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:

[tex] \sqrt{4 \times 5 + \sqrt{4 \times 9} } [/tex]

Answer:

[tex] { \tt{d = (r + c)t}}[/tex]

Divide ( r+c ) on both sides:

[tex]{ \tt{t = { \frac{d}{(r + c)} }}}[/tex]

Answer:

d / ( r + c) = t

Step-by-step explanation:

d = ( r + c ) t

Divide each side by ( r + c)

d / (r + c ) = ( r + c ) t / ( r + c)

d / ( r + c) = t

Answer:

42 teaspoons of vinegar

Step-by-step explanation:

Given

[tex]x \to vegertable[/tex]

[tex]y \to vinegar[/tex]

[tex]x : y = 4 :12[/tex]

Required

Find y when [tex]x = 14[/tex]

[tex]x : y = 4 :12[/tex] implies that:

[tex]14 : y = 4 : 12[/tex]

Express as fraction

[tex]\frac{y}{14} = \frac{12}{4}[/tex]

[tex]\frac{y}{14} = 3[/tex]

Multiply by 3

[tex]y = 14* 3[/tex]

[tex]y = 42[/tex]

Answer:

A math SAT score of 693 is 1.5 standard deviations above the mean

Step-by-step explanation:

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.

Mean µ = 520 and population standard deviation = 115.

This means that [tex]\mu = 520, \sigma = 115[/tex]

What math SAT score is 1.5 standard deviations above the mean?

This is X when [tex]Z = 1.5[/tex]. So

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

[tex]1.5 = \frac{X - 520}{115}[/tex]

[tex]X - 520 = 1.5*115[/tex]

[tex]X = 693[/tex]

A math SAT score of 693 is 1.5 standard deviations above the mean

Answer:

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.

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.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]

n days:

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

Applying the Central Limit Theorem to the z-score formula.

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

What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?

The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.

Answer:

cos(A) = adjacent side / hypotenuse

= 4/5

Answer:

[tex] \small \sf \: cos ( A ) = \green{ \frac{ 4}{ 5}} \\ [/tex]

Step-by-step explanation:

[tex] \small \sf \: cos ( A ) = \frac{ adjacent \: side }{ Hypotenuse} \\ [/tex]

Where, we have given

substitute the values that are given

[tex] \small \sf \: cos ( A ) = \green{ \frac{ 4}{ 5}} \\ [/tex]

Step-by-step explanation:

the answer is in the image above

Step-by-step explanation:

3/4×3/8

9/32

9/32×100

~28%

Answer:

v = 15 mph

Step-by-step explanation:

Given that,

A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.

Total distance, d = 3 + 7 = 10 miles

Total time, t = 15 + 25 = 40 minutes = 0.6667 hours

Average speed,

[tex]v=\dfrac{d}{t}[/tex]

Put all the value,

[tex]v=\dfrac{10}{0.6667}\\\\= $$14.99\ mph[/tex]

or

v = 15 mph

So, the required average speed is equal to 15 mph.

Answer:

7/12

Step-by-step explanation:

They ate  1/4  and 1/3

1/4 +1/3

Get a common denominator

1/4 *3/3 + 1/3 *4/4

3/12 + 4/12

7/12

Answer:

3sqaure root 100/5

Step-by-step explanation:

It would look like this picture Below

Given:-

To find:-

Answer:-

Mass defect arises when the mass of the atom differs from the sum of masses of nucleons . As we know that the nucleus of an atom is made up of neutrons(n) and protons (p) , and the total mass of a atom is the mass of nucleons ( protons and neutrons ) as electrons have mass very low as compared to that of n or p .

If we denote mass number by [tex]\green{A}[/tex] , then ;

[tex]\implies A = n_{\rm neutrons} + n_{\rm protons} [/tex]

Let [tex] Z[/tex] be the atomic number, then ;

[tex]\implies n_p = Z [/tex]

So, the number of neutrons will be;

[tex]\implies n_n = (A-Z) [/tex]

Therefore total mass would be ;

[tex]\implies M = m_pZ +m_n (A-Z) [/tex]

Then the mass defect would be ,

[tex]\implies\underline{\underline{\green{ \Delta M = [Zm_p + (A-Z)m_n - M ] }}} [/tex]

where ,

_______________________________________

Now we know that the Atomic number of Nitrogen is 7(Z) and its mass number is 14(A) .

Now substitute the respective values,

[tex]\implies \Delta M = 7(1.007825) + (14-7)1.008665 - 14.0031 \\ [/tex]

[tex]\implies \Delta M = 7.054775 + 7(1.008665) - 14.00 31 [/tex]

[tex]\implies \Delta M = 7.054775 + 7.060655 - 14.0031 [/tex]

[tex]\implies \Delta M = 14.11543 - 14.0031 [/tex]

[tex]\implies \underline{\underline{\green{ \Delta M = 0.11233 \ u }}}[/tex]

Hence the mass defect is 0.11233 u .

Also this mass defect appears as energy which is responsible for the binding of nucleons together.

and we are done!

9514 1404 393

Answer:

  21 1/3 grams

Step-by-step explanation:

The mass is the product of the volume and the density. The volume of a cube is the cube of its edge dimension.

  M = Vρ

  M = (4 cm)³×(3 g/cm³) = 64/3 g

The mass of the cube is 64/3 = 21 1/3 grams.

[tex]x= \pi[/tex]

Step-by-step explanation:

[tex]\cos^2x+\cos x+1=0[/tex]

Let [tex]u= \cos x[/tex]

Then [tex]u^2+2u+1=(u+1)^2=0[/tex]

or

[tex]\cos x = -1[/tex]

This gives us [tex]x= \pi[/tex] or all integer multiples of [tex]\pi (n \pi)[/tex]

Step-by-step explanation:

a.fourth quadrent

b.third quadrent.

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Step-by-step explanation:

everything can be found in the picture

Answer:

x=15

Step-by-step explanation:

Hi there!

We're given a right triangle with the measures of the 2 legs (sides that make up the right angle). We're also given the measure of the hypotenuse (the side opposite to the right angle) as x

We need to find x

The Pythagorean Theorem states that if a and b are the legs and c is the hypotenuse, then a²+b²=c²

Let's label the values of a, b, and c to avoid any confusion first

a=12

b=9

c=x

now substitute into the theorem

12²+9²=x²

raise everything to the second power

144+81=x²

add 144 and 81 together

225=x²

take the square root of 225

15=x (note: -15=x is technically also an answer, but since lengths cannot be negative, it's an extraneous solution in this case)

Therefore, the side length of x is 15

Hope this helps! :)

============================================================

Explanation:

The distance traveled is d = 80 miles.

When going to work, her speed is r = 60 mph. She takes t = d/r = 80/60 = 4/3 hours which converts to 80 minutes. Multiply by 60 to go from hours to minutes.

Notice how the '80' shows up twice (in "80 miles" and "80 minutes"). This is because traveling 60 mph is the same as traveling 1 mile per minute.

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

Now as she's coming home, her speed becomes r = 40 and she takes t = d/r = 80/40 = 2 hours = 120 minutes.

The difference in time values is 120 - 80 = 40 minutes.

Her commute back home takes 40 more minutes compared to the morning drive to work.

Answer:

100000+45000+500+60+7

Answer:

[tex]\textbf{HELLO!!}[/tex]

[tex]21\left(2-y\right)+12y=44[/tex]

[tex]42-21y+12y=44[/tex]

[tex]~add ~similar\:elements[/tex]

[tex]42-9y=44[/tex]

[tex]Subtract~42~from~both~sides[/tex]

[tex]42-9y-42=44-42[/tex]

[tex]-9y=2[/tex]

[tex]Divide\:both\:sides\:by\:}-9[/tex]

[tex]\frac{-9y}{-9}=\frac{2}{-9}[/tex]

[tex]y=-\frac{2}{9}[/tex]

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

hope it helps...

have a great day!

Answer:

4, -16

Step-by-step explanation:

Answer:

If I've done it right the answer should be A, the figures are congruent because a 270 rotation about the origin a d a reflection of the x-axis

Answer:

use 0-9 to fill in blanks

Step-by-step explanation:

the answer is in the picture

Answer:

1386

Step-by-step explanation:

22 × 9 × 7 = 1386 cubic feet

Answer:

I found answer

Step-by-step explanation:

1) 9

2) 12

3)15

4)20

Answer:

option C

Step-by-step explanation:

Total number of items = 5

Number of items to choose = 2

Therefore, the number of combinations is

                                                       [tex]5C_2 = \frac{5 \times 4}{1 \times 2} = 10[/tex]

Answer:

5k+19

Step-by-step explanation:

Subtract 4 from 23

Answer:

answer is

74....................