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Roger can finish his math homework in 6 hours. Trish can finish the same homework in 5 hours. What part of the homework will Roger and Trish finish if they work together for 1 hours?

Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

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Julieta's claim about the quadrilateral is false.

The statement is given as:

It is impossible to draw a quadrilateral that is not a trapezoid and not a parallelogram.

The condition for a shape to be a quadrilateral is that the shape must have four sides.

An irregular shape that has four sides is a quadrilateral, but neither a quadrilateral nor a parallelogram

Therefore, Julieta's claim is false

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The probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.

The number of successes in a certain number of independent trials is modelled by the binomial distribution, which has just two potential outcomes for each trial, commonly referred to as "success" and "failure."

We can solve this problem by using the binomial distribution formula:

[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]

where:

P(X=k) is the probability of getting exactly k automobiles that fail the emissions test

n is the number of automobiles being tested, in this case, n = 10

k is the number of automobiles that fail the emissions test

p is the probability of a single automobile failing the emissions test, in this case, p = 0.05

Using this formula, we can calculate the probability of getting exactly k failures for k = 0, 1, 2, ..., 10, and then add up these probabilities to get the probability of getting at least one failure.

The probability of getting exactly k failures is:

[tex]P(X=k) = (10\ choose\ k) * 0.05^k * 0.95^{(10-k)[/tex]

Using a calculator or statistical software, we can calculate these probabilities:

[tex]P(X=0) = (10 choose 0) * 0.05^0 * 0.95^10 = 0.5987\\P(X=1) = (10 choose 1) * 0.05^1 * 0.95^9 = 0.3151\\P(X=2) = (10 choose 2) * 0.05^2 * 0.95^8 = 0.0746\\P(X=3) = (10 choose 3) * 0.05^3 * 0.95^7 = 0.0119\\P(X=4) = (10 choose 4) * 0.05^4 * 0.95^6 = 0.0013\\P(X=5) = (10 choose 5) * 0.05^5 * 0.95^5 = 0.0001\\[/tex]

[tex]P(X=6) = (10 choose 6) * 0.05^6 * 0.95^4 = 0.0000\\P(X=7) = (10 choose 7) * 0.05^7 * 0.95^3 = 0.0000\\P(X=8) = (10 choose 8) * 0.05^8 * 0.95^2 = 0.0000\\P(X=9) = (10 choose 9) * 0.05^9 * 0.95^1 = 0.0000\\P(X=10) = (10 choose 10) * 0.05^10 * 0.95^0 = 0.0000\\[/tex]

The probability of getting at least one failure is:

[tex]P(X > =1) = 1 - P(X=0) = 1 - 0.5987 = 0.4013[/tex]

Therefore, the probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.

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The slope of the relation with the equation 5x - 3y = 4 is 5/3

To find the slope of the line whose equation is 5x - 3y = 4, we need to rearrange the equation to be in slope-intercept form, y = mx + b, where m is the slope of the line.

First, we'll subtract 5x from both sides:

-3y = -5x + 4

Next, we'll divide both sides by -3 to isolate y:

y = (5/3)x - 4/3

Now we can see that the slope of the line is 5/3.

So the correct answer is: 5/3

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Answer:

e = 3

Step-by-step explanation:

Use the property of the proportion to find e (cross-multiply):

[tex]10 \times e = 6 \times 5[/tex]

[tex]10e = 30[/tex]

Divide both sides of the equation by 10 to make e the subject:

[tex]e = 3[/tex]

Answer:

3

Step-by-step explanation:

6 x 10 = 60

6 x 5 = 30

5/10 = 30/60

30/ 10= 3

60/ 10 = 6

E/6 = 3/6

E=3

An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (50.25 - 2)/(5 - 0)

Slope (m) = 48.25/5

Slope (m) = 9.65.

At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 9.65(x - 0)

y = 9.65x + 2

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From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.

Simple interest is the interest system that computes interest only on the principal for each period.

Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.

The principal loan amount borrowed by Tamika = $5,000

The interest rate per year = 8%

The loan period = 24 months = 2 years (24/12)

Simple Interest = Principal x Rate x Period

= $800 ($5,000 x 8% x 2)

Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.

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Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?

Answer:

a. 3x = 23-2

3x = 21

x = 21÷3

x = 7

b. 5x - 2 = 4

5x = 4+2

5x = 6

x = 6÷5

x = 1.2

c. 3x = 23-2

3x = 21

x = 21÷3

x = 7

d. 7 = 2x+0.5x

7 = 2.5

x = 2.5÷7

x = 2.8

When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.

The expression 2w⁻²z⁰ can be simplified as follows:

2w⁻²z⁰ = 2/w² * z⁰

Since z⁰ = 1 for any non-zero value of z, we can simplify further:

2w⁻²z⁰ = 2/w² * 1

Now we can substitute w = 10 into the expression:

2(10)⁻² * 1 = 2/100 = 1/50

In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.

So, correct option is A.

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The probability that the water will run out on a given day is  0.0038.

To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:

where;

x = of 380 million gallons,

µ is the mean daily demand of water = 300 million gallons,

σ is the standard deviation = 30 million gallons.

Substituting the given values:

z = (380 - 300) / 30

z = 2.67

Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.

Therefore, the probability that the water will run out on a given day is  0.0038.

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The shaded area of the portion as shown in the diagram is 78.04 cm².

Area is the region bounded by a plane shape.

To calculate the shaded area of the portion, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.

The projection of (v + w) onto u is (-8 √(2)i + 6 √(2)j).

Now, let's consider the given vectors u = - i + j, v = 8i - 2j, and w = - 4j. The question asks us to find the projection of vector v + w onto the vector u, denoted as proj_u(v + w). To find this projection, we need to use the dot product between the two vectors.

First, we need to calculate v + w, which is (8i - 2j) + (-4j) = 8i - 6j. Next, we calculate the dot product of u and (v + w):

u · (v + w) = (-i + j) · (8i - 6j)

= -8i + 6j - 8i + 6j

= -16i + 12j

The dot product measures the similarity between two vectors, and in this case, it gives us the component of (v + w) that is parallel to u. To find the projection of (v + w) onto u, we need to divide this component by the magnitude of u:

proj_u(v + w) = (u · (v + w)) / ||u||

= (-16i + 12j) / √(2)

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Answer:

17

Step-by-step explanation:

11+6=17

(a) The exact value of sin B is 6 / 12.53

(b) The exact value of tan A is 11 / 6

(c) The exact value of cos A is 6 / 11

The value of sin (B), cos (A) and tan (A) is calculated by applying trigonometry ratio as follows;

The trigonometry ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The value of the hypotenuse side of the right triangle is;

L = √ (6² + 11²)

L = 12.53

(a) The exact value of sin B is;

sin B = 6 / 12.53

(b) The exact value of tan A is;

tan A = 11 / 6

(c) The exact value of cos A is;

cos A = 6 / 11

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The value of x in the polygon is 5 centimetres.

A polygon is a two-dimensional geometric figure that has a particular number of sides.

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .

Therefore, using the ratio of the similar polygon, let's find the value of x as follows:

35 / x = 42 / 6

cross multiply

35 × 6 = 42x

210 = 42x

divide both sides of the equation by 42

x = 210 / 42

x = 5 cm

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1. It would be better to use the median to describe the data set.

2. It would be better to use the median to describe the data set.

3. It would be better to use the mean to describe the data set as the average salary of the workers is to be calculated.

4. It would be better to use the mean to describe the data set as the average test grade of the class is to be calculated.

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Answer:

Step-by-step explanation:

x^2 = 8

x=+-√8

Answer:

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

We know that area is the product of two dimensions.

Hence we consider the square of the scale factor when comparing areas of similar figures.

The surface area of solid B is k² times the surface area of solid A:

Substitute and calculate:

Answer:

A.) Newly married couples tend to have two earners.

Step-by-step explanation:

When newly married couples first start off marriage, they tend to both work to make stable income since they recently had to work to make money for only their selves, which is why they both tend to have two earners.

We need to use equations C and D:

C. 4 ÷ 12 = 1/3

D. 16 ÷ 12 = 4/3

We need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:

C. 4 ÷ 12 = 1/3

D. 16 ÷ 12 = 4/3

Equation C shows that each serving is 1/3 of a pound

Equation D shows that Mariana can make 4/3 servings

Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.

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Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr

To determine the speed of the boat in still water, we can write an equation to represent this.

The speed as it travels upstream = x - 2

The speed as it travels downstream = x + 2

The total distance travelled by the boat = 15 + 15 = 30mi

Let's write an equation to represent this;

15/(x - 2) + 15/(x + 2) = 4

simplifying this;

15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)

15x + 30 + 15x - 30 = 4x² - 16

30x = 4x² - 16

4x² - 30x - 16 = 0

Solving for x;

x = -0.5, 8

But since the speed can't be negative, the speed is 8 mi/hr

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Scaled version means adjusted value from the original size. For example, 3:5 could be a scaled version of 6:10.

Scale Version of an object is a replica or model of the original object that has been proportionally reduced or enlarged in size. The scale of a model is the ratio of the size of the model to the size of the original object. For example, if a model of a building is one-tenth the size of the actual building, then the scale of the model is 1:10, which means that every measurement on the model is one-tenth of the corresponding measurement on the actual building.

Scale versions of objects are often used in engineering, architecture, and design to create smaller or larger versions of objects that can be studied, tested, or used for other purposes. For example, architects might create scale models of buildings to study their design and appearance, while engineers might create scale models of machines or structures to test their performance under different conditions.

Scale versions can also be used in maps, where the scale is used to indicate the relationship between the size of the map and the size of the area it represents. In this case, the scale might be represented as a ratio, such as 1:10,000, or as a statement of the size of a unit of measurement on the map, such as 1 inch equals 1 mile.

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Answer:

Y=-10x+1 with x being -5

y = -10 *-5 +1

y = -50+1

y =-49

Answer:

Both sides are equal, and are equvalent to 5 square root of 2

Step-by-step explanation:

This is a special right angled triangle known as the 45-45-90 triangle

The hypotenuse of a 45-45-90 triangle is x square root 2, with x being both sides of the triangle

10=x square root of 2 (Divide both sides by square root of 2)

10/square root of 2=x (Rationalize)

x=5 square root of 2

The area of each circle would be given below:

Circle A= 153.86 in²

Circle B = 314in²

Circle C = 615.44in²

Circle D = 452.16 in²

To calculate the area of a circle, the formula that should be used is given below such as follows:

Area of circle = πr²

For circle A;

radius = 7 in

area = 3.14×7×7 = 153.86 in²

For circle B;

radius = 3+7 = 10in

area = 3.14×10×10 = 314in²

For circle C;

radius = 10+4 = 14 in

area = 3.14×14×14

= 615.44in²

For circle D;

radius = 14-2 = 12in

radius = 3.14×12×12

= 452.16 in²

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Answer:

When you divide 781.253 by 100, you get 7.81253 as the result.

The digit 2 is in the hundredths place in the dividend 781.253. Since we are dividing by 100, which has two decimal places, we move the decimal point two places to the left in the dividend to get the quotient.

Therefore, the digit 2 is in the ten-thousandths place in the quotient 7.81253.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

A. x² + (y - 3)² = 36.

D. x² + (y + 8)² = 36.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = diameter/2 = 12/2 = 6 units.

Center, (h, k) = (0, 3).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 6²

x² + (y - 3)² = 36.

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