the ratio of boys to students in a classroom is 2:5. there is are 30 total students. in the classroom. How many boys and how many are girls?

Answer:

Absolute value is the distance of a point from zero

Step-by-step explanation:

Answer:

1. 52

2. 13.6

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

1. What is 65% of 80

Let's set up an equation.

When we see %, we can put that number over 100.

65% = 65/100 = 0.65

"of" means to multiply.

So, 65% of 80 is

0.65 • 80 = x

Multiply.

x = 52

52

2. 34 is what percent of 40?

"is" symbolizes the equals sign (=)

"of" means to multiply.

"what percent" is our unknown.

34 is what percent of 40

34 = x/100 • 40

Divide both sides by 40.

0.85 = x/100

Multiply both sides by 100.

85 = x

85%

Hope this helps!

Answer:

Not 100% sure but here I go

Step-by-step explanation:

\(g(5) = - 5 - 4 = - 9 \\ g(5) = - 9\)

Answer:

given,

g(x) = -x-4

so

g(5) = -5-4

= -9

Step-by-step explanation:

it's from function.

A function in math is a like a machine that take an input from you and does something.

like here they asked x and they will return -x-4 .

g(5) means if x=5 then what is -5-4?(-9) for this function?

A person who placed a $5 bet on a horse with 11 to 2 odds and that horse won the Preakness race would win $27.50 in addition to having their $5 wager returned.

when odds are expressed in a ratio such as 11 to 2, it means that for every 11 chances the horse will lose, there are 2 chances it will win. This can also be expressed as a probability of 2/13 (2 chances out of a total of 13 possible outcomes).

To calculate the potential payout, you simply multiply the amount of the bet by the odds ratio and then add the original bet back in. In this case, $5 multiplied by 11/2 equals $27.50, which is the amount the person would win if the horse they bet on won the race.

understanding odds and how to calculate potential payouts can help individuals make informed bets and potentially win money at horse races and other betting events.

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Answer:

I don't know isisuwhvqb

Answer:

she will need 2/3 more jars

For a continuous random variable x, the probability of x taking on a specific value a is zero. This is due to the infinite number of possible values that x can take on within its range.

In the case of a continuous random variable, the probability density function (PDF) describes the likelihood of x taking on different values. Unlike discrete random variables, which can only take on specific values with non-zero probabilities, a continuous random variable can take on an infinite number of values within a given range. Therefore, the probability of x being equal to any specific value, such as a, is infinitesimally small, or mathematically speaking, it is equal to zero.

To understand this concept, consider a simple example of a continuous random variable like the height of individuals in a population. The height can take on any value within a certain range, such as between 150 cm and 200 cm. The probability of an individual having exactly a height of, say, 175 cm is extremely low, as there are infinitely many possible heights between 150 cm and 200 cm.

Instead, the probability is associated with ranges or intervals of values. For example, the probability of an individual's height being between 170 cm and 180 cm might be nonzero and can be calculated using integration over that interval. However, the probability of having an exact height of 175 cm, as a single point on the continuous scale, is zero.

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Considering the definition of an equation and the way to solve it, Hailey's age is 18 years.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "x" the age of the youngest child, then you have:

On the other hand, you know that the sum of their ages is 66. Then, the equation is:

x + x + 1 + x + 2 + x + 3 = 66

Solving:

4x + 6 = 66

4x = 66 - 6

4x = 60

x= 60 ÷ 4

x= 15

Remembering that "x + 3" is Hailey's age, then her age is calculated as: x+3= 15 +3= 18

Finally, Hailey's age is 18 years.

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approximately 97.5% of the sample will have values below 600.

The empirical rule states that about 68 % of the sample will be within one standard deviation of the mean, approximately 95 % will be within two standard deviations of the mean, and approximately 99.7 % will be within three standard deviations of the mean.

We must determine the z-score for a value of 600 using the following formula in order to determine the proportion of the sample that has values lower than 600.

z = (x - μ) / σ

If x is the value for which we wish to calculate the probability, is the sample mean, and is the sample standard deviation.

When we enter the values we have, we get:

z = (600 - 500) / 50 = 2

The number of 600 is therefore two standard deviations above the mean.

Approximately 95% of the sample will, under the empirical criterion, lie within two standard deviations of the mean. We can infer that since 600 is two standard deviations above the mean, 2.5% of the sample will have values above 600.

Therefore, approximately 97.5% of the sample will have values below 600.

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The approximate probability of randomly choosing one vegetable and one grain-based side dish from the available options is 0.16667.

To calculate the probability, we need to consider the number of possible outcomes and the total number of equally likely outcomes.

The restaurant offers three vegetable side dishes and five grain-based side dishes. For the first side dish, we have three vegetable options and five grain-based options. The probability of choosing a vegetable side dish first is 3/8, and the probability of choosing a grain-based side dish first is 5/8.

For the second side dish, after selecting one vegetable or grain-based side dish, we have two fewer options in that category. For the vegetable side dish, we would have two vegetable options remaining, and for the grain-based side dish, we would have four grain-based options remaining. Therefore, the probability of choosing a vegetable side dish as the second side dish is 2/7, and the probability of choosing a grain-based side dish as the second side dish is 4/7.

To find the probability of choosing one vegetable and one grain-based side dish, we multiply the probabilities of each step together: (3/8) * (4/7) = 12/56 ≈ 0.21429.

However, since we want the approximate probability, we can round the value to the nearest decimal place, which is 0.16667. Therefore, the approximate probability of randomly choosing one vegetable and one grain-based side dish is approximately 0.16667 or 16.67%.

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The composite result function of ( f ° g )(x) in the given functions f( x ) = x² + 9 and g( x ) = x² - 9 is x⁴ - 18x² + 90.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, we set up the composite result function f(g(x)).

f( x ) = x² + 9

f( g(x) ) = f( x² - 9 ) = ( x² - 9  )² + 9

f( g(x) ) = ( x² - 9  )² + 9

Expand the parenthesis

f( g(x) ) = ( x² - 9 )( x² - 9 )  + 9

f( g(x) ) = ( x²( x² - 9 ) -9( x² - 9 ) + 9

f( g(x) ) = x⁴ - 9x² - 9x² + 81 + 9

Collect and add like terms

f( g(x) ) = x⁴ - 18x² + 81 + 9

f( g(x) ) = x⁴ - 18x² + 90

Therefore,  ( f ° g )(x) in the given functions is x⁴ - 18x² + 90.

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Equation of line is 5y = -3x + 9 .

What is equation of line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

3x+5y-4=0

5y = -3x + 4

y = -3/5 x + 4/5

since it is parallel, its slope, m is -3/5

2x-3y-6=0

3y = 2x - 6

y = 2/3x - 2

at x-intercept, y is zero

2 = 2/3x

x = 3

therefore

y = mx + c

0 = (-3/5  * 3 ) + c

c = 9/5

equation is

y = -3/5x + 9/5

5y = -3x + 9

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The actual distance between the houses is 32.9 miles

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Scaling is the increase or decrease in the size of a figure by a scale factor.

Given that:

1 inch equals 9.4 miles

Two houses are 3.5 inches apart on the map, therefore:

Actual distance = 3.5 inches * 9.4 miles per inch = 32.9 miles

The actual distance is 32.9 miles

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The triangle ABC and XZY are proved to be congruent by SAS.

Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.

By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)

BC=YZ

AC=XZ

∠ACB=∠XZY

By SAS ΔABC≅ΔXYZ

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Answer:

30241530

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

First, find the length of the rectangle. We know the width is 4, and the ratio of the width to length is 2:5, making the width ratio four, it is 4:10. Therefore, the length of the rectangle is 10. Since the pentagon is regular, and one side of the pentagon is 4, multiply 4 by 4 =16. Then we can find the perimeter of the figure: 16+ 10 + 10 + 4 = 40.

Answer:

it is helpful to constuct d because it makes the graph easier to understand

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Given

y = x² + 1

y = x

Equating gives

x² + 1 = x ( subtract x from both sides )

x² - x + 1 = 0

Consider the discriminant Δ = b² - 4ac

with a = 1, b = - 1 and c = 1

b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3

Since b² - 4ac < 0 then there are no real solutions

On solving the provided question we can say that triangle BAD and CBE are congruent by SAS property

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in the triangle BAD and CBE

angle BAD = angle BCE

angle B = angle B

AB = BC( corresponding angles are equal)

so,

triangle BAD and CBE are congruent by SAS property

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Answer:i think its 115 degres

Step-by-step explanation:

The simplest form of the radical expression 4^(3√(3x)) + 5^(3√(10x)) cannot be determined without more information.

The given expression is 4^(3√(3x)) + 5^(3√(10x)). It appears to have a combination of exponentiation and radicals. However, it is unclear whether the exponent applies solely to the base numbers (4 and 5) or to the entire expression within the parentheses (3√(3x) and 3√(10x)). The expression can be interpreted in different ways, depending on the intended grouping of operations.

If the exponent only applies to the base numbers, the expression simplifies to 4^3√(3x) + 5^3√(10x). However, if the exponent applies to the entire expression within the parentheses, the expression would be written as (4^(3√(3x))) + (5^(3√(10x))). These two interpretations yield different results, and without further clarification or grouping, it is not possible to determine the simplest form of the expression.

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Answer:

0 solutions

Step-by-step explanation:

A Modulus can never be equal to a negative

Answer:

D

Step-by-step explanation:

There is an infinite amount of answers. I know this because when a calculated it, I got -11/3, which you can simplify by dividing the numerator and denominator with the same number (Like -11/3 & 3/3). You can also multiply both of them with the same number (I did 10 in this example) and get something like -110/30.

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Answer:

(x+5)²(x²+5)

Step-by-step explanation:

Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25

On factorising we have:

x²+5x+5x+25

= x(x+5) +5(x+5

= (x+5)(x+5)

= (x+5)²

The LCM can be calculated as thus

| x²+5, (x+5)²

x+5| x²+5, (x+5)

x+5| x²+5, 1

x²+5| 1, 1

The factors of both equation are x+5 × x+5 × x²+5

The LCM will be the product of the three functions i.e

(x+5)²(x²+5)

This hives the required expression.

If f and f ◦g are one-to-one, then g is one-to-one.

A function f is one-to-one if it has one and only one preimage in the domain. one-to-one functions are also called injective functions.

i.e., distinct points in the domain will have distinct images.

Mathematically, if f(x) = f(y), then x = y

So here f and f o g are one-to-one.

i.e., f(x) = f(y) ⇒ x = y

and (f o g)(x) = (f o g)(y) ⇒ x = y

So consider g(x) = g(y)

⇒ f(g(x) = f(g(y))

⇒ (f o g)(x) = (f o g)(y)

⇒ x = y [Since f o g is one-to-one]

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Answer:

1.33

Step-by-step explanation:

The cost function for producing x boxes of computer disks is given by C(x) = 8x + 90,000x + 150,000. The total cost function for producing x rolls of film is given by C(x) = 6x + 1,000x.

The marginal cost represents the change in cost when one additional unit is produced. In the case of producing boxes of computer disks, the marginal cost is given as 8 + 90,000. To obtain the cost function, we integrate the marginal cost with respect to x. The integral of 8 with respect to x is 8x, and the integral of 90,000 with respect to x is 90,000x. Adding these two terms to the fixed cost of $150,000 gives us the cost function for producing x boxes of computer disks: C(x) = 8x + 90,000x + 150,000.

For producing rolls of film, the marginal cost is given as 6. To find the total cost function, we integrate this marginal cost with respect to x. The integral of 6 with respect to x is 6x. Adding this term to the fixed cost of $1,000 gives us the total cost function for producing x rolls of film: C(x) = 6x + 1,000x.

Therefore, the cost function for producing x boxes of computer disks is C(x) = 8x + 90,000x + 150,000, and the total cost function for producing x rolls of film is C(x) = 6x + 1,000x.

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Answer:

B

Step-by-step explanation:

Answer:

-16+54x

Step-by-step explanation:

9(-1x+1)-7(2x+5)

-9x+9-7x+45

-9x-7x+9+45

-16x+54