I think I got everything but the c part. Can someone help me

$437.25 ÷ $0.75 = 583 bottles of lemonade

Hope this helps :)

Reducing the equation, we get:

3^(3-3a) = 3^(-2a)

So 3-3a = -2a, a = 3.

The value of the variable 'a' will be 3. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

[tex]7 + 42 \cdot 3^{2 - 3a} = 14 \cdot 3^{-2a} + 7[/tex]

Simplify the equation, then we have

[tex]42 \cdot 3^{2 - 3a} = 14 \cdot 3^{-2a}\\\\3^{2 - 3a} = \dfrac{1}{3} \cdot 3^{-2a}\\\\\left (3 \right )^{2 - 3a } } = (3)^{-1 - 2a}[/tex]

Compare the power of the number 3, then we have

- 1 - 2a = 2 - 3a

3a - 2a = 2 + 1

a = 3

The value of the variable 'a' will be 3. Then the correct option is C.

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Answer:

63 percent student scored below Jake.

Step-by-step explanation:

For finding the percentile

Step 1: Subtracting mean from Jake’s score

=520-500

=20

Step 2: Calculating z-score

The z-Score is found by dividing the difference obtained in step 1 by SD of the data

z-score=  20/60

z-score=0.333

Step 3: Converting the z-score to percentile

The z-score will be converted to percentile using the z-score to percentile conversion table, the value of percentile for 0.3333 is 63rd .  

So, 63 percent students scored below Jake.  

Answer :-      Just try area/2 or half the area of the triangle

Answer:

Step-by-step explanation:

The area of triangle abc would be half the area of the parallelogram.  The two triangles are of equal area.

Answer:

Your dew point would be at 10.

Step-by-step explanation:

30 ounces of the coffee John likes consists of

To this mixture we're adding [tex]x[/tex] ounces of water, so that the new mix has a total volume of [tex]30+x[/tex] ounces and matches the composition of the coffee Lily likes. This means it would consist of

Solve for [tex]x[/tex]:

[tex]0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x[/tex]

[tex]\implies0.39=0.027x[/tex]

[tex]\implies x\approx14.4[/tex]

###

Just to confirm: the new mixture consists of

giving a total volume of [tex]43.2+1.2=44.4[/tex] ounces of coffee, and [tex]\dfrac{43.2}{44.4}\approx0.973[/tex], as required.

Answer:

b. [tex]y=3.9^x[/tex]

Step-by-step explanation:

Remember that the standard exponential function is [tex]y=ab^x[/tex]

where

[tex]a[/tex] is the coefficient

[tex]b[/tex] is the base

If [tex]b>0[/tex], the function is growing

If [tex]0<b<1[/tex] the graph is decaying

We can infer from the graph that the function is growing, so we can discard [tex]y=0.45^x[/tex] and [tex]y=0.73^x[/tex].

Now, to evaluate our tow remaining equations, we are using the test values [tex]x=0[/tex] and [tex]x=1[/tex]:

For [tex]y=1.8^x[/tex]

For [tex]x=0[/tex]

[tex]y=1.8^0[/tex]

[tex]y=0[/tex]

For [tex]x=1[/tex]

[tex]y=1.8^1[/tex]

[tex]y=1.8[/tex]

The graph passes through the points (0,1) and (1, 1.8)

For [tex]y=3.9^x[/tex]

[tex]x=0[/tex]

[tex]y=3.9^0[/tex]

[tex]y=0[/tex]

[tex]x=1[/tex]

[tex]y=3.9^1[/tex]

[tex]y=3.9[/tex]

The graph passes through the points (0,1) and (1, 3.9)

We can see in the graph when [tex]x=1[/tex], [tex]y[/tex] is almost 4, so we can conclude that the correct equation is [tex]y=3.9^x[/tex]

Answer:

The domain is the interval [tex][-6,6][/tex]

The range is the interval [tex][-2,2][/tex]

Step-by-step explanation:

we know that

Observing the graph

The domain is the interval [tex][-6,6][/tex]

All real numbers greater than or equal to -6 and less than or equal to 6

The range is the interval [tex][-2,2][/tex]

All real numbers greater than or equal to -2 and less than or equal to 2

The graph's domain spans from -6 to 6, and the range extends from -2 to 2. In summary, the domain is [-6, 6], and the range is [-2, 2].

In the given graph, the domain represents all possible input values, and it spans from -6 to 6, inclusive. This is because the graph includes every real number greater than or equal to -6 and less than or equal to 6 along the horizontal axis.

The range, on the other hand, corresponds to the output values of the function and extends from -2 to 2, inclusive. This is derived from the observation that the graph encompasses all real numbers greater than or equal to -2 and less than or equal to 2 along the vertical axis.

The domain is [-6, 6], indicating all real numbers between -6 and 6, and the range is [-2, 2], signifying all real numbers between -2 and 2. The graph visually illustrates these intervals as the inclusive bounds for both domain and range.

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Answer:

A. 6m and 2m

E. 11.25m and 3.75m

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

so

Verify each case

case A) 6m and 2m

[tex]\frac{6}{4.5}=\frac{2}{1.5} \\ \\6(1.5)=2(4.5)\\ \\9=9[/tex]

therefore

The legs are proportional

case B) 8m and 5m

[tex]\frac{8}{4.5}=\frac{5}{1.5} \\ \\8(1.5)=5(4.5)\\ \\12\neq22.5[/tex]

therefore

The legs are not proportional

case C) 7m and 3.5m

[tex]\frac{7}{4.5}=\frac{3.5}{1.5} \\ \\7(1.5)=3.5(4.5)\\ \\10.5\neq15.75[/tex]

therefore

The legs are not proportional

case D) 10m and 2.5m

[tex]\frac{10}{4.5}=\frac{2.5}{1.5} \\ \\10(1.5)=2.5(4.5)\\ \\15\neq11.25[/tex]

therefore

The legs are not proportional

case E) 11.25m and 3.75m

[tex]\frac{11.25}{4.5}=\frac{3.75}{1.5} \\ \\11.25(1.5)=3.75(4.5)\\ \\16.875=16.875[/tex]

therefore

The legs are proportional

Answer:

Step-by-step explanation:

Consecutive integer:

... -2, -1, 0, 1, 2, 3, ...

Difference between two consecutive integers is equal to 1.

Therefore two consecutive integers is x and x + 1.

Answer:

THERE IS NO PICTURE OR VISUAL REPRESENTATION

Step-by-step explanation:

Answer:

[tex]\log_2(ab^3)^{\frac{1}{2}}=\frac{1}{2}[\log_2(a)+3\log_2(b)][/tex].

Step-by-step explanation:

The given logarithmic expression is [tex]\log_2\sqrt{ab^3}[/tex].

We rewrite the radical as an exponent to obtain;

[tex]\log_2(ab^3)^{\frac{1}{2}}[/tex].

Recall that; [tex]\log_a(M^n)=n\log_a(M)[/tex]

We apply this rule to obtain;

[tex]=\frac{1}{2}\log_2(ab^3)[/tex].

We now use the rule: [tex]\log_a(MN)=\log_a(M)+\log_a(N)[/tex]

This implies that;

[tex]=\frac{1}{2}[\log_2(a)+\log_2(b^3)][/tex].

We again apply: [tex]\log_a(M^n)=n\log_a(M)[/tex]

[tex]=\frac{1}{2}[\log_2(a)+3\log_2(b)][/tex].

Answer:

[tex]\$10,833[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=1\ years\\ P=\$10,000\\ r=0.08[/tex]  

substitute in the formula above  

[tex]A=\$10,000(e)^{0.08*1}=\$10,833[/tex]  

Compound interest computed continuously after one year on a principal sum of $10,000 with an 8% interest rate will yield $10,833, rounded to the nearest dollar.

Your question relates to the mathematics topic of compound interest. When interest is compounded continuously, we use the formula A = P * e^(rt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.

In your case, you are looking to find how much $10,000, invested at a nominal 8% per year compounded continuously, would amount to at the end of one year. Substituting the given values into the formula, we have:
A = $10,000 * e^(0.08*1).

The value of 'e' is approximately 2.71828. Therefore, we calculate:
A = $10,000 * 2.71828^0.08 = $10,833.

So, the amount in the account at the end of one year, rounded to the nearest dollar, would be $10,833.

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Answer:

It's D.

Step-by-step explanation:

The shorter period loan has the same total interest for the same loan amount, so it has the higher effective interest rate: 80/12 is higher than 89/14.

A payday credit for $1900 that is expected in 12 days with an expense of $80, since it has the less limited time frame. Then the correct option is D.

When buying or recovering proposals in a common asset, a financial backer may be paid a business fee or commission. Deals with fees can be set up in a variety of ways.

Banks and insurance providers may offer their clients a grace period, which allows them to postpone payment for a predetermined amount of time after the time limit (after the payment deadline).

A payday credit for $1900 that is expected in 14 days with a charge of $80 or a payday credit for $1900 that is expected in 12 days with a charge of $800.

A payday credit for $1900 that is expected in 12 days with an expense of $80, since it has the less limited time frame. Then the correct option is D.

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Answer:

Probability of winning first situation:  0.0793

Probability of winning second situation:  0.0146

You should go with the first option

Step-by-step explanation:

See attached photo for answers.   For this situation you need to identify p-hat, p, q and n.

P-hat, p, and q all stay the same for both situations, only n changes.

p-hat is the proportion of green balls we want, which is 0.7

p = 98/159 = 0.62

q = 0.38 because q = 1 - p, which in this case is q = 1 - 0.62 = 0.38

n = 73 for the first situation, and n = 175 for the second situation

Using the normal probability distribution and the central limit theorem, it is found that:

a)

With 73 draws, there is a 0.0808 = 8.08% probability of getting more than 70% green balls.

With 175 draws, 0.015 = 1.5% probability of getting more than 70% green balls.

b)

Due to the higher probability of getting more than 70% green balls, 73 draws should be chosen.

Normal Probability Distribution

In a normal distribution 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]

Central Limit Theorem

Item a:

Out of 73 draws:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6203(0.3797)}{73}} = 0.0568[/tex]

The probability of more than 70% green balls is 1 subtracted by the p-value of Z when X = 0.7, thus:

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.7 - 0.6203}{0.0568}[/tex]

[tex]Z = 1.4[/tex]

[tex]Z = 1.4[/tex] has a p-value of 0.9192.

1 - 0.9192 = 0.0808

With 73 draws, there is a 0.0808 = 8.08% probability of getting more than 70% green balls.

Out of 175 draws:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6203(0.3797)}{175}} = 0.0367[/tex]

Then:

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

[tex]Z = \frac{0.7 - 0.6203}{0.0367}[/tex]

[tex]Z = 2.17[/tex]

[tex]Z = 2.17[/tex] has a p-value of 0.985.

1 - 0.985 = 0.015.

With 175 draws, 0.015 = 1.5% probability of getting more than 70% green balls.

Item b:

Due to the higher probability of getting more than 70% green balls, 73 draws should be chosen.

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Answer:

[tex]\$10,608[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=16\ years\\ P=\$6,800\\r=0.035[/tex]

substitute in the formula above

[tex]A=\$6,800(1+0.035*16)=\$10,608[/tex]

Answer: option c.

Step-by-step explanation:

 To solve this problem you must keep on mind the properties of logarithms:

[tex]ln(b)-ln(a)=ln(\frac{b}{a})\\\\ln(b)+ln(a)=ln(ba)\\\\a*ln(b)=ln(b)^a[/tex]

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

[tex]ln2x+2lnx-ln3y=ln2x+lnx^2-ln3y\\\\=ln(2x)(x^2)-ln3y\\\\=ln(\frac{2x^3}{3y})[/tex]

Therefore, the answer is the option c.

Answer:

C

Step-by-step explanation:

We can use 3 properties here to write this as single logarithm:

1. Log (a^b) = b Log a

2. Log x + Log y = Log (x*y)

3. Log x - Log y = Log (x/y)

We can use property #1 first to write:

[tex]ln2x+2lnx-ln3y\\=ln2x+lnx^2-ln3y[/tex]

Now we can use property #2 and property #3 to write this as single logarithm:

[tex]ln2x+lnx^2-ln3y\\=ln(\frac{(2x)(x^2)}{3y})\\=ln(\frac{2x^3}{3y})[/tex]

Answer choice C is right.

Answer: [tex]x=\frac{37}{9}[/tex]

Step-by-step explanation:

By the negative exponent rule, you have that:

[tex](\frac{1}{a})^n=a^{-n}[/tex]

By the exponents properties, you know that:

[tex](m^n)^l=m^{(nl)}[/tex]

[tex](m^n)(m^l)=m^{(n+l)}[/tex]

Rewrite 4, 8 and 32 as following:

4=2²

8=2³

32=2⁵

Rewrite the expression:

[tex](2^2)^{(x-7)}*(2^3)^{(2x-3)}=\frac{32}{2^{(x-9)}}[/tex]

Keeping on mind the exponents properties, you have:

[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=32(2^{-(x-9)}[/tex]

[tex](2)^{2(x-7)}*(2)^{3(2x-3)}=(2^5)(2^{-(x-9)})\\\\(2)^{(2x-14)}*(2)^{(6x-9)}=(2^5)(2^{(-x+9)})\\\\2^{((2x-14)+(6x-9))}=2^{(5+(-x+9))}[/tex]

As the bases are equal, then:

[tex](2x-14)+(6x-9)=5+(-x+9)\\\\2x-14+6x-9=5-x+9\\\\8x-23=14-x\\9x=37[/tex]

[tex]x=\frac{37}{9}[/tex]

Answer:

[tex]x=4\frac{1}{9}[/tex]

Step-by-step explanation:

We are given the following linear equation and we are to solve it:

[tex] 4 ^ { x - 7 } \times 8 ^ { 2x - 3 } = \frac { 32 } { x ^ { x - 8 } } [/tex]

Changing the constants to the same base to make it easier to solve:

[tex] 2 ^ { 2 ( x - 7 ) } \times 2^ { 3 ( 2x - 3 ) } = \frac { 2 ^ 5 } { 2 ^ { x - 9 } } [/tex]

[tex]2^{2x-14} \times 2^{6x-9} = 2^{5}(2^{-x+9})[/tex]

[tex] 2 ^ { 2x - 14 + 6x - 9 } = 2 ^ { 5 - x + 9 } [/tex]

[tex] 2 x + 6x - 14 - 9 = 5 - x + 9 [/tex]

[tex]8x+x=14+9+5+9[/tex]

[tex]9x=37[/tex]

[tex]x=4\frac{1}{9}[/tex]

Answer:

D

Step-by-step explanation:

This function graphed as the picture attached below show is a function. It passes the vertical test. However, it does not pass the horizontal line. This means the function is not one-to-one but many-to -one.

PARALLEL slopes always have the same slope no matter what because they are parallel

Answer:

[tex]y=47x-654[/tex]

Step-by-step explanation:

To find the line parallel to the given linear equation, we have to use the same slope, because the condition of parallelism is that they must have the same slope.

So, the slope of the given line is [tex]m=47[/tex], because it's expressed in slope-intercept form, where the coefficient of the variable x is the slope.

Now, we know that they new parallel lines must have a slope equal to 47, and must pass through (14,4). Using this data, we apply the point-slope formula to find the equation of the new line:

[tex]y-y_{1}=m(x-x_{1})\\y-4=47(x-14)\\y=47x-658+4\\y=47x-654[/tex]

The image attached shows the parallelism.

Therefore, the answer is [tex]y=47x-654[/tex]

El costo total por concepto de la reparación del automóvil es de 170,56 soles.

¿Cómo calcular el costo total de la reparación de un automóvil?

En este problema se debe determinar el costo total por concepto de la reparación de un automóvil. Dimensionalmente hablando, se tiene que el costo total se determina mediante la siguiente fórmula:

C = c · Δt

Donde:

A continuación, el costo total se calcula según la información suministrada por el enunciado de la pregunta:

C = (32,8 soles / hora) · (1,5 horas + 0,2 horas + 0,75 horas + 1,45 horas + 1,3 horas)

C = 170,56 soles

The base of the middle triangle is 3 and the base of the larger one is 6, so the larger triangle is twice the size of the middle one.

Multiply the height of the middle one by 2 to get the height of the larger one, which is labeled n.

n = 5 x 2 = 10

ANSWER

[tex]S_{30}= - 3390[/tex]

EXPLANATION

The given sequence is

3,-5,-13,.....-229.

The first term of this sequence is

a_1=3

There is a common difference of

[tex]d = - 5 - 3 = - 8[/tex]

The last term of this sequence is -229.

The nth term of this sequence is given by:

[tex]a_n=a_1+d(n-1)[/tex]

We use the last term to determine the number of terms in the sequence.

[tex] - 229 = 3 + - 8(n - 1)[/tex]

[tex]- 229 - 3= - 8(n - 1)[/tex]

[tex]- 232= - 8(n - 1)[/tex]

Divide through by -8;

[tex]29= (n - 1)[/tex]

[tex]n = 30[/tex]

Hence there are thirty terms in the sequence.

The sum of the first n terms is given by:

[tex]S_n= \frac{n}{2} ( a_{1} + l)[/tex]

The sum of the first 30 terms is given by:

[tex]S_{30}= \frac{30}{2} ( 3 + - 229)[/tex]

[tex]S_{30}=15( - 226)[/tex]

[tex]S_{30}= - 3390[/tex]

Answer:

22, no: 24, yes

Step-by-step explanation:

22 wouldn't be a triangle because when you square both sides

8^2+6^2= 81 (but 9^2 is 81) the 2 values surpasses 81

24 would be a triangle because

8^2+6^2=10^2

64+36=100

It would have to be C. point.

Since it says AB that marks two points and a line in between them. If only talking about A, it would be a point.

Option: C is the correct answer.

                c.)  Point

In the symbol AB:

AB represents a line segment which connects point A to point B.

If there would be an arrow over this with right arrow then it would represent a ray which originates at point A an it extends to infinity from the other direction.

Hence the letter A will represent a : Point.

Answer:

10

Step-by-step explanation:

We are taking 5m and dividing by 1/2 m

5 ÷ 1/2

Copy dot flip

5 * 2/1

10

We can get 10 pieces from the rope

10 pieces of rope of length 0.5 meter can be cut from the rope of total length 5 meters.

Given :

Total length of Rope = 5 m.

Division is about breaking something into many pieces. The number you are dividing is called the dividend. The number you are "dividing by" is the divisor. The answers to your division problems are called quotients.

Number of pieces of rope of length 0.5 meter will be calculated as follows:

[tex]=\dfrac{5}{0.5}[/tex]

[tex]=10[/tex]

10 pieces of rope of length 0.5 meter can he cut from it.

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Answer:

15.25

Step-by-step explanation:

Answer:

It is the sum of the initial amount and the additional amount after d days.

Step-by-step explanation:

It is the sum of the initial amount and the additional amount after d days.i have ttm

Answer:

farther

Step-by-step explanation:

The negative sign means that it is 10 feet down while -8 is only 8 feet down

An elevation of -10 feet is farther from the surface of the ocean than - 8 feet.

Time can not be negative as we can not go to past.Time is unidirectional.

According to the given question we have to determine Is an elevation of -10 feet closer or farther from the surface of the ocean than an elevation of -8 feet.

We know that -10 is less than -8 as it is present in the left of -8 in the number line that is one case.

But here we are measuring elevation which is length and we know length can not be negative so going by the idea of length an elevation of -10 feet is farther from the surface of the ocean we are diving 10 feet below here so more distance.

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Answer:

See below  

Step-by-step explanation:

19)

  13² =  4² + AM²

 169 = 16  + AM ²

AM ² = 153

AM =√153 = √(9× 17) = 3√17

sinA = MT /AT  = 4/13

cosA = AM/AT  = (3√17)/13

tanA = MT/AM  = 4/(3√17)   = (4√17)/51

sinT = AM/AT  = (3√17)/13

cosT = MT/AT  = 4/13

tanT = AM/MT = (3√17)/4

20)

10² =  5² + AJ²

100 = 25  + AJ²

AJ² = 75

AJ = √75 = √(25×3) = 5√3

sinA = JT/AT  = 5/10       = ½

cosA = AJ/AT = (5√3)/10 = (√3)/2

tanA = AJ /AJ = 5/(5√3)  = (√3)/3

sinT = AJ/AT = (5√3)/10 = (√3)/2

cosT = AJ/AT = 5/10       = ½

tanT = AJ/JT  = (5√3)/5   = √3

Number of pallets moved in 4.5 hours = 108

converting 4.5 hours in minutes we get,

4*60 + 0.5*60 = 240+30 = 270 minutes

So, 108 pallets were moved in = 270 minutes

1 pallet was moved in = [tex]\frac{270}{108}=2.5[/tex] minutes

As the tie will get over in 2 hours or 2*60 = 120 minutes, the number of pallets that can be moved will be = [tex]\frac{120}{2.5}= 48[/tex] pallets.

Hence, 48 pallets can be moved before quitting time.

Answer:

The answer is 2.5 minutes; 48 pallets

Step-by-step explanation:

Number of pallets worker moved in a warehouse = 108

Number of hours it takes to do so  = 4.5

Rate at which they require to move one pallet is given by

Number of pallets worker moved in a warehouse = 108

Number of hours it takes to do so  = 4.5

Rate at which they require to move one pallet is given by

4.5/108 x 60 minutes = 2.5 minutes

Now, if the worker will be off the clock in 2 hours ,

So, number of pallets he can move before quitting time is given by

In 4.5 hours, number of pallets they moved = 108

In 1 hour, number of pallets they moved = 108/4.5 = 24

In 2 hours, number of pallets they moved = 24 x 2 = 48