pls need help to this question ASAP​

The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Answer:

8

Step-by-step explanation:

-12 x -2 = 24. 24-16=8

The general formula for calculating the doubling time is:

doubling time = ln(2) / growth rate

Here, the growth rate can be found from the given equation as:

q = 100e^(0.5x)

Taking the natural logarithm of both sides:

ln(q/100) = 0.5x

Solving for x:

x = 2 ln(q/100)

The growth rate is therefore 0.5, and the doubling time can be calculated as:

doubling time = ln(2) / 0.5 = 1.3863

Rounding to 4 decimal places, the doubling time is approximately 1.3863 units of x.

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Step-by-step explanation:

find the slope

-1 - 8/ -2 - -4 = -9/2

y - -1 = -9/2(x - -2)

y +1 = -9/2(x+2)

y = -9/2x -10

Answer:

y=-9/2x-10

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-8)/(-2-(-4))

m=-9/(-2+4)

m=-9/2

y-y1=m(x-x1)

y-8=-9/2(x-(-4))

y-8=-9/2(x+4)

y=-9/2x-36/2+8

y=-9/2x-18+8

y=-9/2x-10

Given :

The square of a number, x, is 16 less than eight times the number.

To Find :

The value of x .

Solution :

The mathematical equation with all given data is :

\(x^2=8x-16\\\\x^2-8x+16=0\\\\x^2-4x-4x+16=0\\\\x(x-4)-4(x-4)=0\\\\(x-4)^2=0\\\\x=4\)

Therefore , the value of x is 4 .

Hence , this is the required solution .

The number is 4.

Given that,

Based on the above information, the calculation is as follows:

\(x^2 = 8x - 16\\\\x^2 - 8x + 16 = 0\\\\x^2 -4x - 4x + 16 = 0\\\\x (x - 4) - 4(x - 4) = 0\\\\(x - 4)^2 = 0\\\\x = 4\)

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Greetings,

I hope you and your family are staying safe and healthy!

Answer: x = -1 and y = 3

Step-by-step explanation:

\(10x - 5y = -25 \\10x + 8y = 14\)

Let's start by solving \(10x - 5y = -25\) for \(x\)

\(10x - 5y=-25\)

Add 5y to both sides

\(10x - 5y + 5y = -25+5y \\10x = 5y - 25\)

Now we need to divide both sides by 10

\(\frac{10x}{10} = \frac{5y-25}{10}\)

\(x = \frac{1}{2} y + \frac{-5}{2}\)

That's not the answer for x. We are not done yet :)

Now we need to substitute \(\frac{1}{2} y + \frac{-5}{2}\) for \(x\)

\(10x + 8y = 14\\10(\frac{1}{2} y + \frac{-5}{2} + 8y = 14\)

Now we need to simply both sides

\(13y - 25 = 14\)

Now we need to add 25 to both sides

\(13y - 25 + 25 = 14 + 25 \\13y = 39 \\y = \frac{39}{13} \\y=3\)

We have the valuee for y! Now we need to find the value for x

To find the value of x, we need to substitute 3 for y in:

\(x = \frac{1}{2} y + \frac{-5}{2} \\x = \frac{1}{2} 3 + \frac{-5}{} \\x = -1\)

Therefore,

The answer is x = -1 and y = 3

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

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Answer:

- 5m + 8

Step-by-step explanation:

Given:

(2m + 3) - (7m - 5)

If you want to find the differences between two values, it means you are to subtract

(2m + 3) - (7m - 5)

This means subtract (7m - 5) from

(2m + 3)

Step 1: Open parenthesis

(2m + 3) - (7m - 5)

= 2m + 3 - 7m + 5

Group like terms

= 2m - 7m + 3 + 5

= - 5m + 8

Or

= 8 - 5m

The time it will take both the boat and whale to meet is 18minutes(nearest minutes)

Displacement is defined as the change in position of an object in a specified direction. It is measured in meters and it's a vector quantity.

Since velocity = displacement/time

displacement = velocity ×time

The total space between the boat and the whale is 5miles.

Using addition of vectors

5= v2t - v1t

5= 46t - 30t

5 = 16t

t= 5/16 = 0.3hrs

to minutes, = 0.3 ×60 = 18minutes(nearest minutes)

Therefore it will take the boat and the whale 18minutes to meet.

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The earnings from the car washes will be divided between the two classes, with a portion allocated to cover the cost of using the two locations. The distribution of earnings will be proportional to the car wash activities.

The two classes have come up with a fundraising idea of organizing car washes to generate funds for their class trips. This initiative allows them to actively participate in raising money while providing a valuable service to their community. The earnings from the car washes will be divided between the two classes, ensuring a fair distribution of funds.

To cover the costs associated with using the two locations for the car washes, a portion of the earnings will be set aside. This is necessary to account for expenses such as water, cleaning supplies, and any fees associated with utilizing the locations. The specific proportion allocated for covering these costs may vary depending on the agreement reached by the classes or the arrangement made with the location owners.  

Overall, this fundraising activity not only allows the classes to raise money for their respective trips but also fosters teamwork and a sense of responsibility among the students. By organizing and participating in the car washes, the students learn important skills such as coordination, planning, and financial management, all while contributing to their class goals.    

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If the factor distributes 5% of its profits as dividends among its 500 shareholders with an equal number of shares, the dividend per shareholder is Rs. 1,200.

Dividends refer to the profits declared for sharing among partners or more specifically among shareholders.

Dividends are a means for repaying shareholders for their shareholding interest in the company.

Companies declare dividends when sufficient profits are generated.

The profit per month = Rs 1,000,000

The total profit for the year = Rs 12,000,000 (Rs. 1,000,000 x 12)

Dividends payout = 5%

Dividends declared = Rs. 600,000 (Rs. 12,000,000 x 5%)

The number of shareholders with equal shares = 500

Dividends per shareholder = Rs. 1,200 (Rs. 600,000/500)

Thus, the dividends per shareholder is the quotient of the total dividends and the number of shareholders.

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Answer:

24 second

36 minutes

60 centimeters

Answer:

A: 24 second

B: 36 minutes

C: 60 centimeters

The determinant of A is zero.

We will use row reduction to show that the determinant of A is zero. First, we expand the determinant of A along the first row:

| A | = a | [b+x c+x] | - b | [a+x c+x] | + c | [a+x b+x] |

Next, we subtract a times the first column from the second column, and c times the first column from the third column:

| A | = a | [b+x-a(b+x)/a] c+x-a(c+x)/a ] | - b | [a+x c+x ] | + c | [a+x b+x ] |

= a | [x-a(b+x)/a 0 ] [c-a(c+x)/a x] | - b | [a+x c+x ] | + c | [a+x b+x ] |

Simplifying the first row, we get:

| A | = a(x-a(b+x)/a)(x-a(c+x)/a) - b(a+x)(c+x) + c(a+x)(b+x)

Expanding and simplifying this expression, we get:

| A | = -x^3 + (a+b+c)x^2 - (ab+bc+ca)x

Since the coefficient of x^3 is zero, we can conclude that the determinant of A is zero.

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If the RMS value of the sinusoidal input to a full wave rectifier is Vo / (2)^(1/2) then the RMS value of the rectifier’s output is  \(Vo * (2)^(1/2) / 2.\)

Full wave rectifier length = Vo / (2)^(1/2)

The peak value of the output voltage = Vo.

For a full-wave rectifier, the outcome voltage is the whole value of the input voltage.

The RMS value of a sinusoidal waveform can be calculated using the formula:

Vrms = Vp / \((2)^(1/2)\)

Vrms = Vo / \((2)^(1/2)\)

To simplify this equation, we can multiply both the numerator and the denominator by (2)^(1/2):

\(Vrms = (Vo / (2)^(1/2)) * ((2)^(1/2)/(2)^(1/2))\)

\(Vrms = Vo * (2)^(1/2) / 2\)

Therefore, we can conclude that the RMS value of the rectifier's output is \(Vo * (2)^(1/2) / 2.\)

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Answer:

5

Step-by-step explanation:

Because -5 is a negative number and the opposite of negative is positive and 5 is positive.

Final Answer: \(5\)

Steps/Reasons/Explanation:

Write down \(-5 + x = 0\) because this is our equation with \(-5\) plugged in to get an additive inverse. We will have to add \(5\) to both sides. This means our additive inverse is positive \(5\).

Question: Which number is the additive inverse of \(-5\)?

\(-5 + x = 0\)

Step 1: Regroup terms.

\(x - 5 = 0\)

Step 2: Add \(5\) to both sides.

\(x = 5\)

~I hope I helped you :)~

The length l of an edge of each small cube if adjacent cubes touch but don't overlap is equal to the distance between the two parallel faces of the cube. It is also equivalent to the distance between the centers of opposite faces of the cube.

Let's assume that the length of each side of the cube is l and the distance between the centers of the opposite faces is L. The Pythagorean theorem can be used to determine L in terms of l. By drawing a line from the center of one face to the center of the opposite face through the center of the cube, you can form a right-angled triangle. L, l, and the diagonal of the face are the lengths of the sides of this triangle. Using the Pythagorean theorem, we getL^2 = l^2 + l^2L^2 = 2l^2L = l√2Therefore, the distance between the centers of the opposite faces of the cube is equal to l multiplied by the square root of 2.

Therefore, the length l of an edge of each small cube if adjacent cubes touch but don't overlap is equal to the distance between the two parallel faces of the cube, which is also equivalent to the distance between the centers of opposite faces of the cube. The length of the cube's edge is equivalent to the height of a cube with an edge of l that has two opposite vertices as the centers of the faces. The diagonal of the cube is equivalent to the hypotenuse of the right-angled triangle that is formed by the height and the side of the cube. It follows that the length of the diagonal of the cube is equal to the square root of 2 times the length of the side of the cube. Hence, the diagonal of a cube with sides of length l is l times the square root of 3.

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The X value corresponding to z = -2.00 is 60. The X value corresponding to z = -2.00 is 60. This means that the observation with a z-score of -2.00 is 60 units below the population mean of 80.

To find the X value corresponding to z = -2.00, we can use the formula:
z = (X - µ) / σ
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

The z-score measures the number of standard deviations an observation is from the mean. In this case, the given z-score of -2.00 indicates that the observation is 2 standard deviations below the mean.
To find the corresponding X value, we use the formula:
z = (X - µ) / σ
Where z is the standard normal distribution value, X is the corresponding raw score, µ is the mean of the population, and σ is the standard deviation of the population.
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

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Answer:

4) d = 1

5) w = 11

6) q = 120

Step-by-step explanation:

4) \(9d - 5 = 4\)

Adding 5 on both the sides ,

\( = > 9d - 5 + 5 = 4 + 5\)

\( = > 9d = 9\)

Dividing both the sides by 9 ,

\( = > \frac{9d}{9} = \frac{9}{9} \)

\( = > d = 1\)

5) \(6 - 3w = - 27\)

Substracting 6 from both the sides ,

\(6 - 3w - 6 = - 27 - 6\)

\( = > - 3w = - 33\)

Dividing both the sides by -3 ,

\( = > \frac{ - 3w}{ - 3} = \frac{ - 33}{ - 3} \)

\( = > w = 11\)

6) \( - 4 = \frac{q}{8} - 19\)

Adding 19 on both the sides ,

\( \frac{q}{8} - 19 + 19 = - 4 + 19\)

\( = > \frac{q}{8} = 15\)

Multiplying both the sides by 8 ,

\( = > \frac{q}{8} \times 8 = 15 \times 8\)

\( = > q = 120\)

the line go through 2 points ( -4 ; -5 ) and ( 6 ; 4 )

ANSWER: \(y=\frac{9}{10}x -\frac{7}{5}\)

ok done. Thank to me :>

The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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Answer:

50% chance, 3/6

Step-by-step explanation:

there are 6 numbers on a die, 1,2,3,4,5,6. 3 even and 3 odd

Answer:

50%

Step-by-step explanation:

even numbers on a dice: 2,4,6

odd numbers:1,3,5

3/6= 0.5

probability is 50%

Answer:

1)9 2)18 3)9. 4)4. 5)carpeting

Step-by-step explanation:

1) divide 63 by 7 = 9

2)multiply 54 by 2 = 108 total weight of the boxes then divide 108 by 6 to get 18

3) 75 -30 to get remaining amount which is 45 then divide by 5 to get how much he will pay each month which is 9

4 24- 12= 12 the remaining for the 3 and divide by 3 to get 4

5) multiply 6 * 9 which is $54 which is cheaper than the $81

Answer:

for the first one it is

ED= 26

CF= 13

mED= 136

mHD= 68

mCE= dont know this one but the other ones im positive their right

Step-by-step explanation:

9514 1404 393

Answer:

  ED = 26; CF = 13; arc ED = 136°; arc HD = 68°; arc CE = 88°

  QU = 8; QR= 16; arc ST = 114°; arc QR = 114°; arc XT = 57°

Step-by-step explanation:

Chords the same distance from the center of the circle are the same length. Chords of the same length intercept arcs of the same angle measure. A radius perpendicular to a chord bisects it and the arc it subtends. The sum of arcs in a circle is 360°. These facts are used to solve the problems here.

__

Circle J

ED = 2×GD = 26

CF = GD = 13

arc ED = arc CD = 136°

arc HD = 1/2 arc CD = 68°

arc CE = 360° - 2×136° = 88°

__

Circle Y

QU = 1/2×ST = 8

QR = ST = 16

arc ST = arc QR = 1/2(360° -34° -98°) = 114°

arc XT = 1/2 arc ST = 57°

a. Based on the chi-squared goodness of fit test, we do not have enough evidence to conclude that mice show a preference towards one paw over the other, with a calculated chi-squared value of 2.5 and a critical value of 3.84 at a significance level of 0.05.

b. The problem with repeating the analysis from part (a) with the new dataset of 480 observations is that the data is no longer independent due to repeated measures. A different statistical test that takes into account repeated measures, such as a repeated measures ANOVA, would need to be used to properly analyze this new dataset.

a. To test whether the data suggests that mice show a preference towards one paw over the other, we can use a chi-squared goodness of fit test. The null hypothesis for this test is that there is no preference towards one paw over the other, while the alternative hypothesis is that there is a preference towards one paw over the other.

The observed frequencies are

Right paw: 18 mice

Left paw: 30 mice

We can calculate the expected frequencies assuming no preference using the formula:

Expected frequency = (total number of observations * probability of right paw use) or (total number of observations * probability of left paw use)

Expected frequency of right paw use = 48 * 0.5 = 24

Expected frequency of left paw use = 48 * 0.5 = 24

We can now calculate the chi-squared test statistic using the formula:

chi-squared = sum((observed frequency - expected frequency)^2 / expected frequency)

Substituting the observed and expected frequencies into the formula:

chi-squared = ((18 - 24)^2 / 24) + ((30 - 24)^2 / 24) = 2.5

Using a chi-squared distribution table with one degree of freedom and a significance level of 0.05, the critical value is 3.84.

Since the calculated chi-squared value (2.5) is less than the critical value (3.84), we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that mice show a preference towards one paw over the other.

b. The problem with repeating the analysis from part (a) with the new dataset of 480 observations is that the data is no longer independent. Since each mouse was observed 10 times, the observations for each mouse are not independent, and treating them as such would violate the assumptions of the chi-squared goodness of fit test. To properly analyze this new dataset, a different statistical test that takes into account repeated measures, such as a repeated measures ANOVA, would need to be used.

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The given question is incomplete, the complete question is:

Do mice show a preference for using one paw over the other? Attempting to answer this question, a researcher tested a random sample of 48 mice and observed which forepaw (right or left) the mice used to retrieve food from a narrow tube. Eighteen of the mice used their right paw, while the rest used their left paw.

a. Does this data suggest that mice show a preference towards one paw over the other? Carry out the appropriate test and include all steps for full credit. Given: critical value = 3.84

b. During the experiment, the researcher noticed that individual mice sometimes switched which forepaw they used to retrieve the food. So she repeated this study on the same 48 mice, but measured each one 10 times and she recorded which forepaw was used each time. What would be the problem with repeating the analysis ran in part (a) with her new dataset of 480 observations? Be specific.

Answer:

x = 4

y = - 5

Step-by-step explanation:

equations

-3x-4y=2

3x+3y=-3

Solution

Add the two equations

-y= 5                              Multiply by -1

y = -5

3x + 3y  =  -3

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

3x - 15 = -3                    Add 15 to both sides

3x - 15 + 15 = -3 + 15

3x = 12                          Divide by 3      

3x/3 = 12/3

x = 4

The value of x and y in the two of the given equations is (-2,1).

A system of linear equations is a system which consists of a pair of equations which are linear in nature.

Given a system of linear equations with two variables x and y as:

-3x - 4y = 2                         ............. Equation 1

3x + 3y = -3                        .............  Equation 2

Add the two of the above equation, therefore, equation 1 and Equation 2,

-3x - 4y + (3x + 3y) = 2 - 3

-3x - 4y + 3x + 3y = 2 - 3

-y = -1

Multiply -1 on both sides of the equation,

y = 1

Substitute the value of y in equation 2,

3x + 3y = -3  

3x + 3(1) = -3

3x = -3 -3

3x = -6

x = -2

Further, the value of x and y can also be confirmed by drawing the graph of the given lines as shown. And the point at which it intersects is the solution of the equations.

Hence, the solution of the two equations is (-2,1).

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We can construct a chart, a table for the values of the given function as follows:

1. We need to have the function g(x) = -4x^2.

2. We can obtain the values for the function for the values:

x = -4, x = -2, x = 0, x = 2, x = 4.

3. We need to evaluate the function for each of these values.

4. Finally, we can have a table of the values of x and y.

Having this information into account, we can proceed as follows:

1. x = -4

2. x = -2

3. x = 0

4. x = 2

5. x = 4

Then, having these values, we can construct the values for the function using these values:

We can draw part of this function using these values. We have to remember that, in functions, we can say that y = f(x).

We can also say that the domain of the function is, in interval notation:

And the range, as we can see from the values, is as follows (using interval notation):

This is because the values for y (or f(x)) are less or equal to zero.

In summary, we can have a table to construct a graph using the values for the independent variable and plug these values in the function to obtain the values for y.

We need to remember that y = f(x). Additionally, this function has a domain from -infinity to infinity (all the values in the Real set), and a range for values from -infinity to 0 (including zero).

A graph for this function is as follows:

ANSWER

0.3783

EXPLANATION

The lengths of the pregnancies, X, is normally distributed with a mean of 246 days and a standard deviation of 13 days,

We have to find the probability that a randomly selected pregnancy lasts less than 242 days,

For this, we have to standardize the variable X with the formula,

So the probability we have to solve is,

This is equivalent to,

Which is also equivalent to,

We have to find these equivalences because, usually, normal distribution tables show the probabilities for positive z-scores and to the left of those values - i.e. less than those values. Find z = 0.31 in a z-table,

So, the probability is,

Hence, the probability that a randomly selected pregnancy lasts less than 242 days is 0.3783.

Answer:

(a)  P(Blue) = 0.24

     P(Green) = 0.12

(b)  176

Step-by-step explanation:

Let x be the probability that the spinner lands on green.

Given the spinner is twice as likely to land on blue than green, the probability of it landing on blue is 2x.

The sum of all probabilities must equal 1, so we can set up the equation:

\(0.2 + 2x + x + 0.44 = 1\)

Solve the equation for x:

\(\begin{aligned}0.2 + 2x + x + 0.44 &= 1\\3x+0.64&=1\\3x+0.64-0.64&=1-0.64\\3x&=0.36\\3x\div3&=0.36\div3\\x&=0.12\end{aligned}\)

Therefore, the probability of landing on green is 0.12, and the probability of landing on blue is 0.24.

\(\begin{array}{|c|c|c|c|c|}\cline{1-5}\vphantom{\dfrac12} \sf Colour& \sf Red& \sf Blue& \sf Green& \sf Yellow\\\cline{1-5}\vphantom{\dfrac12} \sf Probability & 0.2 & 0.24 & 0.12 & 0.44\\\cline{1-5}\end{array}\)

\(\hrulefill\)

The expected number of times the spinner is expected to land on yellow can be calculated by multiplying the probability of landing on yellow by the total number of spins:

\(\begin{aligned}\textsf{Expected number of yellow spins}&=\textsf{Probability of yellow} \times\textsf{Total number of spins}\\&= 0.44 \times 400\\&= 176\end{aligned}\)

Therefore, the spinner is expected to land on yellow 176 times out of 400 spins.

The calculated probabilities of the spinner are:

(a)  P(Blue) = 0.24 and P(Green) = 0.12

(b)  176

We are given the probabilities as:

P(Red) = 0.2

P(yellow) = 0.44

Let z be the probability that the spinner lands on green.

We are told that the spinner is twice as likely to land on blue than green, and as such it means that the probability of it landing on blue is 2z

The sum of all probabilities must equal 1, so we can set up the equation:

0.2 + 2z + z + 0.44 = 1

3z + 0.64 = 1

3z = 1 - 0.64

3z = 0.36

z = 0.12

2z = 2 * 0.12 = 0.24

b) If spinner is spun 400 times, then:

N(yellow) = 0.44 * 400 = 176

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