mathematics

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The quadrilateral ABCD is trapezoid.

What is trapezoid?

A quadrilateral with one set of parallel opposite sides is referred to as a trapezium. It can have congruent sides (isosceles) and right angles (a right trapezium), but neither is necessary.

Here in the given figure ,

[tex]\overline{AD}=\overline{BC}[/tex] are parallel to each other.

We can make right angle using ABC.

Hence the given quadrilateral ABCD is trapezoid.

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The mean is 4746
The median wage is #4618

The wages for the five local government trainees are

#4,166, #4,618, #3,742, #5,838 and #5,366

= 4166+ 4618+ 3742+5838+5366/5

= 23,730/5

Mean = 4,746

The median wage is

Arrange the wages orderly

3,742, 4166, 4618, 5366, 5838

The median wage is #4618

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Answer:

∠ BAC = 66°

Step-by-step explanation:

the inscribed angle BAC is half the angle at the centre, subtended on the same arc BC , then

∠ BAC = [tex]\frac{1}{2}[/tex] × 132° = 66°

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$879\\ r=rate\to 19.5\%\to \frac{19.5}{100}\dotfill &0.195\\ t=years\dotfill &1.5 \end{cases} \\\\\\ A = 879[1+(0.195)(1.5)] \implies A=879(1.2925)\implies A \approx 1136.11[/tex]

The surface area of the rectangular prism is 502 mm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The surface area of the prism = 2(8 mm * 13 mm) + 2(8 mm * 7 mm) + 2(7 mm * 13 mm) = 502 mm²

The surface area is 502 mm²

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The value of the square root 3 6/25 is 1⅘

The square root of a number is a value that can be multiplied by itself to give the original number. For example the square root of 225 is 15.

Another example is the square of 16, which can be gotten by finding the prime product of 16

16 = 2×2×2×2. we can group the 2s into two i.e (2×2) × (2×2) . We can now take one out of 2 .

= 2 × 2 = 4. Therefore the the square root of 16 is 4.

Therefore the square root of 3 6/25 can be found by converting the fraction into improper fraction.

= 81/25

therefore the √81/25 = 9/5 = 1⅘.

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(a) G'(a) = 2x - 3

(passing through (0, 3)) y1(x) = -3

(passing through (4, 7)) y2(x) = 5

b) The illustration of the graph is defined below.

In calculus, finding the derivative of a function is an important tool to understand the behavior of a curve at a specific point. One application of this concept is determining the equation of the tangent line to a curve at a given point. In this problem, we will use the derivative of a quadratic function to find the equations of tangent lines to the curve y = x² − 3x + 3 at the points (0, 3) and (4, 7).

To begin, we need to find the derivative of G(x) = x² − 3x + 3. Using the power rule, we have:

G'(x) = 2x - 3

Next, we can use this derivative to find the slope of the tangent line to the curve y = x² − 3x + 3 at any given point (a, G(a)). At the point (0, 3), we have a = 0, so the slope of the tangent line is:

G'(0) = 2(0) - 3 = -3

Using the point-slope equation of a line, we can find the equation of the tangent line passing through (0, 3). The equation of the tangent line is:

y - 3 = -3(x - 0)

Simplifying, we get:

y = -3x + 3

Similarly, at the point (4, 7), we have a = 4, so the slope of the tangent line is:

G'(4) = 2(4) - 3 = 5

Using the point-slope equation again, we can find the equation of the tangent line passing through (4, 7). The equation of the tangent line is:

y - 7 = 5(x - 4)

Simplifying, we get:

y = 5x - 13

To graph these tangent lines on the same screen as the curve y = x² − 3x + 3, we can plot the curve and the two tangent lines using a graphing calculator or software. The graph should show the curve as a parabola and the tangent lines as straight lines intersecting the curve at the points (0, 3) and (4, 7), respectively.

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Answer:

8.5 yrs

Step-by-step explanation:

parent: 41 yrs

eldest son: x

Firstly, we will need to subtract 24 from 41 to get 2x the eldest son's age.

By doing that, we will have an equation that looks like this:

41-24=2x

This equation would basically get us through the whole problem.

Simplify the equation:

17=2x

x=8.5

The eldest son's age is 8.5.

Let's check our work!

8.5 x 2 = 17

17+24=41 (parent's age.)

Hope this helps :)

Log3(14)

= log(14) / log(3) (Change of base formula)

= 4 / 1.965 (log(3) = 1.965)

= 2.041 (rounded to 3 decimal places)

2.041

Answer:

Step-by-step explanation:

To emulate the logarithm using the change of base formula, we need to use a base that is more convenient to evaluate. Let's use base 10:

log3(14) = log10(14) / log10(3)

Using a calculator, we can evaluate the numerator and denominator:

log10(14) ≈ 1.146

log10(3) ≈ 0.477

Dividing the numerator by the denominator gives:

log3(14) ≈ 2.402

Rounding to three decimal places, the final result is:

log3(14) ≈ 2.402

With a p-value of 0.022, there is convincing evidence of a difference in the proportion of men and women who intended to vote for Trump in the city. Type I error could have been made. No, there is not convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump. Increasing the significance level would increase power, but would also increase the likelihood of making a Type I error.

We can use a two-sample z-test to test for the difference in proportions between men and women who intended to vote for Trump.

Let p1 be the proportion of men who intended to vote for Trump and p2 be the proportion of women who intended to vote for Trump. Then the null and alternative hypotheses are

H0: p₁ = p₂

Ha: p₁ ≠ p₂

We can calculate the pooled sample proportion

p = (x₁ +  x₂) / (n₁ +  n₂)

= (120 + 132) / (250 + 240)

= 0.508

where x₁ = 120, x₂ = 132, n₁ = 250, and n₂ = 240.

We can calculate the test statistic

z = (p₁ - p₂) / √(p * (1 - p) * (1/n₁ + 1/n₂))

= (0.48 - 0.55) / √(0.508 * 0.492 * (1/250 + 1/240))

= -2.29

Using a standard normal distribution table, the p-value for a two-tailed test with a test statistic of -2.29 is 0.022. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.

The mistake we could have made is a type I error, which is rejecting the null hypothesis when it is actually true. In this case, it would mean concluding that there is a difference in proportions between men and women who intended to vote for Trump when there is actually no difference.

The confidence interval for the difference in proportions is (-0.158, 0.018), which includes 0. Since 0 is in the interval, we cannot reject the null hypothesis that there is no difference in proportions between men and women who intended to vote for Trump.

Therefore, based on the interval, there is not convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump.

One way to increase the power of the test is to decrease the significance level (i.e., increase the alpha level). This would allow us to reject the null hypothesis more easily and increase the chance of detecting a true difference in proportions.

However, the drawback of making this change is that it increases the chance of making a type I error, which means rejecting the null hypothesis when it is actually true.

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The angles of the triangle are:

A =  95.7°, B = 33.6°, C = 50.7°.

What are the angles of the triangle?

The area created between two of a triangle's side lengths is known as the angle. Both internal and external angles are present in a triangle. In a triangle, there are three interior angles. When the sides of a triangle are stretched to infinity, exterior angles are created.

Here, we have

Given: a = 9, b= 5, c = 7

We have to find all angles in degrees.

Using law of cosines,  a² = b²+c² - 2bc cos(A),

9² = 5²+7² - 2(5)(7) cos(A)

81 = 25 + 49 - 70 cos(A)

7 = -70 cos(A)

cos(A) = -7/70

cos(A) = -1/10

A = cos⁻¹(-1/10)

A = 95.7°

Now, using the law of sines,  

[sin (A)]/(a) =  [sin (C)]/(c)

[sin (95.7°)]/(9) =  [sin (C)]/(7)

0.9955/9 = sin (C)/(7)

0.7742 = sinC

C = sin⁻¹(0.7742)

C = 50.7°

The sum of all the angles of a triangle= 180°

A + B + C = 180°

95.7° + B + 50.7° =  180°

B = 33.6°

Hence, the angles of the triangle are:

A =  95.7°, B = 33.6°, C = 50.7°.

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Based ont he the function y = - 2x + 5 + 2x - 5 is given ,

if  x < -2.5, y = 0

i f  x > 2.5, y = 0

if -2.5 ≤  x  ≤ 2.5 = 0

Without the absolute value symbols

y = -2x + 5 + 2x - 5

Where x < - 2.5

y = -2 (-2.5) + 5 + 2 (-2.5 ) - 5

y =  5 + 5 + (-5)-5

y = 0

Where x > 2.5

y = -2 (2.5) + 5 + 2(2.5) - 5

y = 0

Where -2.5 ≤ x ≤ 2.5

y = -2x + 5 + 2x -5

grouping like terms we have

-2x + 2x +5 -5
y = 0

thus, Where -2.5 ≤ x ≤ 2.5

y = 0

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Answer:

Karl has 2.67 pounds of flour left.

Step-by-step explanation:

First, let us dissect the given.

Second, let us identify the correct solution for this problem.

Note that where the above events are described, the probablity of A occurring given that B occurrs is 6/25.

We can use Bayes' theorem to find the conditional probability

P  (A| B) = P(A and B ) / P( B)

From the problem statement, we know that P(A) = 1/3,

P(B) = 5/6, and

P (A and B) = 1/5.

Substituting to get .....

P(A | B) =  (1/5) / (5/6)

= 1/5 x (6 /5)

= 6/25

Hence, we are corect to state that the probability of A occurring given that B occurs is 6/25.

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* Mary's solar panels cost $2,000.

* The panels will reduce her monthly electricity bill by $40.

* She can earn 12% interest compounded monthly.

* So her monthly savings is $40

* And her 12% monthly interest rate is 12% / 12 = 1% per month.

* So each month her balance grows by 1% of the current balance.

* Let's think through this step-by-step:

* Initial balance = $2,000 (from paying for the solar panels)

* Month 1:

** Savings = $40 (from lower electric bill)

** Interest = 1% of $2,000 = $20

** Balance after Month 1 = $2,000 + $40 + $20 = $2,060

* Month 2:

** Savings = $40

** Interest = 1% of $2,060 = $20

** Balance after Month 2 = $2,060 + $40 + $20 = $2,120

* Month 3: (continue the calculations for Months 3 through 24)

** Savings = $40

** Interest = 1% of $2,121 = $21

** Balance after Month 3 = $2,121 + $40 + $21 = $2,182

* After 24 months, the balance is $3,149 (calculated step-by-step as shown above)

* The initial investment was $2,000

* So it took about 24 months to recoup her investment.

Does this help explain the steps? Let me know if you have any other questions!

Step-by-step explanation:

Charlie's monthly pay, P, can be represented as a linear function of the number of items sold, q. The monthly salary of $2,000 represents the y-intercept of the line, and the commission of $100 per item sold represents the slope of the line.

Thus, the model for Charlie's monthly pay, P(q), can be expressed as:

P(q) = 100q + 2000

where q is the number of items sold in a month, and P(q) is Charlie's monthly pay in dollars.

Expanding the left-hand side of the equation, we get:

(x+6)2 = (x+6)(x+6) = x(x+6) + 6(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36

So now we have the equation:

x^2 + 12x + 36 = 8

Subtracting 8 from both sides, we get:

x^2 + 12x + 28 = 0

We can factor this quadratic equation as:

(x+2)(x+14) = 0

This gives us two possible solutions:

x+2 = 0, so x = -2

x+14 = 0, so x = -14

Therefore, the solutions to the equation (x+6)2 = 8 are x = -2 and x = -14.

Step-by-step explanation:

Here is one way :

(x+6)^2 = 8        Take the square root of both sides

x+6 =   +- sqrt 8

x = -6 +- sqrt8     = -6 + 2 sqrt 2   or   -6 - 2 sqrt 2  =   -  3.17   or - 8.83

Answer:

The first and second one

Step-by-step explanation:

Since they are one-to-one functions, the first table and the first graph (under the table) are the answers.

Be sure to mark this as brainliest and hope this helps!

Answer: The first one and second one.

Step-by-step explanation:

It's a bit cut-off but for the very first function, each x-value has a corresponding y-value so it is a function. For the second one (the graph), if we do the vertical line test, it will pass it (vertical line touches only one point of the function). The third one (the loop graph) , however, will not pass the vertical line test as there's a point on the graph where if we were to draw a vertical line, it would be touch 2 or 3 points of the function.

Answer:

x = -1

Step-by-step explanation:

You will plug in 8 for y then solve for x:

[tex]\frac{12}{3} = (x-1)^2\\4 = (x-1)^2\\\frac{+}{-}2 = x-1 \\ x= +3, and -1[/tex]

Then the answer is -1 because the graph shows the point in the 2nd quadrant meaning x is negative

Answer:

Step-by-step explanation:

...

...

..

..

......

For a standard normal distribution, the approximate value of

P(-0.41) ≤ z ≤ (0.73) is 43%.

Option A is the correct answer.

We have,

To find the approximate value of P(-0.41) ≤ z ≤ (0.73) for a standard normal distribution, we need to use the standard normal table.

Looking at the table,

The value of P(Z ≤ 0.73) = 0.7673.

The value of P(Z ≤ -0.41) = 0.3409.

To find the value of P(-0.41) ≤ Z ≤ (0.73),

We need to subtract P(Z ≤ -0.41) from P(Z ≤ 0.73):

P(-0.41) ≤ Z ≤ (0.73) = P(Z ≤ 0.73) - P(Z ≤ -0.41)

P(-0.41) ≤ Z ≤ (0.73) = 0.7673 - 0.3409

P(-0.41) ≤ Z ≤ (0.73) = 0.4264

Rounding this value to the nearest whole percent, we get 43%.

Therefore,

For a standard normal distribution, the approximate value of

P(-0.41) ≤ z ≤ (0.73) is 43%.

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Answer:

  y = 4x² -8x +10

Step-by-step explanation:

You want to write the equation y = 4(x -1)² +6 in standard form.

The distributive property is used to eliminate parentheses.

  y = 4(x -1)² +6 . . . . . . given equation

  y = 4(x -1)(x -1) +6 . . . . . the meaning of the exponent of 2

  y = 4((x(x -1) -1(x -1)) +6 . . . . . distributive property applied once

  y = 4(x² -x -x +1) +6 . . . . . . . . . . distributive property applied again

  y = 4(x² -2x +1) +6 . . . . . . collect terms inside parentheses

  y = 4x² -8x +4 +6 . . . . . . . distributive property applied

  y = 4x² -8x +10 . . . . . . . . . collect terms

Answer:

84 degrees for number 6

Step-by-step explanation:

the area of a circle is 360 degrees, so just subtract the other angles by 360 i think that's how you do it

I am pretty sure the answer is b. emplyee 2# but im not 100% sure since your graph is really weird and hard to uunderstand

Result:

The weight of the pumpkin in November = 71 ounces more than in October.

How to compare the weights?

To compare the weights, we need to convert both weights to the same unit of measurement, either pounds or ounces.

Let's convert the first weight, which is 3 pounds and 11 ounces, to ounces:

3 pounds = 3 x 16 = 48 ounces

11 ounces = 11

So the first weight is 48 + 11 = 59 ounces.

Now, let's convert the second weight, which is 8 pounds and 2 ounces, to ounces:

8 pounds = 8 x 16 = 128 ounces

2 ounces = 2

So the second weight is 128 + 2 = 130 ounces.

To find how many more ounces the pumpkin weighed in November, we subtract the October weight from the November weight:

130 - 59 = 71

Therefore, the pumpkin weighed 71 more ounces in November than it did in October.

The volume of the cube will be 5.832 cubic inches.

The volume of a cube is given by the formula V = s³, where s is the length of one of its edges.

In this case, the length of one edge is given as 1.8 inches.

So, substituting s = 1.8 inches in the formula, we get:

V = s³ = 1.8³ = 5.832 cubic inches

Therefore, the volume of the cube is 5.832 cubic inches.

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An elephant weighs 110 pounds more on Day 60 than it does on Day 5

Here, function w = 2d +200 represents the weight w of an elephant on a given day during his first year.

From above function , the weight of an elephant on Day 60 would be,

w₆₀ = 2(60) + 200

w₆₀ = 120 + 200

w₆₀ = 320 pounds

and the weight of an elephant on Day 5 would be,

w₅ = 2(5) + 200

w₅ = 10 + 200

w₅ = 210

The difference between these weights is:

w = w₆₀ - w₅

w = 320 - 210

w = 110 pounds

Therefore, an elephant weighs 110 pounds more on Day 60 than on Day 5

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Answer: the slope is 6

Step-by-step explanation: the line y=6x-3

2/7

Assuming I know what standard deviation is, it is there is a 3 ounce "range" that the machine can give, based on that 24 oz mean. So there can be 21,22,23,24,25,26, and 27. Out of those 7, 2 are the numbers we are looking for, so it is 2/7.

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

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

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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