary, you need to use the last of the brackets , the one that reads "17,001 and up". That is, you need to find the 5.75% of the $90,000 in order to determine the taxes owed.

Recall that 5.75% in math terms is: 5.75/100 = 0.0575

Then the 5.75% of $90,000 is mathematically calculated as the product :

0.0575 x 90,000 = 5175

Therefore the tax on a $90,000 salary is: $5175

Answer:

10.9 liters

Step-by-step explanation:

cubical tank size = 30 x 30 x 30

filled with 6 cm x 30 cm x 30 cm = 5400 cu.cm

then added 5500 cu.cm.

total volume on a cubical tank = 5400 cu.cm + 5500 cu.cm

total volume on a cubical tank = 10,900 cu.cm x 1 cu.cm/0.001 liters

total volume on a cubical tank = 10.9 liters

Answer:

Step-by-step explanation:

= 10.9 liters

Answer:

Step-by-step explanation:

Hello, we need first to develop and then identify the like terms.

[tex](x + 7)^2 = (x-7)^2 + ax\\\\(x+7)^2-(x-7)^2=ax\\\\(x+7-x+7)(x+7+x-7)=ax\\\\14*2x=ax\\\\28x=ax[/tex]

So a = 28.

Thank you

Complete Question

The projected worth (in millions of dollars) of a large company is modeled by the equation w =256(1.09)^t .

The variable t represents the number of years since 2000. What is the projected annual

percent of growth, and what should the company be worth in 2008?

Answer:

a) The projected annual percent growth = 9%

b) The company's worth in 2008 = 510.09603627(in million dollars) or $510,096,036.27

Step-by-step explanation:

a) The projected annual percent growth

From the formula of company's worth =

w = 256(1.09)^t

1.09 - 1 = 0.09

Converting decimal to percentage

= 0.09 × 100

= 9%

b) The projected worth of the company is represented as:

w= 256(1.09)^t

t = 2000 - 2008 = 8 years

w = 256(1.09)^8

w = 510.09603627(in million dollars)

or 510.09603627 × 1,000,000

= $510,096,036.27

Answer:

-82°

Step-by-step explanation:

If we go 82° below 0, that means that instead of increasing by 82, we are decreasing by 82.

If we decrease to a number below 0, it becomes a negative number.

For example: If we decrease 10° from 0, we'd be at -10°.

Likewise, if we decrease 2° from 0, we'd be at -2°.

Following this pattern, if we decrease 82° from 0, we'd be at -82°.

Hope this helped!

In a parallelogram opposite angles are identical so K and M are the same. Solve for K first:

6x +3 = -9 + 7x

Add 9 to both sides:

6x + 12 = 7x

Subtract 6x from both sides:

X = 12

K = 6(12) + 3 =72 +3 = 75

Now K + N = 180

N = 180 - 75 = 105

N = 105

Answer:

ANGLE N = 105°

Step-by-step explanation:

The opposite angles of a parallelogram are equal

Therefore,

-9+7x = 6x+3

Bringing variables to one side

7x-6x = 3+9

x= 12

Since , x = 12

So , Angle K = 6x+3= 6(12)+3

= 72+3

=75

In a parallelogram , adjacent angles are supplementary

i.e, Angle K +Angle N = 180°

75 + Angle N = 180°

Angle N = 180 -75

= 105 °

Answer:

directrix: y=4

focus: (-3,2)

vertex: (-3,3)

Step-by-step explanation:

Answer:

11446

Step-by-step explanation:

= [(12*9) - 1 ]^2-3

=[108-1]^2-3

=107^2-3

=11449-3

=11446.

Answer:

Everything in the option.

When you know what you are doing and what you are saying then you can be able to convince your audience.

Answer:

I can easily convince people that I'm right

I back up my opinions with facts

Step-by-step explanation:

Correct on E2020

Answer:

decimal

x = 5.284 or 0.284

fraction

x = (21.136) / 4 or (1.136) / 4

Step-by-step explanation:

2x² - 10x - 3 = 0

x = [-b ± √b² - 4(a)(c)] / 2(a)

x = {-(-10) ± √[(-10)² - 4(2)(-3)]} / 2(2)

x = [10 ± √(100  + 24)] / 4

x = (10 ± √124) / 4

x = (10 ± 11.136) / 4

x = (21.136) / 4 or (1.136) / 4

x = 5.284 or 0.284

Answer:

The answer is attached for better presentation of formulas.

Step-by-step explanation:

The areas under the normal curve between any two ordinates at X=a and X=b equals the probability that the r.v X lies in the interval [a,b]. that is  P (a ≤ X ≤ b) = ∫_a^b▒1/(σ√2π) e^((-(x-u))/(2σ^2))  dx

which is represented by the area of the shaded region. (figure1)

But integrals of this type cannot be solved by ordinary means. They are however evaluated by the methods of numerical integration, and numerical approximations for some function have been tabulated for quick reference.

The table of areas under the unit normal curve gives the areas (probabilities) for the standard normal distribution from the mean, z=0 to a specified value of z say z0. Since normal curves are symmetrical therefore P (0 to z) = P (0 to –z). That is why the areas for negative values of z are not tabulated. Hence to use the table of areas for the normal distribution, the values of the r.v X in any problem are changed to the values of the standard normal variable Z and the desired probabilities are obtained from the table.

Thus to find P (a <X<b) we would change X into Z as follows

P (a <X<b) = P ((a-u)/σ ≤ (X-u)/σ  ≤  (b-u)/σ )

= P ((a-u)/σ ≤ Z ≤  (b-u)/σ )

Where (a-u)/σ and    (b-u)/σ  are the z- values of the standard normal variable Z.

In practice, a normal curve sketch for the given problem, showing under the X scale, a scale for the corresponding values of z will help in solving problem.  (Figure 2)

Answer:

[tex]\frac{1716}{132600}[/tex]

Step-by-step explanation:

Assuming they removed the jokers there are 52 cards in a deck and 13 hearts

You can calculate the odds of something by multiplying the odds together, because you don't put back the card you drew you have to subtract 1 from both the numerator and denominator

[tex](\frac{13}{52})(\frac{12}{51})(\frac{11}{50})=\frac{1716}{132600}[/tex]

Therefore the probability of pulling 3 cards that are all hearts are [tex]\frac{1716}{132600}[/tex]

Answer:

0

Step-by-step explanation:

6-6 equals 0

Answer:

Step-by-step explanation:

The absolute value of  |-6| is 6

Answer:

m∠OKG = 95°

Step-by-step explanation:

In the given question,

Angle OKL and angle OKG are the linear pairs.

And we know that sum of linear pair of angles is 180°.

Therefore, m∠OKL + m∠OKH = 180°

85° + m∠OKH = 180°

m∠OKH = 180° - 85°

              = 95°

Therefore, measure of angle OKG = 95° will be the answer.