Which system of inequalities is graphed below?
-5

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

Laniece had 60 magazines

Step-by-step explanation:

Given: In the  first week, Tamia sold 30% more than Laniece. In the second  week, Tamia sold 12 magazines, but Laniece did not sell any. Tamia sold 50% more than Laniece by the end of the second  week

To find: Number of magazines sold by Laniece

Solution:

Let number of magazines sold by Laniece in the first week be x.

Number of magazines sold by Tamia in the first week = \(x+\frac{30}{100} x=\frac{130x}{100} =\frac{13x}{10}\)

Number of magazines sold by Tamia in the second week = 12

Total number of magazines sold by Tamia at the end of the second week = \(\frac{13x}{10}+12\)

Total number of magazines sold by Laniece at the end of the second week = x

According to question,

\(\frac{13x}{10}+12=x+\frac{50x}{100}=x+\frac{x}{2}\\\frac{13x}{10}+12=\frac{3x}{2}\\\frac{3x}{2}-\frac{13x}{10} =12\\\frac{15x-13x}{10}=12\\\frac{2x}{10}=12\\\frac{x}{5}=12\\x=60\)

Answer:

Option C, 1225

Step-by-step explanation:

y=4.009x-77.531

selling 325 pizzas, so x=325, now putting the value of x in the equation,

y=4.009×325-77.531

or, y=1225.394

y = 1225.394, which is the profit, if we approximate it to the nearest value, it's $1225

The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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Answer:

No, the two sides are not congruent.

I flipped my whole laptop around to check loll

Answer:

VX=33

Step-by-step explanation:

VW=2z-1

WX=z+3

XV=3z

VW=a

WX=b

XV=c

a+b+c=2z-1+z+3+3z

Perimeter=6z+2

P=68

68=6z+2

66=6z

z=11

VX=3x11

VX=33

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

\(\frac{560}{3}\) or 187

Step-by-step explanation:

First convert \(4\frac{2}{3}\) to a improper fraction

It would be \(\frac{14}{3}\)

Now multiply

\(\frac{14}{3}*\frac{40}{1} = \frac{560}{3}\)

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Step-by-step explanation:

0.001374

standard form means writing a value in shortened form, because sometimes values are too big or small to be written, so we use standard form.

in standard for the decimal always comes after the first digit

so,

\(1.374 \times {10 }^{ - 3} \)

the decimal moves 3 digits to the right so it becomes ten raised to the power minus 3.

Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

Answer:

56

Step-by-step explanation:

Answer:

my 16 inch

Step-by-step explanation:

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

We have,

To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.

Probability of rolling a total of 9:

There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).

Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.

The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.

Probability of rolling a total of 10:

There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).

The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.

Probability of rolling a total of 11:

There are two combinations that can result in a total of 11: (5, 6) and (6, 5).

The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.

Thus,

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

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he started with 22$

Step-by-step explanation:

110÷5=22

Answer:

9/10 of a pizza each

Step-by-step explanation:

3 whole pizzas is 30/10 and 3/5 made into /10 is 6/10 and if add them you will get 36/10 and dived that in 4 you will get 9/10

Answer:

d = 0.4

Step-by-step explanation:

-10 (d + 1) = - 14

=> -10d - 10 = -14

=> -10d = -14 + 10

=> -10d = -4

=> 10d = 4

=> d = 4 / 10

=> d = 0.4

Hope it helps :)

Please mark my answer as the brainliest

The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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a. A scatter plot for the data is shown below.

b. An equation of the line of fit is y = -3.69x + 49.07.

c. The slope and y-intercept of the line of fit are -3.69 weeks and 49.07 birds respectively.

d. The number of birds at the feeder at week 11 are 9 birds.

In this exercise, we would plot the number of weeks on the x-axis of a scatter plot while number of birds would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

Part b.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic model of the line of best fit on the scatter plot;

y = -3.69x + 49.07

Part c.

The slope of the line of best fit is equal to -3.69 weeks and the y-intercept is equal to 49.07 birds.

Part d.

Based on the equation of the line of best fit above, the number of birds at the feeder at week 11 can be determined as follows;

y = -3.69x + 49.07

y = -3.69(11) + 49.07

y = 8.5 ≈ 9 birds.

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Problem

Write the slope-intercept form of the line described in the following:

Parallel to 4x + 5y=20

and passing through (12,4)

Solution>

For this case we need to have the same slope, and if we write the equation given we see:

5y = 20 -4x

y = 4 -4/5 x

then the slope m = -4/5

and we also know a point given x= 12, y= 4 and we can do the following:

4 = -4/5 (12) +b

4 = -48/5 + b

And if we solve for the intercept we got:

b= 4 +48/5= -28/5

And our equation would be given by:

y = -4/5 x -28/5

Answer:

42

Step-by-step explanation:

Given m and n are parallel:

x + 138 = 180 because these angles are supplementary

subtract 138 from both sides

x = 42

Answer:

x = 7.2

Step-by-step explanation:

x is the hypotenuse

applies cosine

\(cos(33^{o} )=\frac{6}{x}\)

\(x=\frac{6}{cos(33^{o} )} =7.154\)

Round to the nearest tenth:

x = 7.2

Hope this helps

On solving the provided question, we can say that the quadratic function \(f(x)=x^{2}+10x+24.\) , so f(-2) = 8

Quantities and their variations, equations and related structures, shapes and their placements, and locations where they can be found are all included in the study of mathematics.

The relationship between a group of inputs, each of which has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

the quadratic function \(f(x)=x^{2}+10x+24.\)

By substituting different values of x

For x = 0

if f(0) = 24

For x = 1

if f(1) = 35

For x = 2

if (2) = 48

For x = -2

so f(-2) = 8

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The first equation is 3 - x = 4 while the second equation is 12 = 9 - 3x.

By careful observation, we can see that both sides of the first equation has been multiplied by a constant factor 3 to form the second equation. Because this is an eqaution and both sides of the equation has been multiplied by thesame factor, the solution of the equation will remain the same because a balance is maintained.

Remember that to maintain a balance to an equation, whatever is done to one side of the equation must be done to the other side of the equation.

Thus,

3 + x = 4

After multiplying through by 3, we have

3( 3 + x ) = 3(4)

9 + 3x = 12

Since 3 is multiplying both sides of the equation, The solution to the equations remain equal

Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

The number that is equal to four and five sixths is A. four and eighty three hundredths with the three repeating

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

The number that is equal to 4 5/6 will be illustrated thus:

= 4 5/6

= 4 + 0.8333.

= 4.8333

In this vase, the 3 is repeating. Therefore, the correct option is A.

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Answer:

x=5

Step-by-step explanation:

x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.

Answer:

5

Step-by-step explanation:

Because this is a right triangle, you know that by the Pythagorean theorem:\(\sqrt{(x+7)^2+x^2}=x+8\)

Squaring both sides to get rid of the square root:

\((x+7)^2+x^2=(x+8)^2\)

Expanding all of the parentheses:

\(x^2+14x+49+x^2=x^2+16x+64\)

Combine like terms:

\(x^2-2x-15=0\)

Factor:

\((x-5)(x+3)=0\)

Since x cannot be negative, it is equal to 5. Hope this helps!

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer: See solution and explanations in the attached documents

Step-by-step explanation:

See explanations in the attached documents