What is the sum of (–2.1x + 3.7) and (5 + 4.9x)?
-7.0x + 8.7
-2.8x + 8.7
2.8x + 8.7
7.0x + 8.7

Answer:

5/6

Step-by-step explanation:18 total -3 absent = 15

15 divided by 3

18 divided by 3=

5/6

The ratio for the given two numbers is 5 : 6.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The total number of students are given as 18.

And, the number of students absent is 3.

Then, the number of present students is given as 18 - 3 = 15.

Now, the ratio as per the given case can be obtained as follows,

Number of students present ÷ Number of enrolled students

⇒ 15 ÷ 18

⇒ 15/18

⇒ 5 : 6

Hence, the required ratio for the two numbers is 5 : 6.

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Answer:

c = 55t

Step-by-step explanation:

Since there are no handling fees and the price of tickets is constant, we know the cost will be proportional to the number of tickets purchased. The generic form of an equation expressing a proportional relationship between cost (c) and number of tickets (t) is ...

c = kt

where k is the constant of proportionality (the cost per ticket). We can find k by using any of the data points given in the table. Using the first point, we have ...

110 = k·2

110/2 = k = 55 . . . . . divide by 2

Then using this value for k, the desired equation can be written ...

c = 55t

Answer:

Greater than 90 degrees.

Step-by-step explanation:

Let a vector R make angle [tex]\theta[/tex] with the x-axis. Then, the component along the x-axis would be

[tex]R cos\theta[/tex]

Component along y-axis would be

[tex]R sin\theta[/tex]

For [tex]0<\theta<90[/tex] both the components will be positive and lie in the first quadrant. If angle of vector is more than 90 degrees, one of the components would be negative. For example, angle between 90 to 180 degrees, x-component would be negative while between 180-270 degrees, both the components would be negative.

A pentagon has angle measures of 102°, 100°, 115°, and 110°. Therefore, The fifth angle measures 113°.

The sum of all the angles of Pentagon angles is 540°.

A pentagon has angle measures of 102°, 100°, 115°, and 110°.

To find the fifth angle so we subtract all angles above from 540°

102 + 100 + 115 + 110 = 540

540 - 102- 100 - 115 - 110 = 113°

Therefore, The fifth angle measures 113°.

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Answer:

false

Step-by-step explanation:

took the test

Rami sold 250 bottles of water and 150 bags of trail mix at the concert, totaling $1,475 in sales.

To solve the problem of how many bottles of water and bags of trail mix Rami sold, we need to set up and solve a system of linear equations based on the given information.

Let's define the variables:

- [tex]\( x \)[/tex] = the number of bottles of water sold

- [tex]\( y \)[/tex] = the number of bags of trail mix sold

From the problem, we have two pieces of information that we can turn into equations:

1. The total number of items sold is 400.

2. The total revenue from the items sold is $1,475.

We can write these two statements as equations:

1. [tex]\( x + y = 400 \)[/tex]

2. [tex]\( 3.50x + 4y = 1475 \)[/tex]

We now have a system of linear equations:

[tex]\[\begin{cases}x + y = 400 \\3.50x + 4y = 1475\end{cases}\][/tex]

Step 1: Solve the first equation for [tex]\( y \)[/tex]

[tex]\[y = 400 - x\][/tex]

Step 2: Substitute [tex]\( y \)[/tex] in the second equation

Replace [tex]\( y \)[/tex] in the second equation with [tex]\( 400 - x \)[/tex]:

[tex]\[3.50x + 4(400 - x) = 1475\][/tex]

Step 3: Simplify and solve for [tex]\( x \)[/tex]

Expand and simplify the equation:

[tex]\[3.50x + 1600 - 4x = 1475\][/tex]

Combine like terms:

[tex]\[3.50x - 4x + 1600 = 1475\][/tex]

[tex]\[-0.50x + 1600 = 1475\][/tex]

Subtract 1600 from both sides:

[tex]\[-0.50x = 1475 - 1600\][/tex]

[tex]\[-0.50x = -125\][/tex]

Divide both sides by -0.50:

[tex]\[x = \frac{-125}{-0.50} = 250\][/tex]

So, Rami sold 250 bottles of water.

Step 4: Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]

Substitute [tex]\( x = 250 \)[/tex] back into the first equation:

[tex]\[y = 400 - 250 = 150\][/tex]

So, Rami sold 150 bags of trail mix.

Conclusion

Rami sold:

- 250 bottles of water

- 150 bags of trail mix

To verify, we check the total revenue:

[tex]\[3.50 \times 250 + 4 \times 150 = 875 + 600 = 1475\][/tex]

The numbers match the given total revenue, confirming our solution is correct.

Answer:

A. 1/1287

B. 56/1287

Step-by-step explanation:

Probability of getting all are defective transistors is 5/12.

Given that, a box contains 13 ​transistors, 5 of which are defective.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

a) Probability of getting all are defective

Number of favorable outcomes = 5

Total number of outcomes = 12

Probability of getting all are defective = 5/12

b) Probability of getting none are defective

Number of favorable outcomes = 7

Total number of outcomes = 12

Probability of getting none are defective = 7/12

Therefore, probability of getting all are defective transistors is 5/12.

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The graphs of the linear equations 2x+3y=4 and 5x+6y=7 intersect at the point (2, 0).

The graphs of linear equations 2x+3y=4 and 5x+6y=7 intersect at a single point. To find the point of intersection, we can solve the two equations simultaneously.

Therefore, the graphs of the two equations intersect at the point (2, 0).

The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds

A fraction represents a part of a number or any number of equal parts.

There is a fraction, containing a numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called a proper fraction, otherwise, it is called an improper fraction. A proper fraction is also called a fraction that is less than 1. And an improper fraction is ≥ 1. A mixed fraction contains a sum of whole numbers and a proper fraction.

We have been given that a full bag of dog food weighs [tex]5\dfrac{1}{2}[/tex]  pounds.

First, we need to convert mixed fractions into simple fractions;

[tex]5\dfrac{1}{2}[/tex]  = 11/2

Also,  [tex]3\dfrac{3}{4}[/tex] = 15/4

Therefore, we know there are 3 and 3/4 bags in the cupboard, and each one of them weighs 5 and 1/2 lbs, thus the total amount in the cupboard is just their product.

[tex]5\dfrac{1}{2}[/tex]  × [tex]3\dfrac{3}{4}[/tex]

11/2  × 15/4

= [tex]20\dfrac{5}{8}[/tex]

Hence, The dog food we have if there are 3 3 4 bags in the cupboard is 20 5/8 pounds.

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Answer:

Step-by-step explanation:

Given that two tangents to a circle intersect at a point B outside the circle

A and C are points of contact.

By theorem on circles we have angle ABC is equal to 1/2 the difference of intercepted arcs.

Angle of minor arc =110 and hence major arc [tex]= 360-110 = 250[/tex]

Difference = [tex]250-110 =140[/tex]

Measure of angle ABC 1/2 of 140 = 70 degrees.

THE ANSWER IS 41 FEET

The composite function  (g o f)(x)  of f(x) and g(x) is 5x^2-18.

We have given that,

f(x)= x^2-2, g(x)=5x-8

The  value of (g o f)(x)=g(f(x)

g(f(x)=5(f(x))-8

=5(x^2-2,)-8

=5x^2-10-8

=5x^2-18

Therefore the composite function of f(x) and g(x) is 5x^2-18.

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Answer:

   2916/289 = 10 26/289 ≈ 10.09

Step-by-step explanation:

The ratio of areas of similar figures is the square of the scale factor. Here, the scale factor is the ratio of lengths, so is ...

  k = banner/sign = 54/17

The ratio of areas is k² = (54/17)² = 2916/289 = 10 26/289 ≈ 10.09

The ratio of the area of the school banner to the area of the sign is approximately 3.36:1. This was calculated by first finding the areas of both the banner and the sign, and then dividing the area of the banner by the area of the sign.

The subject of this question falls under Mathematics, and it deals with the concept of ratio and similar figures. In this case, the figures are a school banner and a sign, both of which are rectangular in shape. The ratio of their areas can be determined by calculating the areas of both figures and then finding the ratio of the two values.

Firstly, let's calculate the area of the school banner. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the area of the school banner = 54 inches (length) * 36 inches (width) = 1944 square inches.

Next, the sign's width isn't given, but because the two shapes are similar, the ratio of the banner's length to its width is equal to the ratio of the sign's length to its width. So, if we let 'w' be the width of the sign, then 54/36 = 17/w. Solving this for 'w', the width of the sign = [tex](17 * 36) / 54 = 17*2 = 34[/tex] inches. The area of the sign, then, is 17 inches (length) * 34 inches (width) = 578 square inches.

To get the ratio of the school banner's area to the sign's area, divide 1944 by 578, which equals approximately 3.36. Therefore, the ratio of the areas is 3.36:1. Meaning for every square inch of the sign, there are approximately 3.36 square inches of the school banner.

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This equation represents the circle having a radius of 3 units and a center situated at (-2, 4). Hence, graph D is correct.

Use the concept of a circle defined as:

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.

A circle is also known as the location of points that are evenly spaced apart from the center.

The radius of a circle is measured from the center to the edge.

The given equation of a circle is:

(X+2)²+(y-4)²= 9

Since we know that,

The general equation of the circle is,

(x-a)²+(y-b)²= r²

Where (a, b) is the center of the circle

r is the radius of the circle.

Now compare with the given equation we have,

(a, b) = (-2, 4)

And radius r² = 9

Then r = 3

Then this circle has a radius of 3 units and a center situated at (-2, 4).

Hence,

Graph D is correct.

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The complete question is:

Which of the following graphs matches the circle defined by this equation? (x-a)²+(y-b)²= r²

Answer:

b

Step-by-step explanation:

The equation of the line parallel to y = x + 4 passing through the point (6, 5) is y = x - 1, which has the same slope as the given line but a different y-intercept, determined by the given point.

The question asks for the equation of a line that is parallel to y = x + 4 and passes through the point (6, 5). Since the line we are looking for must be parallel, it will have the same slope as the given line, which in this case is 1 (since the coefficient of x is 1 in the given equation). The general form of the line we're looking for is y = x + b, where b is the y-intercept. To find the specific equation, we substitute the point (6, 5) into the equation to solve for b:

Thus, the equation of the line that meets the conditions is y = x - 1, which is not represented in the options given. Since none of the options match, it's possible that there might have been a mistake in the options provided or an error in the transmission of the question. However, based on the information given, this is the correct equation for the line parallel to y = x + 4 that passes through (6, 5).

A discrete uniform random variable has values which are equally likely to occur. The mean can be calculated by summing all the values of the variable and dividing by the number of values, represented as μ = Σx/k. The variance, a measure of dispersion, can be calculated using the formula σ² = Σ(x − μ)²/k.

In the context of a discrete uniform random variable, the mean (μ) and variance (σ²) can be calculated using specific formulas. This is related to the nature of a discrete uniform distribution, where x assumes the values x1, x2, ..., xk, and the probability of each outcome is equally likely.

Firstly, to find the mean

you simply need to add up all the values of x and divide by the number of values (k). This could be represented as μ = Σx/k.

Secondly, the variance can be calculated using the formula σ² = Σ(x − μ)²/k. In this equation, x represents the values of the random variable, μ is the mean (which we calculated earlier), and k represents the total number of values.

The concept here is essentially determining the central tendency (mean) and dispersion (variance) of a discrete uniform random variable. This is a fundamental topic in the field of probability and statistics.

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Marissa's course average is calculated by weighting each grade by its importance and then summing. This results in an overall average grade of 87.15%.

To calculate Marissa's course average given the percentage weight of each grading category and her averages in each category, we multiply each of her grades by the respective weight, then add the weighted grades together.

So, the calculation would be as follows:

Attendance grade: 100% * 0.05 = 5

Quiz grade: [tex]93 * 0.10 = 9.3[/tex]

Exams grade: [tex]86 * 0.60 = 51.6[/tex]

Final exam grade: [tex]85 * 0.25 = 21.25[/tex]

Adding these up, we get [tex]5 + 9.3 + 51.6 + 21.25 = 87.15[/tex]

So, Marissa's course average is 87.15%

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Answer:

Step-by-step explanation:

21

Answer:

Sample response: A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.

Step-by-step explanation: