Write an equation of the line. The line passes through point (0,-3) an is parallel to a line with slope 1.2.

Also write an equation for the line. The line passes through point (4,0) and has slope .5

Answer:

Side-Angle-Side

Explanation:

In the two triangles:

• Side: ,AB is congruent to EF (side length 1.4).

• Angle: ,B is congruent to F (angle 107.9 degrees).

• Side: ,BC is congruent to FG (side length 2.2).

Therefore, triangle ABC is congruent to triangle EFG by the Side-Angle-Side congruence postulate.

A male at the 70th percentile has a body temperature of 98.26°F.

The body temperature of a male at the 70th percentile, we need to use the cumulative distribution function (CDF) of the normal distribution.

The CDF gives the probability that a random variable (in this case, body temperature) is less than or equal to a certain value.

A standard normal distribution table or a calculator to find the corresponding z-score for the 70th percentile, and then use the formula:

z = \((x - \mu) / \sigma\)

x is the body temperature we want to find, mu is the mean, sigma is the standard deviation, and z is the z-score corresponding to the 70th percentile.

Using a standard normal distribution table, we find that the z-score for the 70th percentile is approximately 0.52.

Plugging in the values we have:

0.52 = (x - 98.1) / 0.30

Solving for x, we get:

x = 98.1 + 0.30 × 0.52

x = 98.26°F

To draw a well-labeled sketch to support the answer, we can start by drawing a normal distribution curve with the mean of 98.1°F and a standard deviation of 0.30°F.

The point on the x-axis corresponding to the body temperature of a male at the 70th percentile, which is 98.26°F.

The area under the curve to the left of this point, which represents the probability that a male has a body temperature less than or equal to 98.26°F.

The resulting sketch would look like this:

Normal Distribution Curve with 70th Percentile

The shaded area under the curve represents the probability that a male has a body temperature less than or equal to 98.26°F, is approximately 0.70 or 70%.

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Answer:

s = -35/6

Step-by-step explanation:

Let's evaluate your equation:

-6s = 35          <---- In order to evaluate this equation we must divide.

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

-6      -6

s = -35/6  <--- Final answer :D

I hope this helps :)

Answer:

\(s=-\frac{35}{6}\)

Step-by-step explanation:

\(-6s=35\\\\6s=-35\\\\s=-\frac{35}{6}\)

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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Answer:

6.55 cm

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.

Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:

c² = a² + b² - 2ab*cos(C)

Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:

QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)

QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270

QR² = 43

QR = 6.55 cm

Answer:

c= 1/ 90  f

Step-by-step explanation:

Step-by-step explanation:

remember, i = sqrt(-1)

let's go left to right :

(3i)(5i) = 3×sqrt(-1)×5×sqrt(-1) = 3×5×sqrt²(-1) = 15×-1 = -15

-15×(6+5i) = -90 - 75i

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Answer:

A: Y = X + 2.5

B: 10

Step-by-step explanation:

A: To form the equation you have to use one of the numbers in X (U.k Size) for this example we'll use 3 and to form the equation you have to see how much to add to X ( UK size) to get Y ( US size) and in this case it's +2.5

B: You can use the equation we just formed to get this answer by adding 2.5 to 7.5 which will give you 10

To find the work done in pumping the entire contents of the fuel tank into the tractor, we need to calculate the potential energy difference between the initial position of the gasoline in the truck's tank and its final position in the tractor's tank.

Given:

- Diameter of the cylindrical gasoline tank: 4 feet

- Length of the cylindrical gasoline tank: 5 feet

- Opening on the tractor tank is 5 feet above the top of the tank in the truck

First, let's calculate the volume of the cylindrical gasoline tank using the formula for the volume of a cylinder:

Volume = π * (radius^2) * height

The radius of the tank is half the diameter, so the radius is 4 feet / 2 = 2 feet.

Volume = π * (2^2) * 5 = 20π cubic feet

Since the entire contents of the fuel tank need to be pumped, the volume of gasoline to be pumped is 20π cubic feet.

To calculate the work done in pumping the gasoline, we need to find the vertical height through which the gasoline is lifted. This height is the sum of the height of the tank and the distance between the top of the tank and the opening on the tractor tank.

Height = 5 feet + 5 feet = 10 feet

The work done in pumping the gasoline can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the gasoline, and the distance is the height through which it is lifted. To calculate the weight of the gasoline, we need to know the density of gasoline. The density of gasoline can vary, but an average value is around 6.3 pounds per gallon.

Let's convert the volume of gasoline from cubic feet to gallons:

1 cubic foot = 7.48052 gallons (approximately)

Volume in gallons = 20π * 7.48052 ≈ 149.61π gallons

Weight of gasoline = Volume in gallons * Density of gasoline

Assuming the density of gasoline as 6.3 pounds per gallon:

Weight of gasoline = 149.61π * 6.3 ≈ 940.06π pounds

Finally, we can calculate the work done:

Work = Weight of gasoline * Height

Work = 940.06π * 10 ≈ 9400.6π foot-pounds

Therefore, the work done in pumping the entire contents of the fuel tank into the tractor is approximately 9400.6π foot-pounds.

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Answer:

23.9

Step-by-step explanation:

it just is so right

a) The magnitude of Pˉ is P.  b) The direction cosine of Pˉ with respect to the x-axis is 110/P.  c) The directional angle of Pˉ with respect to the z-axis is arctan(60/√(110^2+(-0.58P)^2)).

a) To find the magnitude of vector Pˉ, we use the formula for the magnitude of a vector in three dimensions, which is the square root of the sum of the squares of its components.

b) The direction cosine of a vector with respect to a specific axis is the ratio of the component of the vector along that axis to its magnitude. In this case, the x-component of Pˉ is 110, so the direction cosine with respect to the x-axis is 110 / P.

c) The directional angle of a vector with respect to a specific axis can be found using the arctan function. In this case, we use the y-component and z-component of Pˉ to find the angle between Pˉ and the z-axis.

Therefore, the magnitude of Pˉ is given by P, the direction cosine with respect to the x-axis is cos(θ_x), and the directional angle with respect to the z-axis is θ_z.

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The number of significant figures in each given number is as follows: 1. log5.403×10^−8 has 4 significant figures, 2. log0.001237 has 5 significant figures, 3. log3.2 has 2 significant figures, 4. log1237 has 4 significant figures, 5. Antilog 4.3 has 2 significant figures, 6. 10^4.37 has 4 significant figures, 7. pH=7.00 has 3 significant figures, 8. pKa=8.34 has 4 significant figures, 9. pKsp=11.30 has 4 significant figures, and 10. 10^−2.6 has 3 significant figures.

Significant figures are used to indicate the precision of a number. In general, non-zero digits are always significant, while zeros may or may not be significant depending on their position in the number.

log5.403×10^−8: The number has 4 significant figures, as all digits are non-zero.

log0.001237: The number has 5 significant figures, as all digits are non-zero.

log3.2: The number has 2 significant figures, as there are only two non-zero digits.

log1237: The number has 4 significant figures, as all digits are non-zero.

Antilog 4.3: The number has 2 significant figures, as there are only two non-zero digits.

10^4.37: The number has 4 significant figures, as all digits are non-zero.

pH=7.00: The number has 3 significant figures, as the trailing zeros after the decimal point are significant.

pKa=8.34: The number has 4 significant figures, as all digits are non-zero.

pKsp=11.30: The number has 4 significant figures, as all digits are non-zero.

10^−2.6: The number has 3 significant figures, as the trailing zeros after the decimal point are not significant.

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The equation of the circle with center (5,5) containing the point (0,-2) is \((x - 5)^2 + (y - 5)^2 = 74\)

The standard equation of a circle is given by: (x-h)2 + (y-k)2 = r2 Where (h,k) is the coordinates of center of the circle and r is the radius.

To determine the equation of the circle, we need to find the radius first. Since the center of the circle is (5,5), we can use the distance formula to find the distance between the center and the given point (0,-2):

\(distance = \sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}\\distance = \sqrt{[(0 - 5)^2 + (-2 - 5)^2]}\\distance = \sqrt{[(-5)^2 + (-7)^2]}\\distance = \sqrt{[25 + 49]}\\distance = \sqrt{[74]}\)

Therefore, the radius of the circle is sqrt[74].

Now, we can use the standard form of the equation of a circle to find the equation of the circle:

\((x - h)^2 + (y - k)^2 = r^2\)

where (h,k) is the center of the circle, and r is the radius.

Plugging in the values we have:

\((x - 5)^2 + (y - 5)^2 = (\sqrt{[74]})^2\)

Simplifying the equation:

\((x - 5)^2 + (y - 5)^2 = 74\)

Therefore, the equation of the circle with center (5,5) containing the point (0,-2) is \((x - 5)^2 + (y - 5)^2 = 74.\)

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Answer:

5/8 is a fraction

Answer:

x=8.1 /hour during the week

y=10.4 /hour in  the weekend

Step-by-step explanation:

x=earnings during the week

y= earnings in the wekend

13x+14y=250.90  |*-4

15x+8y=204.70    |*7

-52x-56y=-1003.6

105x+56y=1432.9

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

53x=429.3

x=8.1 /hour during the week

15*8.1+8y=204.7

121.5+8y=204.7

-121.5        -121.5

8y=83.2

:8    :8

y=10.4 /hour in  the weekend

The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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Answer:

os(390)   sin(330)   csc(60)

Step-by-step explanation:

Answer:

36/125

Step-by-step explanation:

Answer:

y = \(\frac{4}{3}\) x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

8x - 6y + 12 = 0 ( subtract 8x + 12 from both sides )

- 6y = - 8x - 12 ( divide terms by - 6

y = \(\frac{-8}{-6}\) x + 2 , that is

y = \(\frac{4}{3}\) x + 2 ← in slope- intercept form

I'll do problem 1 to get you started.

set A = multiples of 3 between 5 and 25 = {6, 9, 12, 15, 18, 21, 24}

there are 7 items in set A, so we can say n(A) = 7

set B = multiples of 5 between 5 and 25 = {5,10,15,20,25}

Here we have n(B) = 5

set C = multiples of 3 and 5, between 5 and 25 = {15}

n(C) = 1 which we can rewrite as n(A and B) = 1.

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

To summarize so far,

From those three facts, then we can say,

n(A or B) = n(A) + n(B) - n(A and B)

n(A or B) = 7 + 5 - 1

n(A or B) = 11

There are 11 values between 5 and 25 that are multiples of 5, multiples of 3, or both.

Those 11 values are: {5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25}

This is out of 25-5+1 = 21 values overall which are in the set {5,6,7,...,24,25}

So we have 11 values we want out of 21 overall, which leads to the probability 11/21

Final Answer:   11/21

Answer:

Solution given:

total outcomes between 5 to25 inclusive

n[T]=25-5+1=21

multiple of 5n[5]=5,10,15,20,25=5

multiple of 3n[3]=6,9,12,15,18,21,24=7

now

probability of getting multiple of 5p[5]=5/21

and

probability of getting multiple of 3 p[3]=7/21=1/3

again

the probability that the number is a multiple of 5 or 3 P[5or 3]=p[5]+p[3]=5/21+1/3=4/7

2:

.Good Limes n[GL] =10

Good Apples n[GA]= 8

Bad Limes n[BL] = 6

Bad Apples n[BA]= 6

total fruits n[T]=10+8+6+6=30

no of good apple n[G]=10+8=18

no of bad apple n[B]=6+6=12

again

I. Both are good limes

=\(\frac{n[GL]}{n[T]}×\frac{n[GL]-1}{n[T]-1}\)

=10/30*9/29=3/29

II.Both are good fruits

=\(\frac{n[BL]}{n[T]}×\frac{n[BL]-1}{n[T]-1}\)

=6/30*5/29=1/29

III. One is a good apple and the other a bad lime

=n[G]/n[T] *n[B]/(n[T]-1)

=18/30*12/29=36/145

The mode is 18.5.

What is mode?

In statistics, there  are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.

Formula for mode for grouped data is given by:

Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)

Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.

In the given problem l= 15.5

                                   f₀= 8

                                  f₁= 10

                                  f₂= 8

                                  h= 6

Putting all the values in equation (1) we obtain mode

                     mode= 15.5 +{(10-8)/(2×10-8-8)} ×6

                              = 15.5+(2/4)×6

                              = 15.5+ 3

                               = 18.5

Hence, the mode is 18.5.

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Answer:

8.5

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

41×178

4

1

×

17

8

Applying the fractions formula for multiplication,

=4×171×8

=

4

×

17

1

×

8

=688

=

68

8

Simplifying 68/8, the answer is

=812

Answer:

-34.

Step-by-step explanation:

This is an arithmetic sequence with first term a1  and common difference -2.

nth term = a1 + d(n - 1)

23rd term = 10 - 2(23-1)

= 10 - 44

= -34.

Answer:

-34

Step-by-step explanation:

The sequence starts with 10. Each subsequent term is 2 less than the previous term.

The common difference is -2.

The second term is 10 + (-2) × 1

The third term is 10 + (-2) × 2

The fourth term is 10 + (-2) × 3

Each term you subtract a multiple of -2 from 10. The multiple is 1 less than the number of the term multiplied by -2.

For term n, you get 10 + (-2) × (n - 1).

The 23rd term is:

10 + (-2) × (23 - 1) = 10 - 2 × 22 = 10 - 44 = -34

Answer:

C)  2

Step-by-step explanation:

step 1:  Find mean of data set

2+4+4+5+7+8 = 30

30/6 = 5

Mean = 5

step 2: subtract each data value from the mean and square it

5-2 = 3;   3² = 9

5-4 = 1;   1² = 1

5-4 = 1;   1² = 1

5-5 = 0;   0² = 0

5-7 = -2;   (-2²) = 4

5-8 = -3;   (-3²) = 9

Add the squared results:

9+1+1+0+4+9 = 24

Divide 24 by 6 to get the Variance of 4

Take the square root of the Variance to get the Standard Deviation

\(\sqrt{4}\) = 2

A tape diagram to represent 8-2+2 will be:

 +-----+-----+-----+-----+-----+-----+-----+-----+

 |     |     |     |     |     |     |     |     |

 +-----+-----+-----+-----+-----+-----+-----+-----+

  ^                                   ^

  |                                   |

  |                                   |

 8-2                                 +2

  |                                   |

  |                                   |

  v                                   v

 +-----+-----+                       +-----+

 |     |     |                       |     |

 +-----+-----+                       +-----+

    6                                 2

A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.

In this diagram, the first segment with 8 boxes represents the starting quantity of 8. Then, we subtract 2 from that by crossing out 2 boxes, leaving us with 6. Finally, we add 2 by drawing a new segment of 2 boxes, bringing us to a total of 8.

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