Rafael is putting money into a savings account. He starts with $350 in the savings account, and each week he adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Rafael has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 19 weeks.

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.

Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.

Answer:

A).   AC ≅ AE

Step-by-step explanation: took test on edge

Answer:

Maybe D-DE

Step-by-step explanation:

Because D has been decrease to E

Answer:

387

Step-by-step explanation:

The required sum of the arithmetic series 19+25+31+37+… Where n=9 is 387.

An arithmetic series is given,19+25+31+37+… sum of this series is to be determined where n=9.

Arithmetic progression is the series of numbers that have a common difference between adjacent values.

Here,
The Sum of an arithmetic series is given as
[tex]Sn=n/2(2a+(n-1)d)[/tex]
Where n (total terms) =9
            a  (first term) = 19
             d (common difference) = 6
Now,
[tex]S_9=9/2(2*19+(9-8)6)\\ S_9=9/2(38+64)\\S_9=9/2*86\\S_9=387[/tex]

Thus, the required sum of the arithmetic series 19+25+31+37+… Where n=9 is 387.

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Solve for one half on the triangle with height 6 and base would be 4/2 = 2

Use the Pythagorean theorem:

X = sqrt( 6^2 + 2^2)

X = sqrt( 36 + 4)

X = sqrt(40)

The answer is D

Answer:

56

Step-by-step explanation:

The range is the right line value minus the left line value

140 - 84

56

Answer:

[tex]\frac{\sqrt{21}}{3}[/tex] is the answer.

Step-by-step explanation:

To rationalize the denominator of [tex]\sqrt{\frac{7}{3}}[/tex] we will remove the square root or cube root from the denominator.

For which we multiply with the same value given in the denominator to numerator and denominator both.

[tex]\sqrt{\frac{7}{3}}=\frac{\sqrt{7} }{\sqrt{3} }[/tex]

[tex]\frac{\sqrt{7}}{\sqrt{3}}=\frac{\sqrt{7}}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}[/tex]

    [tex]=\frac{\sqrt{7\times 3}}{(\sqrt{3})^2}[/tex]

    [tex]=\frac{\sqrt{21}}{3}[/tex]

[tex]\frac{\sqrt{21}}{3}[/tex] is the rationalized form.

Therefore, [tex]\frac{\sqrt{21}}{3}[/tex] will be the answer.

Answer: Estimated the standard deviation α  = 5.35

Step-by-step explanation:

According to Empirical rule, the largest value is approximately:

ц + 3α

And the smallest value is approximately:

ц + 3α

Based on the given figures in the question, we can say

ц + 3α = 140.6

ц - 3α = 108.5

Now subtracting these two; we have

ц + 3α - ( ц - 3α  ) = 140.6 - 108.5

ц + 3α - ц + 3α = 32.1

6α = 32.1

α = 32.1 / 6

α = 5.35

Estimated the standard deviation α  = 5.35

Answer:

12 / 253

Step-by-step explanation:

There are a total of 4 + 4 + 9 + 6 = 23 cookies in the bag, therefore, there are 23 * 22 = 506 ways to pick one cookie, eat it, and then pick another cookie. There are 6 ways to choose the first cookie (because there are 6 oatmeal cookies) and 4 ways to choose the second cookie (because there are 4 chocolate chip cookies) so there are 6 * 4 = 24 successful ways. The probability is thus 24 / 506 = 12 / 253.

Answer:

98.5

Step-by-step explanation:

The dude above do be wrong doh

Answer:

t = kp, i think

Answer:

Measure of angle W + measure of angle Z = 180°

Step-by-step explanation:

The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)

Answer:

D is your answer

Step-by-step explanation:

I have no explanation

we need to add 64 on both sides and required equation is x=-8±2√5-8

Two or more expressions with an Equal sign is called as Equation.

The given equation is x²+16x=-44

Now we need to make the coefficient of x variable half and to square it.

(16/2)²=8²=64

Now add 64 on both the sides

x²+16x+64=-44+64

x²+16x+64=20

(x+8)²=20

x+8=±√20

x+8=±2√5

Now subtract 8 on both sides

x=-8±2√5-8

Hence, we need to add 64 on both sides and required equation is x=-8±2√5-8

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Answer:

Continous distributions:

- A probability distribution showing the average number of days mothers spent in the hospital.

- A probability distribution showing the weights of newborns.

Step-by-step explanation:

A probability distribution showing the number of vaccines given to babies during their first year of life will have a discrete distribution as only a natural number can represent the number of vaccines (0, 1, 2 vaccines and so on).

A probability distribution showing the average number of days mothers spent in the hospital can be described as continous because we are averaging days and this average can be fractional, so it is not discrete.

A probability distribution showing the weights of newborns is continous, as the weights are a continous variable (physical measurement), not discrete.

A probability distribution showing the amount of births in a hospital in a month is a discrete distribution, as the number of births can only be represented by natural numbers.

The option that describes a continuous distribution include:

A continuous distribution simply means the probabilities of the values of a continuous random variable.

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Answer:

Point C

Step-by-step explanation:

Point c is the only point on the number line which is in between 2 and 3.

Thus,

point c is the answer.

Hope this helps :)

Answer:

(a d)/(bc)

Step-by-step explanation:

a/b ÷ c/d

Copy dot flip

a/b * d/c

ad / bc

Answer:

1.580 Liters

Step-by-step explanation:

We know that  1000 mL = 1 Liter

1580 ml * 1L/1000 ml

1.580 Liters

Answer:

1.58

Step-by-step explanation:

1 milliliter = .001 liter

Step-by-step explanation:

Q8.  

Step 1.

35.4 - 31 = 4.4

Step 2.

4.4 ÷ 31 = 0.1419....

Step 3.

0.1419.... x 100 = 14.19...

Step 4.

To one decimal place = 14.2% increase

Q9.

Step 1.

£10 ÷ 40 articles = £0.25 = 25p (this is the answer to part a)

Step 2.

32p x 40 articles = £0.32 x 40 articles = £12.80 (this is the answer to part b)

Step 3.

£12.80 - £10 = £2.80 (this is the answer to part c)

Step 4.

£2.80 ÷ £10 = 0.28

Step 5.

0.28 x 100 = 28% (this is the answer to part d)

Hope this was what you were looking for :)

(Also, hi to a fellow Brit - there aren't that many of us around here)

Bluey :)

Answer:

Hey there!

1/2 x (4+8)

1/2 x (12)

6

Hope this helps :)

Answer: 6x

Step-by-step explanation:

.5x*(4+8)

.5x*(12)

6x

Hope it helps <3

Answer:

Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.

He makes such steps:

1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:

7x+7y+7x+4x-y-7z=14+16,

11x+6y=30.

2. He multiplies equation (3)  4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:

8x-2y-14z+3x+2y+z=32+8,

11x-13z=40.

Thus, he did not eliminate the same variables in steps 1 and 2.

Answer: correct choice is he did not eliminate the same variables in steps 1 and 2.

Hope this helps you :)! If you would mark me brainliest, that would be awesome!

Answer:

correct answer is c

Step-by-step explanation:

edge 2020

Answer:

With calculator;√24.5 = 4.9497

With differentials;With calculator;√24.5 = 4.95

The value of the square root gotten using differentials is an approximate value of the one gotten with a calculator

Step-by-step explanation:

With calculator;√24.5 = 4.9497

Using differentials;

The nearest number to 24.5 whose square root can be taken is 25, so let us consider that x = 25 and δx = dx = - 0.5

Now, let's consider;

y = √x - - - (eq 1)

Differentiating with respect to x, we have;

dy/dx = 1/(2√x) - - - - (eq 2)

Taking the differential of eq 2,we have;

dy = (1/(2√x)) dx

Using the values of x = 25 and dx = 0.5,we have;

dy = (1/(2√25)) × 0.5

dy = 0.05

Now;

√24.5 = y - dy

√24.5 = √x - dy

√24.5 = √25 - 0.05

√24.5 = 5 - 0.05

√24.5 = 4.95

Answer:

(a) 25 degrees

(b) -11 degrees

(c) 38 degrees

Step-by-step explanation:

The temperature function is:

[tex]T(t) = -t^2+4t+34[/tex]

(a) The average value for a temperature is:

[tex]M=\frac{1}{b-a}* \int\limits^b_a {f(x)} \, dx[/tex]

In this particular case, the average temperature is:

[tex]M=\frac{1}{9-0}* \int\limits^9_0 {T(t)} \, dt \\M=\frac{1}{9}* \int\limits^9_0 {(-t^2+4t+34)} \, dt \\M=\frac{1}{9}* {(-\frac{t^3}{3}+2t^2+34t)}|_0^9\\M=\frac{1}{9}*( {(-\frac{9^3}{3}+2*(9^2)+34*9)-0)[/tex]

[tex]M=25[/tex]

The average temperature is 25 degrees.

(b) The expression is a parabola that is concave down, therefore there are no local minimums, which means that the minimum temperature will be at one of the extremities of the interval:

[tex]T(0) = -0^2+4*0+34=34\\T(9) = -9^2+9*4+34=-11[/tex]

The minimum temperature is -11 degrees.

(c) The maximum temperature will occur at the point for which the derivate of the temperature function is zero:

[tex]T(t) = -t^2+4t+34\\T'(t)=-2t+4=0\\2t=4\\t=2[/tex]

At t = 2, the temperature is:

[tex]T(2) = -2^2+4*2+34=38[/tex]

The maximum temperature is 38 degrees.

Answer:

Q(1,1), N(3,2) A(2,5)

Step-by-step explanation:

Greetings from Brasil...

See the attached figure. The smaller the θ angle, the smaller the AB side will be. If the angle θ = 90º, then AB = 25. As θ < 90, then AB < 25

5X - 10 < 25

5X < 25 + 10

X < 35/5

X < 7

The AB side can be neither zero nor negative. So

5X - 10 > 0

5X > 10

X > 10/5

X > 2

Answer: options 2,3and 6

Answer:

option

2-Twelve students answered Mr. Chiu’s question.

3-Three people studied for two hours.

6-Four people studied for four or more hours.

Step-by-step explanation:

hope this helps:)

Answer:

The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].

Step-by-step explanation:

Let be [tex]r = \ln (6\cdot a + 9\cdot b)[/tex], which is now solved as follows:

1) [tex]\ln(6\cdot a + 9\cdot b)[/tex] Given.

2) [tex]\ln [3\cdot (2\cdot a + 3\cdot b)][/tex] Distributive property.

3) [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex] ([tex]\ln (x\cdot y) = \ln x + \ln y[/tex]) Result.

The equivalent expression of [tex]\ln(6\cdot a + 9\cdot b)[/tex] is [tex]\ln 3 + \ln (2\cdot a + 3\cdot b)[/tex].

We want to find an equivalent expression to ln(6a + 9b). We will get:

ln(6a + 9b) = ln(3) + ln(2a + 3b)

Here we will be using the rule:

ln(x) + ln(y) = ln(x*y)

Now let's see our expression:

ln(6a + 9b) = ln(3*(2a + 9b))

Now we use the above rule to write:

ln(3*(2a + 3b)) = ln(3) + ln(2a + 3b)

Then the equivalent expression is:

ln(6a + 9b) = ln(3) + ln(2a + 3b)

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Answer:

Step-by-step explanation:

From the give information: A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                           53                    17                      70

Not Vaccinated                    62                    143                   205

Total                                     115                     160                  275

In this study, we have two variables   ( Vaccination and diseases status ) The null and the alternative hypothesis can be stated as follows:

Null hypothesis: The two variables   ( Vaccination and diseases status ) are independent

Alternative hypothesis : The two variables   ( Vaccination and diseases status ) are dependent

The Chi-square test statistics can be computed as:

The Expected Values for the table can be calculated by using the formula:

[tex]E_i=\dfrac{row \ total \times column \ total}{grand \ total}[/tex]

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       29.273                 40.727              70

Not Vaccinated                85.727                 119.273             205

Total                                     115                     160                  275

[tex]Chi - Square \ X^2 = \dfrac{(O_i-E_i)^2}{E_i}[/tex]

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       19.232                13.823              33.055

Not Vaccinated                6.564                 45.573              52.137

Total                                  25.796               59.396             85.192

Therefore;

the Chi-Square Test Statistics = 85.192

For this study; we two rows and two columns

Therefore, the degree of freedom = (rows-1) × (columns-1)

the degree of freedom = (2 - 1) × (2 - 1)

the degree of freedom =  1 × 1

the degree of freedom =  1

Using the level of significance of ∝ = 0.05 and degree of freedom = 1 for the chi-square test

The p-value for the test statistics  = 0.00001

Decision rule: Since the P-value is lesser than the level of significance , therefore we reject the null hypothesis at the level of significance of 0.05

Conclusion:

We accept the alternative hypothesis and  conclude that the two variables

(Vaccination and diseases status ) are dependent  i.e the  vaccination and disease status are related

Answer:

A.50,000 units

B.62,500 units

C.Process A with a profit of $700,000 to maximize profit

Step-by-step explanation:

A.Calculation for the breakeven volume for Process A

Using this formula

Breakeven volume for Process A= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process A=500,000/(35-25)

Breakeven volume for Process A=500,000/10

Breakeven volume for Process A=50,000 units

B.Calculation for the breakeven volume for Process B

Using this formula

Breakeven volume for Process B= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process B=750,000/(35-23)

Breakeven volume for Process B=750,000/12

Breakeven volume for Process B=62,500 units

C. Calculation for what the company should do if the total demand (volume) is 120,000 units

Using this formula

Profit=(Total demand*(Sales per units-Variable cost per units for Process A)- Process A fixed cost

Let plug in the formula

Profit =120,000*($35-$25)-$500,000

Profit=120,000*10-$500,000

Profit=1,200,000-$500,000

Profit= $700,000

Therefore If total demand (volume) is 120,000 units, then the company should select Process A with a profit of $700,000 to maximize profit.

Answer:

See below

Step by step explanation

[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A) = - 1 [/tex]

L.H.S

[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A ) [/tex]

We know that ,

[tex] \tan(A + B) = \frac{tan \: A + tan \: B}{1 - \tan \: A \: \tan \: B } [/tex]

[tex]( \frac{ \tan( \frac{\pi}{4} + \tan \: A ) }{1 - \tan \frac{\pi}{4} \tan \: A} ) \: (\frac{ \tan \frac{3\pi}{4} + \tan \: A}{1 - \tan \frac{3\pi}{4} \tan( \: A) } )[/tex]

[tex]( \frac{1 + \tan \: A }{1 - \tan\: A} )( \frac{ \tan( x - \frac{x}{4} + \tan \: A ) }{1 - \tan(\pi - \frac{\pi}{4} ) \: \tan \: A }) [/tex] (tan π / 4 = 1 )

[tex]( \frac{1 + \tan \: A}{ -1 - \: \tan \: A } )( \frac{ - \tan( \frac{\pi}{4} + \tan \: A ) }{1 - ( - \tan \: \frac{\pi}{4}) \: \tan \: A } )[/tex] [ tan ( π - B ) = - tan∅ ]

[tex]( \frac{1 + tan \: A}{1 - tan \: B} )( \frac{ - 1 + \tan\: A }{1 + \tan \: A } )[/tex]

[tex] = \frac{ - (1 - \tan\: A)}{(1 - \tan \: A) } [/tex]

[tex] = - 1[/tex]

Hope this helps..

Best regards!!

Given Information:

Starting population = P₀ = 47,597

rate of growth = 1.8%

Required Information:

Equation that defines the population t years = ?

Answer:

The following equation defines the population t years after 2010.

[tex]$ P(t) = 47,597e^{0.018t} $[/tex]

Step-by-step explanation:

The population growth can be modeled as an exponential function,

[tex]$ P(t) = P_0e^{rt} $[/tex]  

Where P₀ is the starting population in 2010, r is the rate of growth of the population and t is the time in years after 2010.

We are given that the starting population is 47,597 and rate of growth is 1.8%

So the population function becomes

[tex]$ P(t) = 47,597e^{0.018t} $[/tex]

Therefore, the above function may be used to estimate the population for t   years after 2010.

For example:

What is the population after 10 years?

For the given case,

t = 10

[tex]$ P(10) = 47,597e^{0.018(10)} $[/tex]

[tex]$ P(10) = 47,597e^{0.18}$[/tex]

[tex]$ P(10) = 47,597(1.1972)$[/tex]

[tex]$ P(10) = 56,984[/tex]

Answer:

Option (1)

Step-by-step explanation:

Congruent complements theorem;

"If two angles are complementary to the same angle, then these angles are congruent to each other."

It's given that ∠4 and ∠5 are the complements and ∠1 and ∠5 are compliments.

Which shows ∠1 and ∠4 are complimentary to the same angle ∠5.

Therefore, ∠1 and ∠4 will be congruent.

Option (1) will be the answer.

Answer:

1

Step-by-step explanation: