Find x in this 45°-45°-90° triangle.

x=

7) The negation of the conditional statement "If it is red, then it is not an egg" is "It is red and it is an egg" (A). 8) The contrapositive of the statement "If the electricity is out, then I cannot use the computer" is "If I can use the computer, then the electricity is not out" (D).

The truth table lists all the possible combinations of truth values for the statement propositions and evaluates the truth value of the statement under each combination. Let's say we have two propositions, P and Q. The truth table for the statement "P implies Q" would look like this:

| p | q | (p ∧ q) ∨ ¬q |
|--- |--- |------------------|
| T | T  |       T           |
| T | F  |       T           |
| F | T  |       F           |
| F | F  |       T           |

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Answer:

It is (9,-3) because x increased by 1 unit and y increased by 4 units.

Answer:

\((9,-3)\)

Step-by-step explanation:

\((8,-7)\)

If it moves right, add the value to the x-coordinate. If it moves left, subtract the value from the x-coordinate. In this case, because the point was translated 1 unit right, we add 1 to the x-coordinate 8.

\((9,-7)\)

If it moves up, add the value to the y-coordinate. If it moves down, subtract the value from the y-coordinate. In this case, because the point was translated 4 units up, we add 4 to the y-coordinate.

\((9,-3)\)

I hope this helps!

The statement that is NOT true regarding control charts is A. A process is in control if it is capable of meeting customer specifications.

A process being in control means that it is stable and predictable, with the variation due to common causes only. It does not necessarily mean that it is capable of meeting customer specifications. A process may be in control but have too much variability to meet the specifications, indicating that it needs improvement. Similarly, a process may be capable of meeting customer specifications but not in control if it is unstable and unpredictable due to special causes of variation. Therefore, control charts are used to monitor and improve processes to make them capable of meeting customer specifications while being in control.

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We can represent 0.614 using only 5 tenths as \(\mathbf{\dfrac{6.14}{10}}\)

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

The accepted method for representing both integer and non-integer numbers is the decimal number system.

From the given information, we are to represent 0.614 by using only 5 tenths.

Representing 0.614 in the same form, we have:

\(\mathbf{=\dfrac{0.614\times 1000}{1\times 1000}}\)

\(\mathbf{=\dfrac{614}{1000}}\)

\(\mathbf{=\dfrac{6.14}{10}}\)

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Answer: 6.14/10

Step-by-step explanation:

The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.

The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.

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The equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5) is 20x + 4y + 8z = -9.

In order to determine the distance of this plane (x, y, z) with the given points, we would use the distance formula.

Mathematically, the distance between three (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

For these points (x, y, z) and (−7, 1, 1), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x₂ - (-7))² + (y₂ - 1)² + (z₂ - 1)²]

Distance = √[(x₂ + 7)² + (y₂ - 1)² + (z₂ - 1)²]

By using the algebraic formulas, the expanded expression is given by:

(a - b)² = a² - b² - 2ab

(a + b)² = a² + b² + 2ab

Distance = √[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)]   .......equation 1.

For these points (x, y, z) and (3, 3, 5), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x - 3)² + (y - 3)² + (z - 5)²]

Distance = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]    .....equation2.

Since both distances are equidistant, we would equate eqn. 1 and eqn. 2 and then simplify:

√[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]

(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1) = (x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)

x² + 14x + 49 + y² - 2y + 1 + z² - 2z + 1 = x² - 6x + 9 + y² - 6y + 9 + z² - 10z + 25

14x + 6x - 2y + 6y - 2z + 10z + 52 - 43 = 0

20x + 4y + 8z + 9 = 0

20x + 4y + 8z = -9.

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Answer:

11.1666666667

Step-by-step explanation:

Add all numbers together. Answer 67

Divide by the amount of numbers. Answer 6

Then your finial answer will come out to 11.666666667 or 12

Answer:

now how did you knew people was doing it

Step-by-step explanation:

it C trust

Answer:

The answer is 28 (option D)

Step-by-step explanation:

Im big Brain

Answer:

x = 24
y - 16

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf x = 16, \ y = 24}\)

Step-by-step explanation:

Let the smaller number be x and larger number be y.

x + y = 40 ----------------(1)

x = y - 8 ------------------(2)

Put Eq. (2) in (1)

y - 8 + y = 40

2y - 8 = 40

2y = 40 + 8

2y = 48

y = 48/2

Put y = 24 in Eq. (2)

x = 24 - 8

\(\rule[225]{225}{2}\)

Using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, they require at least 100 sushi pieces.

24 pieces of sushi had previously been ordered and paid for by Sofia.

Roll sushi is available.

Each roll = 12 pieces at $8

R = additional rolls that Sofia orders

Additional sushi = Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

A roll contains 12 pieces.

76/12 = 6.33

Rolls must be ordered by Sofia.

She will therefore place 7 additional sushi rolls, each with 12 pieces.

12*7=84 pieces

Remember that they need at least 100 pieces, so there may be more than 100 in total.

84 pieces plus the 24 pieces Sofia has previously ordered.

The total number of pieces will be 108.

Therefore, using mathematical operations, we know that Sofia will spend $56 and order 7 additional rolls of sushi (84 pieces).

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Complete question:
Sofia ordered sushi for a company meeting. They change plans and increase how many of people

will be at the meeting, so they need at least 100 pieces of sushi in total.

Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.

The sushi comes in rolls, and each roll contains 12 pieces and costs $8. How many more sushi Sofia will order and of what amount?

Using translation concepts, the values of k are given as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem:

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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Answer:

51 degrees

Step-by-step explanation:

18+33=51

y = (At + B) e^(rt)

where A = -r/2 and B = 3r/2, as expected.

When the two roots of the characteristic equation are both equal to r, we say that the roots are equal or repeated. In this case, the general solution to the corresponding second order linear homogeneous ODE with constant coefficients is of the form:

y = (At + B) e^(rt)

where A and B are constants to be determined by the initial or boundary conditions.

However, the form given in the question, (at+b)âe^rt, is not correct. The â symbol is not standard notation for mathematical expressions and its meaning is unclear. It is possible that it was intended to represent a coefficient or parameter, but without more information, we cannot determine its value or significance.

To see why the correct form of the solution is y = (At + B) e^(rt), we can use the method of undetermined coefficients. Suppose that y = e^(rt) is a solution to the homogeneous ODE with repeated roots. Then, we can try the solution y = (At + B) e^(rt) and see if it satisfies the ODE.

Taking the first and second derivatives of y, we get:

y' = A e^(rt) + r(At + B) e^(rt) = (Ar + r(At + B)) e^(rt)

y'' = A r e^(rt) + r^2(At + B) e^(rt) = (Ar^2 + 2rAt + r^2B) e^(rt)

Substituting y, y', and y'' into the homogeneous ODE with repeated roots, we get:

(Ar^2 + 2rAt + r^2B) e^(rt) = 0

Since e^(rt) is never zero, we can divide both sides by e^(rt) to get:

Ar^2 + 2rAt + r^2B = 0

This is a linear equation in A and B, and we can solve for them by using the initial or boundary conditions. For example, if we are given that y(0) = 1 and y'(0) = 0, we have:

y(0) = A e^(0) + B e^(0) = A + B = 1

y'(0) = (Ar + rB) e^(0) + A e^(0) = Ar + A = 0

Solving this system of equations, we get:

A = -r/2, B = 3r/2

Therefore, the general solution to the homogeneous ODE with repeated roots is:

y = (-rt/2 + 3r/2) e^(rt)

which can be rewritten as:

y = (At + B) e^(rt)

where A = -r/2 and B = 3r/2, as expected.

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The median for the students is 4 and the median for the teachers is 3 compares the medians of the data.

The dot plots display the number of siblings reported by two different groups: seventh graders and teachers at a local middle school. The students' dot plot shows varying numbers of dots above each value on the number line, indicating the frequency of students reporting that specific number of siblings. Similarly, the teachers' dot plot represents the number of teachers reporting each value.

Looking at the dot plots, it is evident that the students' distribution is skewed towards higher numbers of siblings, with the highest frequency above 2 and 3. Conversely, the teachers' distribution appears to be more spread out, with a peak around 4 and a decline towards higher numbers.

To determine the median, we identify the middle value in each distribution. In the students' dot plot, the middle value falls around 4, as there are equal numbers of dots on either side. In the teachers' dot plot, the median is around 3 since the distribution is more symmetrical.

Therefore, comparing the medians of the data, we can conclude that the median for the students is 4 and the median for the teachers is 3.

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a. The equation computed shows that the number of paid vacation days has she earned will be 17 days.

b. The time when she will reach the maximum number of paid vacation days allowed is 6 years.

a. The equation computed shows that the number of paid vacation days has she earned will be:

= 2 + 3x

x = 5

= 2 + 3(5)

= 2 + 15

= 17 days.

b. The maximum number of days for a pod vacation will be:

= 4 × 5

= 20 days.

The time when she will reach the maximum number of paid vacation days allowed will be:

20 = 3x + 2

3x = 20 - 2.

3x = 18

x = 18/3

x = 6 years

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1. Finding the function f given the slope of the tangent line and a point:
To find the function f(x) given that the slope of the tangent line at any point (x, f(x)) is f’(x) and the graph passes through the point (5, 7/2), we need to integrate f’(x) with respect to x.

Given f’(x) = 3(2x – 9)², we can integrate it to find f(x):

∫ f’(x) dx = ∫ 3(2x – 9)² dx

Using the power rule of integration and simplifying:

F(x) = ∫ 3(4x² - 36x + 81) dx
= 3 ∫ (4x² - 36x + 81) dx
= 3 [ (4/3)x³ - 18x² + 81x ] + C

Applying the limits using the given point (5, 7/2):

F(5) = 3 [ (4/3)(5)³ - 18(5)² + 81(5) ] + C
7/2 = (4/3)(125) – 18(25) + 81(5) + C
7/2 = 500/3 – 450 + 405 + C
7/2 = 55/3 + C

Simplifying further:

7/2 – 55/3 = C
(21 – 55)/6 = C
-34/6 = C
-17/3 = C

Finally, substituting the value of C back into the equation:

F(x) = 3 [ (4/3)x³ - 18x² + 81x ] – 17/3

Therefore, the function f(x) is f(x) = (4/3)x³ - 18x² + 81x – 17/3.

2. Finding the expression g(t) for life expectancy at birth:

To find the expression g(t) for life expectancy at birth, we need to integrate g’(t) with respect to t and apply the given initial condition.

Given g’(t) = 3.7544 / (1 + 1.04t)⁰.⁹, we can integrate it to find g(t):

∫ g’(t) dt = ∫ 3.7544 / (1 + 1.04t)⁰.⁹ dt

Using substitution, let u = 1 + 1.04t:

Du = 1.04 dt
Dt = du / 1.04

Now we can rewrite the integral in terms of u:

∫ (3.7544 / u⁰.⁹) (du / 1.04)

Simplifying and integrating:

G(t) = (3.7544 / 1.04) ∫ u⁻⁰.⁹ du
G(t) = (3.61308) ∫ u⁻⁰.⁹ du
G(t) = (3.61308) [u¹.¹ / (1.1)] + C

Applying the initial condition where g(0) = 36.1:

G(0) = (3.61308) [1.1 / (1.1)] + C
36.1 = 3.61308 + C

Simplifying further:

36.1 – 3.61308 = C
32.48692 = C

Finally, substituting the value of C back into the equation:

G(t) = (3.61308) [u¹.¹ / (1.1)] + 32.48692

Therefore, the expression g(t) giving the life expectancy at birth in years is:

G(t) = (3.61308) [(1 + 1.04t)¹.¹ / (1.1)] + 32.48692.

3. Finding the life expectancy at birth of a female born in 2000:

To find the life expectancy at birth of a female born in 2000, we need to substitute t = 2000 into the expression g(t) we found.
G(2000) = (3.61308) [(1 + 1.04(2000))¹.¹ / (1.1)] + 32.48692

Calculating the expression:

G(2000) ≈ 107.17 years (rounded to two decimal places)

Therefore, the life expectancy at birth of a female born in 2000 in that country is approximately 107.17 years.

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Answer:

The height of the cliff CD is approximately 539.76 m

Step-by-step explanation:

The given parameters are;

The first angle of elevation with which the captain sees the person on the cliff = 61°

The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°

The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°

∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;

The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°

By sine rule, we have;

AB/(sin(a)) = BC/(sin(c))

Which gives;

92/(sin(8°)) = BC/(sin(61°))

BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m

BC ≈ 578.165 m

The height CD = BC × sin(69°)

∴  The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.

The height of the cliff CD ≈ 539.76 m.

Answer:

x=-3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−21+6x=3(3x−5)−x

−21+6x=(3)(3x)+(3)(−5)+−x(Distribute)

−21+6x=9x+−15+−x

6x−21=(9x+−x)+(−15)(Combine Like Terms)

6x−21=8x+−15

6x−21=8x−15

Step 2: Subtract 8x from both sides.

6x−21−8x=8x−15−8x

−2x−21=−15

Step 3: Add 21 to both sides.

−2x−21+21=−15+21

−2x=6

Step 4: Divide both sides by -2.

−2x

−2

=

6

−2

Answer:

(10x-y)^2

Step-by-step explanation:

1

Rewrite it in the form {a}^{2}-2ab+{b}^{2}a2−2ab+b2, where a=10xa=10x and b=yb=y.

{(10x)}^{2}-2(10x)(y)+{y}^{2}(10x)2−2(10x)(y)+y2

2

Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}(a−b)2=a2−2ab+b2.

{(10x-y)}^{2}(10x−y)2

Answer:

15 divided by 3 = 5

Step-by-step explanation:

21 divided by 3 = 7

6 divided by 3 = 2

Have a Good Day : )

Answer:

5

Step-by-step explanation:

y=x/3

substituting x=15 in the above equation

y=15/3

y=5

Mark me as the brainliest if I helped you, i need it thanksss!!

a.

tx) = -9x^2 + 12x - 4
t"x) = -18x + 12

Entering these into a graphing calculator or software, we can examine the table.

b.

To find any critical values, we set the first derivative t'(x) = 0.

t'(x) = -18x + 12 = 0
Solving for x, we get x = 2/3.

We can check if this is a maximum or minimum by using the second derivative test. The formula for f"(x) is the derivative of t'(x), which is t"(x).

t"(x) = -18
t"(2/3) = -18, which is negative. This means that at x = 2/3, there is a local maximum.

Therefore, the answer is:

OB. The function has a critical number at 2/3. At this critical number, the second derivative is negative.
Hi! I understand that you want to find the critical numbers of the given function f(x) = -3x + 6x^2 - 4x - 1. Let's first find the first and second derivatives, and then analyze them to find the critical numbers.

a. The first derivative, f'(x), is found by taking the derivative of f(x) with respect to x:

f'(x) = d(-3x + 6x^2 - 4x - 1)/dx = -3 + 12x - 4

The second derivative, f''(x), is found by taking the derivative of f'(x) with respect to x:

f''(x) = d(-3 + 12x - 4)/dx = 12

b. To find critical numbers, set f'(x) = 0 and solve for x:

0 = -3 + 12x - 4

Combine the constants and simplify:

0 = 12x - 7

Now, solve for x:

x = 7/12

So, there is one critical number at x = 7/12. To determine the nature of this critical number, check the value of the second derivative, f''(x), at this point:

f''(7/12) = 12

Since the second derivative is positive, the function has a local minimum at this critical number.

In conclusion, the function has one critical number at x = 7/12, and there is a local minimum at this point.

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Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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Given: The box plot shown in the figure

To Determine: The percent of the data that is below 16

Solution

The given box plot can be interpreted as beow

From the abov, we can sobserve that

Therefore, the percent of that data below 16 falls in the 1st quartile.

Hence, the percent of that data below 16 is 25 %

The chi-square goodness-of-fit test can provide information on categorical data match an expected distribution and which categories are contributing to any deviation from that distribution.

The chi-square goodness-of-fit test is a statistical test used to determine whether a set of observed categorical data matches an expected distribution. Specifically, the test compares the observed frequencies of each category to the expected frequencies based on a hypothesized distribution, and calculates a chi-square statistic. This statistic measures the degree of difference between the observed and expected frequencies, with larger values indicating greater deviation from the expected distribution. If the chi-square statistic is large enough to reject the null hypothesis (i.e., the observed data do not match the expected distribution), the test can provide information on which categories are contributing the most to the discrepancy. This can help identify which categories are over-represented or under-represented in the observed data, and can inform further investigation into potential causes of the deviation. In summary, the chi-square goodness-of-fit test can provide information on whether observed categorical data match an expected distribution and which categories are contributing to any deviation from that distribution.

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Answer:

the answer is 10

Step-by-step explanation:

*please give me brainliest, i only need four more*

Answer:

-10

I did the math

(-4)-6

Answer:

7

Step-by-step explanation:

Because the parts of the circle are congruent, the segments are as well, we can use that to make an equation then solve it like normal

9x-34=4x+1

-1 on both sides

9x-35=4x

-9x on both sides

-35=-5x

x=7

Answer:

3 1/12

Step-by-step explanation:

The solution to the mathematical statement is -39/8y

From the question, we have the following statement that can be used in our computation:

-4/y plus (-7/8y) equals what

Mathematically, this can be represented as

-4/y + (-7/8y) =

Remove the brackets

This gives

-4/y + -7/8y =

Take the LCM

So, we have

-4/y + -7/8y = (-32 - 7)/8y

Evaluate the like terms

-4/y + -7/8y = -39/8y

Hence, the solution is -39/8y

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Answer:

57 inches

Step-by-step explanation:

It rained 5*6.5+7*3.5=32.5+34.5=57 inches in the past 12 days