51 is a multiple of 2,3,5,6,9,10 or none

Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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Answer:

1:7

Step-by-step explanation:

To solve the system of equations:

x - 5y = 15 (Equation 1)

4x - 3y = 26 (Equation 2)

There are several methods for solving a system of equations, but we will use the elimination method here. We will eliminate one variable by adding or subtracting the two equations.

Multiplying Equation 1 by 4, we get:

4x - 20y = 60 (Equation 3)

Now we can subtract Equation 2 from Equation 3:

(4x - 20y) - (4x - 3y) = 60 - 26

Simplifying, we get:

-17y = 34

Dividing both sides by -17, we get:

y = -2

Substituting this value of y in Equation 1, we get:

x - 5(-2) = 15

Simplifying, we get:

x + 10 = 15

Subtracting 10 from both sides, we get:

x = 5

Therefore, the solution to the system of equations is:

x = 5 and y = -2

In other words, the two equations intersect at the point (5, -2).

The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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Answer:

D. The answer is D. He pays approximately $150 each month

Some data in the question are missing. The complete question is :

The health center of a small, private university requires students to have appointments for visits. Each appointment takes an average of 5.6 minutes with a standard deviation of 3.5 minutes. The health center makes 100 appointments each day and is scheduled to be open for 10 hours. What is the probability that the total time spent for 100 students who have appointments for tomorrow will exceed 10 hours? (Hint: 10 hours=600 minutes.) Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Solution :

Let the time spent by \($i^{th} $\) students for the appointment be = \($X_i$\)

∴ E(\($X_i$\)) = 5.6

   V(\($X_i$\)) = \($3.5^2$\)

n = 100

The required probability

\($P\left( \sum_{i=1} ^{100} X_i \leq 600 \right)$\)

Now, \($E\left( \sum_{i=1} ^{100} X_i \right) = 100 \times E (X_i) $\)

                            = 100 x 5.6

                            = 560

\($V\left( \sum_{i=1} ^{100} X_i \right) = (100)^2 \times (3.5)^2 $\)

Standard deviation = 3.5 x 100

                                = 35

\($P\left( \sum_{i=1} ^{100} X_i \leq 600 \right)$\)

\($\Rightarrow P\left( \frac{\sum_{i=1}^{100} X_i -560} {35} \leq \frac{600-560}{35}\right)$\)

\($= \phi (1.14286)$\)

= 0.8735

= 0.874  (round to 3 decimal places)

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

We have,

To convert 6 kiloliters (kL) to fluid ounces (fl oz), we need to use the conversion factor between these two units.

The conversion factor states that 1 kiloliter is equal to 33814.0227 fluid ounces.

This means that for every kiloliter, there are 33814.0227 fluid ounces.

To convert 6 kiloliters to fluid ounces, we multiply the given value (6 kL) by the conversion factor (33814.0227 fl oz/kL).

= 6 kL x 33814.0227 fl oz/kL

= 202884.1362 fl oz

Therefore,

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

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Answer:

The answer is 12/5.

Step-by-step explanation:

5 + 2/5=

10/5 + 2/5=

12/5

The percentage of women with weights that are within the limits is:

60.93%

Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:

z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74

z-score for upper limit = (217 - 168.7) / 48.8 = 0.99

Next, we can use a z-table to find the corresponding probabilities for these z-scores:

Probability for lower limit = 0.2296

Probability for upper limit = 0.8389

Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093

Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.

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Answer:

m<EAG = 132°

Step-by-step explanation:  

First we have to solve for x.

W=7x+12

G=8x-15

A=180-(12x+24)

All 3 of those added together should equal 180.

7x+12+8x-15+180-(12x+24)=180

7x+12+8x-15+180-12x-24=180

3x+153=180

3x=180-153

3x=27

x=9

SO, m<EAG = 12x+24 = 12(9)+24=108+24=132

Answer:

\(\Huge \boxed{\text{13.66$\%$}}\)

Step-by-step explanation:

To find the rate, we need to use the following formula:

\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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Answer:

It could be any number from a range of -2 to 4.

Step-by-step explanation:

No, the trapezoids are not similar because their corresponding angles do not have the same measures.

The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.

Let's examine the angles of the trapezoids:

In trapezoid ABCD:

Angle A = 137 degrees

Angle B = 90 degrees

Angle C = 90 degrees

Angle D = 43 degrees

In trapezoid EFGH:

Angle E = 136 degrees

Angle F = 90 degrees

Angle G = 90 degrees

Angle H = 44 degrees

By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.

However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.

Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.

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Answer:

Angle sum Theorem says that the sum of the measures of the interior angles of a triangle is 180 degrees. ... This creates alternate interior angles that are congruent. Sum of two interior angles equals the opposite exterior angle...33 + 87 = yy = 120°

Step-by-step explanation:

The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are R' (2, 1), S' (4, 2), T' = (5, 4), and U' = (3, 3).

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle RSTU, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair R  = (1, -2) → Ordered pair R' = (-(-2), 1) = (2, 1).

Ordered pair S  = (2, -4) → Ordered pair S' = (-(-4), 2) = (4, 2).

Ordered pair T  = (4, -5) → Ordered pair T' = (-(-5), 4) = (5, 4).

Ordered pair U  = (3, -3) → Ordered pair U' = (-(-3), 3) = (3, 3).

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Answer:

distance moved by kayaker is 54m

23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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$127 is the answer.. can i have a brainliest? :)

Simplify the expression 5^6/5^2.

Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.

Therefore, the answer is the first option.

The option "On a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1" is the correct alternative.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. We can write -

\($y =log_{e} x\)

We have logarithmic function as -

\($y =log_{e} x\)

Refer to the graph of the logarithmic function attached. It can be seen that on a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1.

Therefore, the option "On a coordinate plane, a curve starts in quadrant 4 and curves up into quadrant 1" is the correct alternative.

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Answer:

x = -8

Step-by-step explanation:

-23 + 7 = -16

-16 ÷ 2 = -8

2 × -8 =-16 - 7 = -23

Answer:

how many times does 18 go into 97 and then subtractact then subtract the number you got with two your answer should be 0.185

Step-by-step explanation:

Answer:

The answer is 23 I just took this test and got it right

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

Answer:

suusy

Step-by-step explanation:

sus

Answer: cos4

Step-by-step explanation: 50 meters

B. 50-√3 meters

C. 100 meters

D. 100-√3 meters

40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.

The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."

A. sin 22

B. cos 22

C. tan 22

D. cot 22

Given

There are a pair of numbers that satisfy both constraints

1) the sum is 12

2) the difference is 5

So, let the numbers are (x) and (y)

From the first constraint ⇒ x + y = 12

From the second constraint ⇒ x - y = 5

So, we can draw the following lines

As shown the point of intersection between the lines = (8.5, 3.5)

So, the answer will be the numbers pair = 3.5 and 8.5

Answer: one number is 8 and the other number is 4.

8 + 4 = 12

8 - 4  =  4

Step-by-step explanation:

Equation 1: Sum:

x + y = 12

Equation 2: Difference:

x - y = 4

Solution:

x + y = 12

x  - y =   4

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Add the two equations together:

2x = 16

Divide both sides by 2:

x = 8

Solve for y:

Use equation 1 substituting for x:

x + y = 12

8 + y = 12

Subtract 8 from both sides:

y = 4