The length of the batter's box on a softball field is 1 ft more than twice the width. The area of the batter's box is 78 ft2. Find the length and width of the rectangular batter's box.

A container holds 2300 ounces fruit punch. A factory places the fruit punch into 32-ounce bottles, factory can produce 71  full bottles.

The uncia, an ancient Roman unit of measurement, is the source of the ounce (/ans/), any of numerous possible measures of mass, weight, or volume.

Although it is frequently used outside of the Anglosphere, it is predominantly employed in the United States to measure packaged foods and food portions, postal items, the areal density of fabric and paper, boxing gloves, and other items.

Although the avoirdupois ounce is the standard unit of mass for most applications, the actual weight of precious metals like gold, silver, platinum, palladium, rhodium, etc. is measured in "troy ounces," which are equal to 31.1034768 g.

Solving the question,

[tex]\frac{2300}{32} = 71.875[/tex]

Thus, we can say that a factory can produce 71 full bottles.

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Summary: The solution to the equation (x - 3)(x + 9) = -27 is x = 0 and x = -6.

Answer:

[tex]y=4x[/tex]

Step-by-step explanation:

Slope-intercept form:

[tex]y=mx+b\\[/tex]

m is the slope

b is the y-intercept

Parallel lines have the same slope, therefore we know that our new line will have the slope m = 4.

Since the point is the origin (0,0) we also know that the y-intercept will be 0.

Using this information, write the equation of the line:

[tex]y=4x+0[/tex]

Simplify:

[tex]y=4x[/tex]

A. The number of beds that are at the hostel will be 700 beds.

B. The planned capacity will be 105 beds.

C. The box of silver is heavier.

A. In a hostel , 30% of the beds are vacant and T

there are 210 guest beds at the hostel currently. The number of beds will be:

= 30% of x = 210

0.3x = 210

x = 210/0.3

x = 700

The number of beds is 700.

B. The planned capacity will be:

= 15% × 700

= 0.15 × 700

= 105 beds.

C. When the jeweler is trying to determine which box has the greatest weight and a box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. It should be noted that 14/25 = 0.56. Therefore, the silver is heavier.

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The number of days it will take the crew to lay all the track is; 27 days

The number of miles of track the crew has left to lay after 18 days is; 65 miles

We are given the equation that represents the length L (in miles) that is left to lay after d days as;

L(d) = 189 - 7d

where;

L is length in miles

d is number of days

Thus, the number of days it will take to lay all the tracks is;

Number of days = 189/7

Number of days = 27 days

The length L (in miles) that is left to lay after 18 days is;

L= 189 - 7(18)

L= 189 - 126

L= 65 miles

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Complete question is;

A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function. L(d) = 189 - 7d​

(How many days will it take the crew to lay all the track?)

(How many miles of track does the crew have left to lay after 18 days?)

Given:

Let's find the values of the variables so that the matrices are equal.

To find the values of the variables, divide the values of the result by the corresponding values of the main matrix.

We have:

• x = 4

• 7y = 21

Divide both sides by 7:

7y/7 = 21/7

y = 3

• z = 4

Therefore, we have:

• x = 4

• y = 3

• z = 4

ANSWER:

• x = 4

• y = 3

• z = 4

The cost is given as

Where x is the number of hours

The y-intercept is obtained from the graph as shown below

The value of the y-intercept is obtained to be 10

The y-intercept represents the value represents the fixed cost.

The slope of the cost is obtained from the cost function to be 0.5.

The slope represents the change in cost with respresent to time (hour).

Hence,

lank 1: 10

Blank 2: The fixed cost

Blank 3: 0.5

Blank 4: Change in cost or charge with respect to time used in hours

Blank 5:

Answer:

donde están lo calisado los continentes

Answer:

Hachem saves $875.

Step-by-step explanation:

$2,500 - 35% = $1,625

$2,500 - $1,625 = $875

Answer: The population

From the unique line postulate, we can draw unique line segment PM and as we are given that P is a point on the perpendicular bisector I of MN, the proof below has shown that using the definition of reflection, point P is the image of itself and point N is the image of point M

We are given :

Point P is a point on the perpendicular bisector, l, of MN.

Now, we want to prove that PM = PN

A Reflection in transformation can be defined as the transformation in which the figure is the mirror image of the other figure. This means that every point is a mirror reflection of itself .

With the aid of the definition of reflection, we can form the statement that point P is the image of itself , and point N is the image of M .

The line l which is the perpendicular bisector of MN acts as a Line of symmetry or axis of reflection.

Finally, when talking about transformations, it is common knowledge that reflections preserve length which means that the required proof PM = PN will hold true

Therefore, we will conclude that point N is the image of M .

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Answer: 1/2 + 1/3 = 3/6 + 2/6

Step-by-step explanation: you multiply 1/2 by 3/3 (1 x 3 and 2 x 3), which gives you 3/6, and then multiply 1/3 by 2/2 (1 x 2 and 3 x 2), which gives you 2/6.

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The number of wallets does Julian need to make in order to break even are 35.

X 1, ldots, and x n are the variables, and display style b, a 1, ldots, and a n are the coefficients. In mathematics, a linear equation is an equation that can be written as x 1, ldots, and x n + a n + b = 0. Ax + By = C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y). frequently actual numbers. The first-degree equations are linear equations. The following is the equation for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.

In order to "break even," his earnings and expenses have to be equal. The number of wallets (x) is represented in both equations. Simply put, you have to work out the equations in the system.

Both the given equation are equal to y

So,

16x - 130 = 8x + 150

16x - 8x = 150 + 130

x = 280/8

x = 35

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The slope of the equation, represented by the value of y/x for the given values of x and y, is 3/1, 3/1, 3.

The slope of a line can be used to gauge how steep it is. Slope is theoretically determined as "rise over run" (change in y divided by change in x).

The slope is the ratio of the rise in height between two points to the fall in elevation between those same two points.

The x and y values are provided.

The equation's slope is shown by the ratio y/x.

if y = -3 and x = -1,

y/x = 3/1

if y = 3 and x = 1

y/x = 3/1

if y = 6 and x = 2

y/x = 6/2 = 3

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From the given picture we can see

A right triangle DEC, where

The side opposite to angle C, ED has a length of 12 feet

The hypotenuse DC has length x feet

To find the value of x, we will use the sine ratio

Since the opposite side DE = 12

Since the hypotenuse DC = x

Reason:

The angles shown must add to 180 degrees if we want the top and bottom lines to be parallel. These angles are same side interior angles.

(x+4)+(3x) = 180

4x+4 = 180

4x = 180-4

4x = 176

x = 176/4

x = 44

Answer:

x=42because of 3x and f or g

The statement that are true about the equations − 3 ⁢ x − 8 = 19  and − 3 ⁢ x − 2 = 25 is that he equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

From the first equation, we were given,  − 3 ⁢ x − 8 = 19

then if we add 6 to the both sides of the equation then we will have

− 3 ⁢ x − 8 + 6 = 19 + 6

Then if we perform the simplification on this equation we have,

− 3 ⁢ x − 2 = 25

Which is the given equation i.e the second equation, hence the statement in the third option is correct.

Therefore, option C is correct.

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The solutions for the quadratic equation x² + 8x + 7 = 0 is option B x = -7 and x = -1

Given,

The quadratic equation : x² + 8x + 7 = 0

We have to find the solutions for this quadratic equation using the quadratic formula.

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = 1, b = 8 and c = 7

Now,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

= [tex]\frac{-8(+-)\sqrt{8^{2} -4(1)(7)} }{2(1)}[/tex]

= [tex]\frac{-8(+-)\sqrt{64-28} }{2}[/tex]

= (-8±√36)/2

= (-8±6)/2

Now,

Solve for

(-8 + 6) / 2 = -2/2 = -1

Solve for

(-8 - 6) / 2 = -14/2 = -7

That is,

The solutions for the quadratic equation x² + 8x + 7 = 0 is x = -1 and x = -7

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The most appropriate choice for fraction will be given by -

Each person get [tex]1\frac{5}{6}[/tex] baskets of apples.

What is fraction?

Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

Here,

Number of person = 3

Total baskets of apple picked = [tex]5\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex] baskets

Number of baskets each person got =

                                                                 [tex]\frac{11}{2} \div 3\\\frac{11}{2} \times \frac{1}{3}\\\frac{11}{6}\\1\frac{5}{6}[/tex]

Each person got [tex]1\frac{5}{6}[/tex] baskets of apples

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Answer:

$27

Step-by-step explanation:

[tex] \frac{3}{4} (20) + \frac{3}{5} (20) = 15 + 12 = 27[/tex]

Answer:

Step-by-step explanation:

You want to classify a number of functions as even, odd, or neither.

An even function has a graph that is symmetrical about the y-axis. It has the characteristic that ...

  f(x) = f(-x)

A polynomial function will be an even function if it consists entirely of even-degree terms. (A constant is degree zero, hence even degree.) A rational function will be an even function if it can be reduced to the ratio of even functions.

An odd function has a graph that is symmetrical about the origin. It has the characteristic that ...

  f(x) = -f(-x)

A polynomial function will be an odd function if it consists entirely of odd-degree terms. A rational function will be an odd function if it reduces to the ratio of an even and an odd function.

A function is neither even nor odd if it does not have one of the symmetries mentioned above. A polynomial consisting of a mix of even- and odd-degree terms will be neither even nor odd.

This is the ratio of a "neither" function to an even function. It is neither even nor odd.

The ratio can be reduced to ...

  [tex]\dfrac{2x^4+8x^3}{x^3+4x^2}=\dfrac{2x^3(x+4)}{x^2(x+4)}=2x[/tex]

This consists only of an odd-degree term. It is an odd function.

This is the ratio of an odd function to an even function. It is an odd function.

This is the ratio of two even functions. It is an even function.

As in problem 2, the function can be reduced:

  [tex]\dfrac{2x^3+8x^2}{x^3+4x^2}=\dfrac{2(x^3+4x^2)}{x^3+4x^2}=2[/tex]

It is an even (degree 0) function.

This is the ratio of an even function to a "neither" function. It is neither even nor odd.

The function reduces to x+2, which is neither even nor odd.

This is the ratio of two even functions. It is an even function.

This is the ratio of two odd functions. It can be reduced to the ratio of two even functions, so it is an even function.

  [tex]\dfrac{4x^3+2x}{7x^5+3x^3}=\dfrac{2x(2x^2+1)}{x^3(7x^2+3)}=\dfrac{4x^2+2}{7x^4+3x^2}[/tex]

a) It is 0.1275 times more probability that fewer than five of them have type o negative blood.

b) The probability that less than five of them are type o negative blood types is 0.9933.

c) 0.2708 probability that there are no donors who have type O negative blood. It would not be odd to have no type o negative donors because this likelihood is higher than 0.05.

There are only two outcomes that can occur for any individual. Type o negative blood is either present or absent. Any other person has no effect on a person's likelihood of having type O negative blood. To answer this question, we thus employ the binomial probability distribution.

The probability of precisely x successes on n repeated trials is known as a binomial probability, and X can only have two possible outcomes.

P(X=x)= [tex]C_{n,x.P^{x}.(1-P)^{n-x} }[/tex]

Additionally, p is the probability that X will occur.

This means that P=0.07

This mean that n = 18

Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So

P(X<3) + P(X≥3)=1

We want P(X≥3)

So,

P(X≥3) = 1-P(X<3)

In which

P(X< 3)= P(X = 0)+P(X = 1)+P(X = 2) = 0.2708 + 0.3669 +0.2348 = 0.8725

P(X≥3) = 1-P(X<3) = 1- 0.8725=0.1275

It's 0.1275 times more likely that fewer than five of them have type O negative blood.

P ( x < 5 )= P(X=0)+P(X=1)+P(X=3)+P(X=3)+P(X=4)

P(X=x)= [tex]C_{n,x.P^{x}.(1-P)^{n-x} }[/tex]

P(X=0)= [tex]C_{18,0(0.07)^{0}.(0.93)^{18} }= 0.2708[/tex]

P(X=1)=   [tex]C_{18,1(0.07)^{1}.(0.93)^{17} }= 0.3669[/tex]

P(X=2)= [tex]C_{18,2(0.07)^{2}.(0.93)^{16} }= 0.2348[/tex]

P(X=3)= [tex]C_{18,3(0.07)^{3}.(0.93)^{15} }= 0.0942[/tex]

P(X=4))= [tex]C_{18,4(0.07)^{4}.(0.93)^{14} }= 0.0266[/tex]

P(X < 5)=P(X=0)+P(X=1)+P(X=3)+P(X=3)+P(X=4)

0.2708+0.3669+0.2348+0.0942+0.0266=0.9933

P(X=0)= [tex]C_{18,0(0.07)^{0}.(0.93)^{18} }= 0.2708[/tex]

Probability of having no type O negative blood donors is 0.2708. It would not be odd to have no type o negative donors because this likelihood is higher than 0.05.

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The probability that the exactly 5 are white and 2 are red is126/1716 and,

the probability that at least 5 of the balls are white is 133/1716

Given that:-

Total number of balls in the urn = 13

Number of white balls = 6

Number of red balls = 7

Number of randomly selected balls = 7

We have to find the probability that the exactly 5 are white and 2 are red and the probability that at least 5 of the balls are white.

Probability that exactly 5 balls are white and  2 are red, P(x = 5) = [tex]\frac{^6C_5*^7C_2}{^{13}C_7}[/tex] = 126/1716 = 21/286

We know that,

Probability that atleast 5 balls are white = P(x = 5) + P(x = 6)

We know that,

P(x = 6) = [tex]\frac{^6C_6*^7C_1}{^{13}C_7}[/tex] = 7/1716

Hence,

Probability that atleast 5 balls are white = 126/1716 + 7/1716 = 133/1716.

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answer:

vertical

explanation:

vertical angles are angles opposite each other.

For x = 2

Since:

The function is discontinuous at x = 2. Besides since the function has a vertical asymptote on one of the sides, we can conclude it is a infinite discontinuity.

For x = 6:

Since:

The function is discontinuous at x = 6, at this point the function has a jump discontinuity

Answer

Option C is correct.

Side-Side-Side (SSS)

Explanation

The key to proving that two triangles are similar or congruent is to prove that three of either side lengths or angles are congrunet, similar or the same.

For the figure given, we have already been told that

Side AB = Side CD

Side AD = Side CB

Since the two triangles share a similar side in BD, we can complete this by saying

Side BD = Side BD

Side AB = Side CD

Side AD = Side CB

Side BD = Side BD

So, three of the sides of the triangles are equal or congruent.

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The unit rate of muffins per cup of almonds that the baker is for every 9 muffins, he uses 1 cup of almonds.

The unit rate is the ratio of a variable against another variable.

The unit rate explains the quantity relationship between the number of muffins produced and the cups of almonds used by the baker.

For this situation, a cup of almonds can make 9 muffins.

The total number of muffins made = 36

The total number of cups of almonds used = 4

The ratio of muffins to cups of almonds = 36:4 or 9:1

The unit rate of muffins per cup = 9 (36/4)

Thus, the baker is producing 9 muffins per cup of almonds used.

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Using the normal distribution, it is found that:

a) The sampling distribution is approximately normal, with mean 45 and standard deviation 4.

b) The answer is not dependent on the sample size, as the underlying distribution is normal.

c) 0.0001 = 0.01% probability that the average is less than half an hour.

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 given as follows:

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

For this problem, the parameters are given as follows:

[tex]\mu = 45, \sigma = 12, n = 9[/tex]

Hence the standard error of the approximately normal sampling distribution of sample means of size 9 is:

s = 12/sqrt(9) = 12/3 = 4.

As stated in the problem, the underlying distribution is normal, hence this is not dependent on the sample size.

For item c, the probability is the p-value of Z when X = 30, hence:

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

By the Central Limit Theorem:

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

Z = (30 - 45)/4

Z = -3.75

Z = -3.75 has a p-value of 0.0001.

Hence the probability is of 0.0001 = 0.01%.

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