at the present time, gerald is eight less than five times his nephews age. seven years ago gerald was 9 times his nephews age.
(A)if g represents geralds age now and n represents his nephews age today. use a system of equations that could be used to model this scenario?
(B)than use the equations to determine algebraically the ages of both Gerald and his nephew.
(C)than determine in how many years Gerald will be three times as old as his nephew?

Answer:

381 cm³

Step-by-step explanation:

Volume of the pot = volume of a cylinder

Volume of the pot = πr²h

Where,

π = 3.14

radius (r) = 4.5 cm

h = 6 cm

Substitute

Volume of the pot = 3.14*4.5²*6

Volume of the pot = 381.51 ≈ 381 cm³ (nearest whole number)

9514 1404 393

Answer:

  C.  4/9

Step-by-step explanation:

There are a couple of ways you can do this.

  [tex]\log_3{4x}-2\log_3{x}=2\\\\\log_3{4}+\log_3{x}-2\log_3{x}=2\\\\\log_3{4}-2=\log_3{x}\\\\4\cdot3^{-2}=x\qquad\text{take antilogs}\\\\\boxed{x=\dfrac{4}{9}}\\\\\textsf{or}\\\\\dfrac{4x}{x^2}=3^2\qquad\text{take antilogs}\\\\\dfrac{4}{9}=x\qquad\text{cancel $x$, multiply by $\dfrac{x}{9}$}[/tex]

-10

thats it, thats what i know

Answer:

se supone que debes usar el SINE RATIO ya que se trata del lado opuesto y la hipotenusa.

Answer:

a) 0.0171 fluid ounces.

b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces

c) The mean should be of 6.153 fluid ounces.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 0.08 fluid ounces.

This means that [tex]\sigma = 0.08[/tex]

(a)What is the standard deviation of the average fill volume of 22 bags?

This is s when n = 22. So

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]s = \frac{0.08}{\sqrt{22}}[/tex]

[tex]s = 0.0171[/tex]

(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?

We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]

[tex]Z = -12.3[/tex]

[tex]Z = -12.3[/tex] has a p-value of 0.

0% probability that the average fill volume of 22 bags is below 5.95 ounces.

(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?

[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]

[tex]6.1 - \mu = -3.09*0.0171[/tex]

[tex]\mu = 6.153[/tex]

The mean should be of 6.153 fluid ounces.

I think it's: 4,674.14$

Answer:

A = $4724.36

Step-by-step explanation:

P = $3500

r = 7.5% = 0.075

t = 4years

n = 365

     [tex]A = P(1 + \frac{r}{n})^{nt}\\\\[/tex]

        [tex]=3500(1 + \frac{0.075}{365})^{365 \times 4}\\\\=3500(1.00020547945)^{365\times4}\\\\= 3500 \times 1.34981720868\\\\= 4724.36023037\\\\= \$ 4724.36[/tex]

Step-by-step explanation:

Is it helpful ?

plz let me know

Answer:

( h + 5 )^2 + ( y - 8 ) ^2 = 49

Step-by-step explanation:

Equation of a circle:

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

Where ( h , k ) = center and r = radius

We are given that the circle has a center at ( -5 , 8 ) meaning that h = -5 and k = 8

We are also given that the circle has a radius of 7 meaning that r = 7

Now that we have identified each variable we plug the values into the equation

( h - (-5)^2 + ( y - 8 )^2 = 7^2

Our final step is to simplify

we get that the equation of the circle is

( h + 5 )^2 + ( y - 8 ) ^2 = 49

By the way ^ means exponent

Answer: B ACE is similar to DCB

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

∠K and ∠ R are congruent (equal)

Triangle Sum Theory - angles of all triangles add to 180

180 - 79 - 26 = 75

Answer: The coefficient before x^4 is 60

Step-by-step explanation:

Hey! So I am not an expert at this, but you have to use the binomial theorem

I have attached of the Pascals Triangle (one shows the row numbering as well)

Basically in a pascal triangle, you add the two numbers above it to get the next number below

As you can see, the rows start from 0 instead of 1

The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms

NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)

Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)

It would be 15 × 2^4 × (1/2)^2 = 60

The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power

Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)

Answer:

a) A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

b) attached below ( Matrix dose not exist )

c) attached below  ( Matrix does not exist )

Step-by-step explanation:

a) Matrix

A =   [tex]\left[\begin{array}{ccc}1&0\\0&0\\0&1\end{array}\right][/tex] 3*2

From the matrix ; Column 1 and Column 2 Belong to COL(A)

while : (1,1)^T  =  ( 1,0 )^T +  ( 0,1 )^T  i.e. (1,1)^T  ∈  Row( A )

and (1, 2)^T. = ( 1,0 )^T + 2 ( 0,1 )^T   i.e. (1, 2)^T  ∈  Row( A )

Hence ; all requirements are fulfilled in Matrix A

b)  The column space is generated by (1,1,1)7T, the null space (or kernel) is generated by (1,2,3)T

Matrix is Non-existent because condition is not met

attached below

c) Rank | A |

dimension of column space= 4 , dimension of Row space = 3

Given that ; column space ≠ Row space

Hence Matrix does not exist

Answer:

Step-by-step explanation:

-1<x<3.   I hope it helpful!

Answer:3/6 in simplest fraction form is 1/2.

Step-by-step explanation:EASY and my chanel is FireFlameZero if u can check dat out

Answer:

3:1

Step-by-step explanation:

90:30 simplified is 3:1

Answer:

The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).

Step-by-step explanation:

Midpoint of a segment:

The coordinates of the midpoint of a segment are the mean of the coordinates of the endpoints of the segment.

Midpoint of s1:

Using the endpoints given in the exercise.

[tex]x = \frac{3 + \sqrt{2} + 4}{2} = \frac{7 + \sqrt{2}}{2}[/tex]

[tex]y = \frac{5 + 7}{2} = \frac{12}{2} = 6[/tex]

Thus:

[tex]M_{s1} = (\frac{7 + \sqrt{2}}{2},6)[/tex]

Midpoint of s2:

[tex]x = \frac{6 - \sqrt{2} + 3}{2} = \frac{9 - \sqrt{2}}{2}[/tex]

[tex]y = \frac{3 + 5}{2} = \frac{8}{2} = 4[/tex]

Thus:

[tex]M_{s2} = (\frac{9 - \sqrt{2}}{2}, 4)[/tex]

Find the midpoint of the segment with endpoints at the midpoints of s1 and s2.

Now the midpoint of the segment with endpoints [tex]M_{s1}[/tex] and [tex]M_{s2}[/tex]. So

[tex]x = \frac{\frac{7 + \sqrt{2}}{2} + \frac{9 - \sqrt{2}}{2}}{2} = \frac{16}{4} = 4[/tex]

[tex]y = \frac{6 + 4}{2} = \frac{10}{2} = 5[/tex]

The midpoint of the segment with endpoints at the midpoints of s1 and s2 is (4,5).

Answer:

c.the mean of each data set

Answer:

A

Step-by-step explanation:

9514 1404 393

Answer:

  x = -7, 5

Step-by-step explanation:

The equation is written as a product equal to zero. The "zero product rule" tells us that a product is zero if and only if one or more factors are zero. Each factor will be zero when x takes on a value equal to the opposite of the constant in that factor.

  x -5 = 0   ⇒   x = 5

  x +7 = 0   ⇒   x = -7

The solutions to the equation are x = -7, 5.

Ans : the measure of WX = 8

Answer:

9 (a) [tex]d = \frac{\sqrt{e}}{\sqrt{3}}[/tex]

9 (b) [tex]d = \frac{\sqrt{7k}}{\sqrt{2}}[/tex]

Step-by-step explanation:

Hope this helped!

Answer:

Graph A (first graph from top to bottom)

Step-by-step explanation:

Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.

Factoring the polynomial:

[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]

Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).

The graph that corresponds with this is graph A.

Answer:

It discusses the role of the God in influencing our decisions

Answer:

I believe it is choice D

Step-by-step explanation:

in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️

Answer:

(a) average calls = 5  

(b) probability that there is exactly one call in 6 consecutive monts = 0.038

Step-by-step explanation:

Let event of a customer requiring help in a particular month = H

and event of a customer not requiring help in a particular month = ~H

Given

p= 0.01,  therefore

Number of households, n = 500.

Binomial distribution:

x = number of households requiring help in a particular month

P(x,n,p) = C(x,n)*p^x*(1-p)^(n-x)

where

C(x,n) = n!/(x!(n-x)!) is the the number of combinations of x objects out of n

(a) Average number of households requiring help = np = 500*0.01 = 5

(b)

Probability that there are no calls requiring help in a particular month

P(0), q= C(0,n)*p^0(1-p)^(n-0)

= 1*1*0.99^500

= 0.006570483

Applying binomial probability over six months,

q = 0.006570483

n = 6

x = 1

P(x,n,q)

= C(x,n)*q^x*(1-q)^(n-x)

= 6!/(1!*5!) * 0.006570483^1 * (1-0.006570483)^5

= 0.038145

Therefore the probability that in 6 consecutive months there is exactly one month that no customer has called for help = 0.038

The answer would be 18 square units

Step-by-step explanation:

When talking about surface area, just add up all the units that is listed in the question. - just a tip ;)

Anyways, Hope this helps!! If it's wrong, feel free to curse me out.. haha...

Answer:

a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.

b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.

c) Expected number of acceptable specimens among the ten is 7.938.

d) Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

Step-by-step explanation:

a )

[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]

b )

[tex]c = 1.96 * 3 = 5.88[/tex]                    { Since Z = 1.96 for 95% CI refer table.}

c )

Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]

d )

Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]