A reservoir is 90% filled with liquid. The reservoir holds 1,330 gallons of liquid. How many gallons of liquid are needed to fill the reservoir to the top?
Choose the correct answer below.
A. 1,197 gallons
B. 133 gallons
C. 74 gallons
D. 1,330 gallons

Answer:

angle "E" =70°

Step-by-step explanation:

<ABC=<ADC

<ADC=<EAD (alternate angles)

<EAD=<DEA (because /DA/=/DE/

and <DEA=angle E, therefore answer=70°

The coordinates of point Q in the parallelogram is (2b + 2a,2c)

The coordinates are given as:

P(2b, 2c) Q(?, ?) S(0, 0) R(2a, 0)

The parallelogram form of the object indicates that the distances PQ and RS are equal.

The distance RS is calculated as:

RS = ( 2a - 0, 0)

This gives

RS = (2a, 0)

Coordinate Q is calculated as:

Q = P + RS

This gives

Q = (2b,2c) + (2a,0)

Evaluate the sum

Q = (2b + 2a,2c)

Hence, the coordinates of point Q is (2b + 2a,2c)

Midpoint of SQ=(b+ a ,c)

Midpoint of PR=(a+ b, c)

hence, SQ and PR bisect each other.

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The circumference of Circle C is found as 53π.

In the given figure:

AD = 28 and DB = 45

∠ADB = 1/2 *∠ACB

∠ADB = 90

Applying Pythagorean theorem in ΔABD.

AB² = AD² + DB²

AB² = 28² + 45²

AB = √2809

AB = 53

Radius = 53/2

circumference of Circle C:

C = 2πr

C = 2*π* (53/2)

C =  53π

Thus, the circumference of Circle C is found as 53π.

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Answer:

y=6x-8

Step-by-step explanation:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope m = 6 and a point on the line (1,-2). We can use point-slope form to find the equation and then simplify it to slope-intercept form.

Point-slope form: y - y1 = m(x - x1)

Substitute the values of m, x1, and y1:

y - (-2) = 6(x - 1)

Simplify the right side:

y + 2 = 6x - 6

Subtract 2 from both sides:

y = 6x - 8

This is the equation of the line in slope-intercept form.

The solution of the match is

(1) Orthocenter          (C) The point at which the altitudes of a triangle                                                

                                              meet.

(2) Centroid                 (D) The point at which the medians of a triangle

                                             meet.

(3) Circumcenter         (A) The point of intersection of the perpendicular                  

                                             bisectors of the sides of a triangle.

(4) Incentre                 (B) The point at which the three angle bisectors      

                                             of a triangle meet.

The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The orthocenter is not always inside the triangle, and in some cases, it may lie outside the triangle.

The centroid of a triangle is the point where the three medians of the triangle intersect. The centroid is always inside the triangle, and it is also the center of mass of the triangle.

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.  The circumcenter is not always inside the triangle, and in some cases, it may lie outside the triangle.

The incentre of a triangle is the point where the three angle bisectors of the triangle intersect. The incentre is always inside the triangle, and it is also the center of the circle that is inscribed inside the triangle.

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Complete Question:

Match the following.

(1) Orthocenter         (A) The point of intersection of the perpendicular                  

                                             bisectors of the sides of a triangle.

(2) Centroid                 (B) The point at which the three angle bisectors of

                                             a triangle meet.

(3) Circumcenter         (C) The point at which the altitudes of a triangle

                                              meet.

(4) Incentre                 (D) The point at which the medians of a triangle

                                             meet.

The area of the polygon with vertices P(1,2), Q(1,4), R(-1,6), and S(-3,2) is given as 10 units. Option B

We can find the area of the polygon with the given vertices by dividing it into triangles and adding their areas.

One way to divide the polygon into triangles is to draw a diagonal from vertex P to vertex R. This creates two triangles, PQR and PRS.

[tex]\frac{1 }{2} ((4 - 2) + (6--4) + (-2 - - 18) + (-6 - 2)[/tex]

= 1 / 2 ( 2 + `10 + 16 - 8)

= 1 / 2 ( 20

= 10

The area of the polygon is 10 units

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The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

What is variability?

To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.

To calculate the range, we subtract the smallest value from the largest value:

Largest value: 58

Smallest value: 10

Range = Largest value - Smallest value = 58 - 10 = 48

Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

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0.4

The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.

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Answer:

Step-by-step explanation:

Circle centre: (4,7)

Radius: 3

Equation is:

  [tex](x-h)^2+(y-k)^2=r^2[/tex]   (where (h,k) is center, r is radius)

  [tex](x-4)^2+(y-7)^2=3^2[/tex]

  [tex](x-4)^2+(y-7)^2=9[/tex]     (This is the general standard form )

in expanded form,

  [tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]

  [tex]x^2+y^2-8x-14y+56=0[/tex]

Note: Unless stated either form is an acceptable answer.

The trade balance must be negative.

If Canada imports more goods and services than it exports, the trade balance must be negative.

Here's a step-by-step explanation of why this is true and why options A and E are wrong:

1. The trade balance is calculated as the value of exports minus the value of imports. If imports are greater than exports, the trade balance will be negative (C). This m that Canada is seen spending more on goods and services from other countries than it is receiving from the sale of its own goods and services to other countries.

2. The current account balance includes the trade balance, but also considers other transactions such as income from investments and transfers like foreign aid. While it is possible that a negative trade balance could be offset by other positive inflows, we do not have enough information to determine whether the current account balance must be negative (A) or positive (B). Therefore, we cannot definitively say that A or B is true.

3. The financial account (formerly called capital account) balance records the net change in ownership of financial assets, such as stocks and bonds, between a country and the rest of the world. A negative financial account balance means that a country's residents are purchasing more foreign assets than foreign residents are purchasing of that country's assets. A positive financial account balance means the opposite. Since we only have information about the trade balance and not the financial transactions, we cannot determine whether the financial account balance must be negative (D) or positive (E).

Based on the information given, we can only conclude that the trade balance must be negative (C) if Canada imports more goods and services than it exports.

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The length of the minute hand of the clock is given as follows:

10.6 inches.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The ordered pairs for this problem are given as follows:

(0,0) and (7.5, 7.5).

Hence the distance between the two points, representing the length of the minute hand, is given as follows:

d = sqrt(7.5² + 7.5²)

d = 10.6 inches.

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Answer:

1/12

Step-by-step explanation:

Out of the total number of candies, 1/2 of the pink candies are round.

To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:

pink candies = 5/6

round candies among the pink ones = 1/5

Therefore, the fraction of candies that are pink and round is:

(5/6) x (1/2) x 1/5 = 1/12

So, 1/12 of the candies are pink and round.

The angle of x in the given circle is 51 degrees.

In the case when a tangent line and a secant line originate from the same external point, the mean of the exterior angle is equal to half the difference between the major arc and the minor arc that are created by the tangent and secant lines.

From the given figure we observe that the secant line and tangent line start from the same exterior angle.

Thus, according to the theorem of secant and tangent line of circle we have:

angle x = (DA - DB) /2

angle x = (178 - 76) / 2

angle x = 102 /2

angle x = 51 degrees.

Hence, the angle of x in the given circle is 51 degrees.

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When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique

Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.

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The distance from each landing point to the boat pulled ashore at point C is given by:-d = sqrt(25^2 (y^2/x^2 + 1))

WHAT IS TRIGONOMETRY ?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving distances, heights, angles, and other geometric measurements. Trigonometric functions such as sine, cosine, and tangent are used to relate the angles of a triangle to its sides. Trigonometry has many practical applications in fields such as engineering, physics, and architecture, and is essential for understanding and solving problems involving waves, oscillations, and periodic phenomena. It is also used in navigation, surveying, and astronomy, among other areas.

To solve this problem, we need to use the concept of right triangle trigonometry.

Let's assume that point C is directly opposite the midpoint of AB, and that the distance from point C to the midpoint of AB is x. Then we can draw a right triangle with legs of length x and 25 (half of 50) and a hypotenuse of length d (the distance from point C to each landing point).

Using the Pythagorean theorem, we can write:

d^2 = x^2 + 25^2

We also know that the angles opposite the legs of the right triangle are complementary, so we can use the tangent function to write:

tan(theta) = x/25

where theta is the angle between the hypotenuse and the side of length 25.

We can rearrange this equation to solve for x:

x = 25 tan(theta)

Now we can substitute this expression for x into the equation for d^2:

d^2 = (25 tan(theta))^2 + 25^2

Simplifying this equation, we get:

d^2 = 25^2 (tan^2(theta) + 1)

Finally, we can use the fact that tan(theta) is equal to the height of the opposite bank divided by the distance from point C to the midpoint of AB. Let's call this distance y. Then we have:

tan(theta) = y/x

Substituting this expression for tan(theta) into the equation for d^2, we get:

d^2 = 25^2 (y^2/x^2 + 1)

So the distance from each landing point to the boat pulled ashore at point C is given by:

d = sqrt(25^2 (y^2/x^2 + 1))

where x and y are the distances from point C to the midpoint of AB and the opposite bank, respectively.

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The model will be as follows: y = b0 + b1x1 + b2x2 + u

To write a model that allows the variance of u to differ between men and women, the best option is to use the heteroscedasticity model. This model will enable the variances to differ between the genders without depending on other factors.

The model will be as follows: y = b0 + b1x1 + b2x2 + u, Where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model. However, this model does not allow the variance of u to differ between men and women.

To achieve this, we need to modify the model to allow the variance of u to differ between men and women. This can be done by using the weighted regression model. The model will be as follows: y = b0 + b1x1 + b2x2 + u, where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model.

The weights can be represented as: wi = 1/σ^2i, where: wi = weight for observation, iσi = standard deviation of the ith observation. This model will allow the variance of u to differ between men and women without depending on other factors.

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Gillian pocket money is x, then Gillian  has [tex]5/12x[/tex]left after spending on snacks and bus fare.

The term "spending" refers to the act of spending money to buy goods or services. It is the act of exchanging money for something, usually a product, service, or experience. Buying groceries, paying for transportation, or purchasing clothing are all examples of spending. To avoid debt and achieve your financial goals, it is critical to manage your spending wisely in personal finance.

If Gillian spends one-third of her pocket money on snacks and one-quarter on bus fare, she spends 7/12 of her pocket money on snacks and bus fare.

This means she only has [tex]1 - 7/12 = 5/12[/tex] of her pocket money remaining.

As a result, if her pocket money is x, she has 5/12x left after paying for snacks and bus fare.

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Answer:

Step-by-step explanation:

Let's call the length of the shorter leg of the isosceles trapezoid "a" and the length of the longer leg "b".

From the problem, we know that:

a = 0.1x - 0.5 (length of one leg is 0.1.x - 0.5 meters)

b = 0.3x - 2.1 (length of the other leg is 0.3.x-2.1 meters)

Since we know that the trapezoid is isosceles, we know that a = b. So we can set the two expressions equal to each other:

0.1x - 0.5 = 0.3x - 2.1

Now we can solve for x:

0.2x = 1.6

x = 8

Now that we know x, we can substitute it back into the expressions for a and b to find their lengths:

a = 0.1(8) - 0.5 = 0.3 meters

b = 0.3(8) - 2.1 = 0.3 meters

Therefore, each of the legs of the solar panel are 0.3 meters long.

The volume of the ball is 9π (optionC)

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center.

The ball takes the shape of the sphere. The volume of a sphere is therefore calculated as ;

V = 4/3 πr³

r = d/2 = 3.8/2 = 1.9

V = 4/3 × π × 1.9³

V = 27.44 π/3

V = 9π ( nearest whole number)

therefore the volume of the ball is 9π (nearest whole number)

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The false statement regarding the normal distribution is given as follows:

99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The percentage of scores within 1 standard deviation of the mean is obtained considering that:

Hence the percentage is given as follows:

84.13 - 15.87 = 68.26%, which is different of 99.72%.

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The correct answer is that all of the following are characteristics of the normal probability distribution as given below.

A subfield of statistics known as probability studies random events and their likelihood of happening.

The statement "99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean" is actually a characteristic of the normal probability distribution.

The correct answer is that all of the following are characteristics of the normal probability distribution:

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Answer:

Step-by-step explanation:

asdf

48 is  length of chord AC.

How is a chord defined?

Three or more notes come together to form a chord. A single note, referred to as the root, serves as the foundation for chords. Triads will be covered in this lesson.

                         A root, third, and fifth are used to make them. A line segment connecting two locations on the circle's circumference is what is referred to as the chord of a circle. The diameter, which runs through the centre of the circle, is the lengthiest chord of the circle.

since OD intersects AB to form a right angle at point B, so it bisects the chord AC.

so AB = BC      (1)

given AB = 7x - 4

and CB = 6x  

from (1) we have

7x - 4 = 6x

x = 4

so AB = 7(4) - 4 = 24

CB = 6(4) = 24

length of chord AC = AB + BC = 24 + 24 = 48

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The complete question is -

Segment OD intersects AB to form a right angle at point B.

If AB = 7x - 4 and CB = 6x, what is the length of the chord AC?

The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.

The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.

To find the angle we use the trigonometric functions:

tan(θ) = grade = rise/run

Given that, the grade of the incline is 78%, then grade = 0.78.

θ = arctan(0.78) ≈ 38.7 degrees.

Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.

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Answer:

(2, 180)

Step-by-step explanation:

w(x)=-5x^2+20x+160

a=-5 b=20

x=-20/2x(-5)

x=2

w(2)=180

2, 180

The mass of dog having weight as 19 kg has its mass in grams as 1.9 x 10⁴ grams, option C.

In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.

Measuring units to determine the size, weight, or quantity of any object. Seven fundamental measurement units are utilized in daily life and across the globe.

A dog has a mass of 19 kg

The mass of the dog in grams is:

1 kilogram = 1000 grams

19.5 kg × (10³ g/1 kg) = 1.95 × 10⁴ g.

Thus, the mass of the dog in grams is 1.95 × 10⁴ g.

1000 grammes make to 1 kilogram (kg) (g).

1 kg = 1000 g

The mass m in kilogram (kg) multiplied by 1000 gives the mass m in grams (g)

m(g) = m(kg) × 1000.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.

The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c

a( b + c ) = ab + ac

Using this property, we can rewrite the expression 2(10+12) as

2( 10 + 12 ) = 2(10) + 2(12)

Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:

2(10+12) = 20 + 24

Simplifying further, we get

2(10+12) = 44

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The length of dDC is 16 cm. We can use the similarity of triangles ACD and ABE to find the length of DC.

We know A,B and c lie on a straight line segment A , E and d lie on a straight line segment

Substituting the given values, we get:

Simplifying the equation, we get:

AD = 20

Now, we can use the similarity of triangles ACD and ABE again, to find the length of DC.

CD/BE = AD/AE

Substituting the values, we get:

CD/4 = 20/(20+5)

Simplifying the equation, we get:

CD = 16

Therefore, the length of dDC is 16 cm.

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The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]

To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula

CI = X ± Zα/2 (σ/√n)

where

X = sample mean = 35.8

Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.

σ = sample standard deviation = 2.5

n = sample size = 40

Substituting these values into the formula, we get

CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].

Therefore, the correct option is (a) [34.7296, 36.8704]

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