Solve the linear equation

[tex]4^{x+7} = 8^{2x-3}[/tex]

Answer:

∠P = 65°

Step-by-step explanation:

The measure of arcs LP and PY are given as 80° and 150°, so their sum is 230°. Arc LY completes the circle of 360°, so is 130°. Inscribed angle P is half that measure, so ...

∠P = 130°/2 = 65°.

Answer:

Each person will have the amount of 4/20 ft piece of gum equivalent to 1/5 ft

Step-by-step explanation:

we know that

For sharing the 1/4 piece of gum equally with 5 people, first divide each piece of 1/4 by 5

so

[tex]\frac{(1/4)}{5}=\frac{1}{20}\ ft[/tex]

At this moment we have 20 pieces and each one is 1/20 ft

The number of pieces that corresponds to each person is 20 divided by 5.

so

[tex]20/5=4[/tex]      

[tex]4*\frac{1}{20}=\frac{4}{20}\ ft[/tex]

each person will have the amount of 4/20 ft piece of gum

simplify

[tex]\frac{4}{20}=\frac{1}{5}\ ft[/tex]

Answer:

each person gets 4/20 pieces

Step-by-step explanation:

(1/4)/5

Answer:

A

Step-by-step explanation:

The statement "If x = 3, then x^2 = 3x" was formed by multiplying x = 3 by x on both sides. Thus x = 3 becomes x*x=3*x. This simplifies to x^2 = 3x. This property is the multiplication property of equality.

The multiplication property of equality is used to arrive at the conclusion from 'x = 3' to 'x^2 = 3x'. This property allows you to multiply both sides of an equation by the same non-zero number, maintaining equality.

The property of equality used to reach the conclusion from 'x = 3' to 'x^2 = 3x' is the multiplication property of equality. This property states that if you multiply both sides of an equation by the same non-zero number, the equation will still be equal. Here, 'x' is being replaced by '3' in 'x^2', leading to '3x'. Therefore, the multiplication property of equality is applied.

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The first one is 4/9 and the second one is 5/9

Final answer:

The probability that the first horse selected is tan and the second horse selected is brown, out of a total of 5 brown horses and 4 tan horses, is 5/18.

Explanation:

The question asks for the probability that the first horse selected is tan, and the second horse selected is brown when there are 5 brown horses and 4 tan horses in a barn. To find this probability, we will multiply the probability of each event happening in sequence.

First, the probability of selecting a tan horse out of the total 9 horses (5 brown + 4 tan) is 4/9. Once a tan horse is selected, there are now 8 horses left, 5 of which are brown. Therefore, the probability of then selecting a brown horse is 5/8.

To find the total probability of both events occurring in sequence (first selecting a tan horse, then a brown horse), we multiply the two probabilities together: 4/9 * 5/8 = 20/72, which simplifies to 5/18.

Final answer:

Toshi has 1 1/4 hours left before he can leave work, which is found by subtracting the time he has already worked (1 3/4 hours) from his total shift (3 hours).

Explanation:

The student asked how many more hours Toshi has to work before he can leave the car wash, given that he has to work a total of 3 hours and has already worked 1 3/4 hours. To find this out, we subtract the time already worked from the total work time required:

Convert 1 3/4 hours to an improper fraction: 1 3/4 = 7/4 hours.

Convert 3 hours to 4/4 hours increments to have a common denominator: 3 hours = 12/4 hours.

Subtract the time worked from the total time: 12/4 - 7/4 = 5/4 hours.

Convert the answer back to mixed numbers: 5/4 hours = 1 1/4 hours.

Therefore, Toshi has 1 1/4 hours left before he can leave work.

Answer:

A

Step-by-step explanation:

The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.

This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.

An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.

Answer:

A.

Step-by-step explanation:

I just got 100% on the quiz.

Answer:

x=2

Step-by-step explanation:

10=16(x-2)^2+10

Subtract 10 from each side

10-10=16(x-2)^2+10-10

0 =16(x-2)^2

Divide by 16

0/16 = 16/16 (x-2)^2

0 = (x-2)^2

Take the square root of each side

sqrt(0) = sqrt(  (x-2)^2)

0 = x-2

Add 2 to each side

0+2 = x-2+2

2 =x

[tex]Cancel \ 10 \ on \ both \ sides.\\\\0 = 16(x - 2)^2\\\\\\Divide \ both \ sides \ by \ 16.\\0 = (x - 2)\\\\\\Now take the square root of both sides.\\\\0 = x - 2\\\\\\Add 2 to both sides.\\\\2 = x\\\\Switch sides.\\\\\fbox{x = 2}[/tex]

Answer:

The probability that the sample mean would be greater than 77.21 WPM = 0.9945

Step-by-step explanation:

Mean number of Words per Minute  = u  = 81

Standard Deviation = s = 17

sample size = n = 130

Target value = x = 77.21

we can find the probability by converting x to z-score.

The formula for z-score = [tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]

using given values, z-score =  [tex]\frac{77.21-81}{\frac{17}{\sqrt{130} } }[/tex]

=> -2.54

using the z table, we can find the find the probability of -2.54, that is 0.9945.

Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945  

The probability that the sample mean would be greater than 77.21 WPM is approximately [tex]\(0.9945\)[/tex] (rounded to four decimal places).

To find the probability that the sample mean is greater than 77.21 WPM, we need to use the Central Limit Theorem.

Here's the step-by-step process:

1. Identify the given information:

Population mean [tex](\(\mu\))[/tex]: 81 WPM

Population standard deviation [tex](\(\sigma\))[/tex]: 17 WPM

Sample size [tex](\(n\))[/tex]: 130

Sample mean [tex](\(\bar{x}\))[/tex]: 77.21 WPM

2. Calculate the standard error of the mean (SEM):

[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{130}} \approx \frac{17}{11.4018} \approx 1.4910 \][/tex]

3. Find the Z-score for the sample mean:

[tex]\[ Z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{77.21 - 81}{1.4910} \approx \frac{-3.79}{1.4910} \approx -2.543 \][/tex]

4. Use the Z-score to find the probability:

We look up the Z-score of -2.543 in the standard normal distribution table.

[tex]\[ P(Z < -2.543) \approx 0.0055 \][/tex]

This is the probability that the sample mean is less than 77.21 WPM. Since we need the probability that the sample mean is greater than 77.21 WPM, we subtract this value from 1.

[tex]\[ P(\bar{x} > 77.21) = 1 - P(Z < -2.543) = 1 - 0.0055 = 0.9945 \][/tex]

i think the answer is B

The value of x2 is 24.

Two variables are inversely varying if one variable value increases then other variable value decreases. We can represent this relation with an equation

y ∝ 1/x

⇒ y=k/x

where k is a constant.

According to asked problem y is varying inversely with x.

given, x1=6

y1=8

putting these values in the above equation,

8=k/6

⇒k=48

Now we have the value of k.

So the inversely varying equation will become,

y=48/x

By putting the value y2=2

2=48/x

⇒x=48/2

⇒x=24

The value of x2 is 24.

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Answer:

On the surface of the sea

Step-by-step explanation:

Six feet below sea level is marked as -6

Go up 6 feet

-6+6 =0 feet below sea level

That would mean we are at 0, which would be sea level

We would be on the surface of the sea

The price increased so it would be a positive net change.

Subtract the new price from the original price:

45.83 - 30.46 = 15.37

The net change was C. $15.37

Answer:

C) 15,37

Step-by-step explanation:

You can to obtain the net change in the stock price with a substract:

Vt = [Pf - Pi]

Vt = [$45.83 - 30.46]

Vt = 15.37

Its a positive variation

Best regards

Answer:

81 : 8

Step-by-step explanation:

Cube 1 has side lengths of 3, so it's volume is 3³ = 81

Cube 2 has side lengths of 2, so it's volume is 2³ = 8

So the ration of volume of the larger cube to the smaller cube is 81 : 8

Answer:

D 12½%

Step-by-step explanation:

∆=1.5/2-2/3

=4.5/6-4/6

=0.5/6

∆=0.083 $/lb

X=∆/(original price)•100

=0.083/(2/3)•100

=0.1245•100

X=12.45%

The first answer is correct

Answer:

3 + 9 + 27 + ...

Step-by-step explanation:

3 + 9 + 15 + ... is not a geometric series because it has no common ratio.

[tex]\frac{15}{9}\ne \frac{9}{3}[/tex]

3 + 9 + 27 + ... is a geometric series because there is a common ratio;

[tex]r=\frac{27}{9}=\frac{9}{3}=3[/tex]

3, 9, 27, ... is a geometric sequence and not a series. The sum of all the  terms in a geometric sequence forms a geometric series.

3, 9, 15, ... is a not a geometric series.

Answer:

g(x) = 2sin(x) + 3

Step-by-step explanation:

f(x) = sin(x)

transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.

so

g(x) = 2sin(x) + 3

Answer:

[tex]\boxed{0.2}[/tex]

Step-by-step explanation:

Put -2 where x is in the function and do the arithmetic. Any number of calculators will compute this for you.

  x ≈ 0.23781036584 ≈ 0.2

_____

Comment on the above result

The number above came from the Google calculator (2nd attachment). Surprisingly, it is rounded incorrectly in the last displayed digit. To 20 significant digits, the value is ...

  0.23781036584658190876

It appears the Google calculator didn't carry enough digits to get the answer correct in the last displayed decimal place.

Answer:

your answer would be 0.2

Step-by-step explanation:

➷ cos41 = x/55

x = cos41 x 55

x = 41.50902

The correct option would be 41.51

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

41.51

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]

Multiply both sides by 55

55 × cos41° = x

⇒ x = 41.51 ( to the nearest hundredth )

Answer: 6.85

Step-by-step explanation: 4 divided by 5 equals .8, so you need to write any number that is greater than 6.8, but less than 7. Other options would be 6.86, 6.9 or 6.95.

Answer:

A) 0.947; B) 0.0392; C) 0.7257; D) 6th

Step-by-step explanation:

For part A,

We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.

[tex]z=\frac{X-\mu}{\sigma}\\\\z=\frac{1000-1252}{129}\text{ and } z=\frac{1500-1252}{129}\\\\z=\frac{-252}{129}\text{ and } z=\frac{248}{129}\\\\z=-1.95\text{ and }z=1.92[/tex]

Using a z-table, we see that the area to the right of z = -1.95 is 0.0256.  The area to the right of z = 1.92 is 0.9726.  This means the area between them is

0.9726 - 0.0256 = 0.947.

For part B,

To find the probability that fewer than 1025 chips are in the bag, we find the z-score:

[tex]z=\frac{X-\mu}{\sigma}=\frac{1025-1252}{129}=\frac{-227}{129}\\\\=-1.76[/tex]

Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.

For part C,

Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this.  To find the proportion greater than this, we subtract from 1:

[tex]z=\frac{X-\mu}{\sigma}=\frac{1175-1252}{129}=\frac{-77}{129}=-0.60[/tex]

In the z-table, we see that the area under the curve less than this is 0.2743.  This means that the area greater than this is 1-0.2743 = 0.7257.

For part D,

We again find the area under the curve less than this.  This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.

[tex]z=\frac{1050-1252}{129}=\frac{-202}{129}=-1.57[/tex]

In the z-table, we see the area to the right of this is 0.0582.  This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.

These questions are solved by converting the specified number of chips to a Z-score and using it to find the corresponding probability in a standard normal distribution table. The various calculated probabilities provide the answers to the different parts of the question.

In order to answer these questions, we need to convert the number of chips to a Z-score, which is a measure of how many standard deviations an element is from the mean, and then find the corresponding probability from a standard normal distribution table.

(a) To calculate the probability of a bag containing between 1000 - 1500 chips, you subtract the mean from each and divide by the standard deviation to get Z-scores. Then one can find the corresponding probabilities in a Z-table and subtracting the smaller probability from the larger. This will give you the probability of number of chips falling between those two amounts.

(b) Similarly, to compute the probability of a bag containing fewer than 1025 chips, find the Z-score for 1025 and look it up in the Z-table. The probability that corresponds to that Z-score is the likelihood of having fewer than 1025 chips.

(c) For the the proportion of bags that contains more than 1175 chips, first compute the Z-score for 1175. The corresponding probability in the Z-table gives the proportion for those with numbers equal or less than 1175. To get the proportion for bags with more than 1175 chips, you need to subtract that value from 1 (since the total probability is always 1).

(d) Finally, for the percentile rank, it's again the same process. You find the Z-score for 1050, look up its corresponding probability and multiply it by 100 to convert it into percentile rank.

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Answer:

b. [tex]\frac{40}{3}[/tex]

Step-by-step explanation:

The given geometric series is;

[tex]20-10+5-\frac{5}{2}+...[/tex]

The first term of this series is

[tex]a_1=20[/tex]

The common ratio is

[tex]r=\frac{-10}{20}=-\frac{1}{2}[/tex]

The sum to infinity of this series is

[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]

Substitute the given values to obtain;

[tex]S_{\infty}=\frac{20}{1--\frac{1}{2}}[/tex]

This implies that;

[tex]S_{\infty}=\frac{20}{\frac{3}{2}}[/tex]

[tex]S_{\infty}=\frac{40}{3}[/tex]

Answer:

B edge

Step-by-step explanation:

Answer:

The measures would be 30, 60, and 90 degrees.

Step-by-step explanation:

60 is 30 more than 30, and 90 is the sum of 30 and 60. Also the sum of the measures of triangle is always 180, and 30 + 60 + 90 = 180.

If One angle of a triangle is 30 degrees more than the smallest angle. The largest angle is the sum of the other angles. Then 30, 60 and 90 are

measures of all three angles.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

One angle of a triangle is 30 degrees more than the smallest angle.

x=30+y

The largest angle is the sum of the other angles

z=x+y

By angle sum property the sum of three angles is 180 degrees

x+y+z=180

30+y+y+z=180

30+y+y+30+y+y=180

60+4y=180

Subtract 60 from both sides

4y=120

Divide 4 on both sides

y=30

Now substitute y value in x

x=60

z=90

Hence the measure of all three angles are 30,60 and 90 degrees.

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Answer:

x = 12

Solve for x:

Using Pythagorean Theorem

a^2 + b^2 = c^2

a = 9

c = 15

b = x

9^2 + x^2 = 15^2

81 + x^2 = 225

x^2 = 144 | sqrt

x = 12

Answer:

Choice A

Step-by-step explanation:

The scenario presented relates to exponential growth models; the population of bacteria is growing at an exponential rate given by the equation;

[tex]B=1000e^{kt}[/tex]

In this case B represents the population of the bacteria, t the time in minutes, k the growth constant and 1000 represents the initial population at time 0.

After 15 minutes, the population of bacteria grows to 8520. This implies that B is 8520 while t is 15. We substitute this values into the given equation and solve for k, the growth constant;

[tex]8520=1000e^{15k}[/tex]

Divide both sides by 1000;

[tex]8.52=e^{15k}[/tex]

The next step is to introduce natural logs on both sides of the equation;

[tex]ln8.52=ln(e^{15k})\\ln8.52=15k\\k=\frac{ln8.52}{15}=0.143[/tex]

Answer:

150 ft

Step-by-step explanation:

triangle area formula= (b*h)/2

25 time 12 is 300. divide 300 by 2 and get 150.

Answer:

A = 150 ft^2

Step-by-step explanation:

The area of a triangle is found by using

A = 1/2 b*h where b is the base and h is the height

A = 1/2 (12)*25

A = 6*25

A = 150 ft^2

Events A and B are independent events because the product of their probabilities (P(A)P(B)) equals the probability of the intersection of both events (P(A∩B)).

To determine if events A and B are independent events, we need to check if the product of their probabilities equals the probability of their intersection. According to the formula for independent events:

P(A AND B) = P(A)P(B)

Given:

P(A) = 1/4

P(B) = 2/5

P(A∩B) = 1/10

Let's calculate the product of P(A) and P(B):

P(A)P(B) = (1/4) × (2/5) = 1/10

Since P(A∩B) also equals 1/10, which is the same as the product of P(A) and P(B), it is therefore true that:

P(A AND B) = P(A)P(B)

This implies that events A and B are indeed independent because their combined probability equals the product of their probabilities.

Answer:

Car 1 : 40 gallons

Car 2 : 15 gallons

Step-by-step explanation:

F = Car 1 Fuel Efficiency

S = Car 2 Fuel Efficiency

F + S = 55

40F + 35S = 2125

Using the first equation...

S = 55 - F

Then substitute into the second equation.

40F + 35(55 - F) = 2125

Simplify

40F + 1925 - 35F = 2125

5F + 1925 = 2125

5F = 200

F = 40

Then plug it back into S = 55 - F

S = 15

Plug it back into F + S = 55 to check.

Hope this helps.

Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

Let car 1 fuel efficiency = x

Let car 2 fuel efficiency = y.

Based on the information given,

x+ y = 55 ...... i

40x + 35y = 2125 ...... ii

Therefore, y = 55 - x ..... iii

Put equation iii into ii

40x + 35(55 - x) = 2125

40x + 1925 - 35x = 2125

Collect like terms

40x - 35x = 2125 - 1925

5x = 200

x = 200/5

x = 40

Since x + y = 55.

y = 55 - 40 = 15

Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.

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Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

i.e.  0.2<0.42<0.7<0.87

Step-by-step explanation:

Since we have given that

1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles

Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]

2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples

Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]

3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens

Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]

4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls

Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]

We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:

So, 0.2<0.42<0.7<0.87

Hence, it becomes

the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens  < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.

Answer:

a ∆ABC and ∆EDC are similar

b. AB = 83.3 ft

Step-by-step explanation:

a.  We need to determine if  ∆ABC and ∆EDC are similar.

We know B = D = 90

We know C = C because they are vertical angles and vertical angles are equal

Therefore A = E because they are triangles, and if 2 angles in a triangle are equal the third angles must be equal.

∆ABC and ∆EDC are similar

b.  We know that because they are similar triangles

AB      BC

------ = ---------

ED        DC

Substituting in

AB       62

------ = ---------

125        93

Using cross products

93 AB = 62*125

93 AB = 7750

Divide by 93

AB = 7750/93

AB = 83.3333333333(repeating)

Rounding to the nearest tenth ft

AB = 83.3 ft