Create a system of linear equations that has one solution.

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

\(\Huge \boxed{\bold{\text{12 Boys}}}\)

\(\Huge \boxed{\bold{\text{30 Girls}}}\)

Step-by-step explanation:

Let the number of girls be \(g\) and the number of boys be \(b\).

According to the problem: \(b = \frac{2}{5} \times g\)

We also know that the total number of students is 42, so \(b + g = 42\).

Now, we have two equations with two variables:

We can solve these equations to find the values of \(b\) and \(g\).

Step 1: Solve for \(\bold{b}\) in terms of \(\bold{g}\)

From the first equation, we have\(b = \frac{2}{5} \times g\)

Step 2: Substitute the expression for \(\bold{b}\) into the second equation

Replace \(b\) in the second equation with the expression we found in step 1.

\(\frac{2}{5} \times g + g = 42\)

Step 3: Solve for \(\bold{g}\)

Now, we have an equation with only one variable, \(g\):

\(\frac{2}{5} \times g + g = 42\)

To solve for \(g\), first find a common denominator for the fractions:

\(\frac{2}{5} \times g + \frac{5}{5} \times g = 42\)

Combine the fractions:

\(\frac{7}{5} \times g = 42\)

Now, multiply both sides of the equation by \(\frac{5}{7}\) to isolate \(g\):

Step 4: Find the value of \(\bold{b}\)

Now that we have the value of \(g\), we can find the value of \(b\) using the first equation:

So, there are 12 boys and 30 girls in the class.

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For us to be able to determine how far will 32 gallons of gasoline will go, we will be using ratios and proportions.

We get,

Let x = the distance it can travel at 32 gallons

Therefore, 32 gallons of gasoline can make the motorcycle travel 640 miles.

Since lines mn are parallel lines, the value of x is equal to 32°.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

In Mathematics, the Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair.

By applying the Linear Pair Postulate to the two (2) angles on the straight lines cut by a transversal, we have the following:

x + 148° = 180°

x + 148° = 180°

x = 180° - 148°

x = 32°.

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Answer:

$65,000 , $50,000 and $35,000

Step-by-step explanation:

Lets us assume the CDs be C, stocks be S and Bonds be B

Given that

Total scholarship fund received = $150,000

i.e

C + S + B = $150,000 ......................... (1)

Now the each items invested percentage is given

And, the annual income from investment is $10,805

So, the next equation is

0.06C + 0.022B + 0.117S = $10,805 ....................... (2)

And, it is mentioned that

The $15,000 more in bonds than in CDs

B = C + $15,000 ........................ (3)

Now put the equation 3 in equation C is

2C + S = $135,000  ........................... (4)

0.082C + 0.117S = $10,475 ........................... (5)

Now multiply the 0.117S in equation 4

So

0.234C + 0.117S = $15,795

0.082C + 0.117S = $10,475

After solving this

0.152C = $5,320

C = CDS = $35,000

So

B = $35,000 + $15,000

B=   Bonds = $50,000

And S = Stock = $65,000

Answer:

CDs = 35000, Bonds = 50000, Stock = 65000

Step-by-step explanation:

Let amount invested in : CDs be 'C' , stock be 'S' , bonds be 'B'

As per total funds : C + B + S = 150000 [E1]

As per interest rates : 0.06C + 0.022B + 0.117S = 10805 [E2]

Given (15000 more invested in bonds than CDs :  B = C + 15000 [E3]

Putting equations : [E3] in [E2] & [E1]

C + (C+15000) + S = 150000 → 2C + 15000 + S = 150000

0.06C+0.022(C+15000)+0.117S = 10805 → 0.06C+0.022C+330+0.117S = 10805

By putting value of S from [E4] in [E5] :

0.082C + 0.117 (135000 - 2C) = 10475 → 0.082C + 15795 - 0.234C = 10475

5320 = 0.152C  → C = 5320 / 0.152 = 35000 [CDs]

B = C + 15000 = 35000 + 15000 = 50000 [Bonds]

By [E1]: 35000+50000+S = 150000 → S = 150000 - 85000 = 65000 [Stocks]

The inequality relation  -q > -7  can be represented in the form of q as q < 7

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

The value of A is - q > - 7

Now , multiplying by (-1) on both sides of the equation , we get

( -1 ) ( -q ) > ( -1 ) ( - 7 )

The inequality relation will change the sign from > to < and ,

q < 7

So , the value of the inequality relation A is q < 7

Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

Hence , The inequality relation  -q > -7  can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

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The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

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Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

Answer:So that's the change in Y. Now notice that X is increasing. By one unit each time. So we can calculate the slope. The slope is the change in Y divided by the change in X

Step-by-step explanation:

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

Nina's average cost per day for these four services is $5.

Since, Nina's monthly cost for the cable TV services is $99, and her monthly cost for cell phone calls and text messages is $59.70.

So her total monthly cost is:

$99 + $59.70 = $158.70

Now we need to find the number of days in a month.

Since, There are different ways to do this, but if we assume a month has 30 days,

= $158.70 / 30

= $5.29 (rounded to the nearest cent)

Therefore, Nina's average cost per day for these four services is $5.29. Rounded to the nearest dollar, her average cost per day is $5.

So, Nina's average cost per day for these four services is $5.

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Answer:

20 lb of 31 cent candy, 30 lb of 46 cent candy

Step-by-step explanation:

sorry don't have one

here is a smiley face for you

:D

The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we can assume the separate weights of each type of candies to be represented by variables.

Let we have:

x pounds of first type of candy is mixed with y pounds of second candy.

The weight of the mixture = x + y = 50 pounds

The cost of the mixture = 40 cents per pound  = \(40 \times 50 = 2000\) cents

Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = \(31x + 46y\)
Thus, we get \(31x + 46y =2000\)

Therefore, we got a system of two linear equations as:

\(x +y = 50\\31x + 46y =2000\)

From first equation, we get:

\(x = 50 -y\)

Substituting this value in second equation, we get:

\(31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30\)

Putting this value of y in equation for x, we get:

\(x = 50-y = 50-30 = 20\)

Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

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Answer:

its the first one you listed

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A graph which represents the solution to the given inequality (-0.25 ≥ -0.5n) is: graph .

An inequality is to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Translating the word problem into an inequality, we have:

-0.25 ≥ -0.5 × n

Next, we would find the solution to this given inequality in order to determine its graph:

-0.25 ≥ -0.5n

Dividing both sides by -0.5, we have:

n ≥ -0.25/-0.5

n ≥ 0.5

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Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Answer:

-2

Step-by-step explanation:

Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).

Answer:

N(h²) = - h² + 3

Step-by-step explanation:

Since N(t) = - t + 3

N(h²) is obtained by replacing t by h².

N(h²) = - h² + 3

Answer:

yes in what can I help you

For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.

f(x) = 7/8x² - 14

Substitute f(x) with 0 -

0 = 7/8x² - 14

Add 14 to both sides -

7/8x² = 14

Multiply both sides by 8/7 -

x² = 16

Take the square root of both sides -

x = ±4

Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.

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Answer:

Interest rate = .02 / 4 = .005 per quarter for 240 quaarters

A = 385 (1 + 005)^240

A = 3.31 * 385 =$1274

Yes, it would double

Answer:

the standard form of the equation is: a. y=7x^2-42x+67

Answer:

answer is in the picture above

Answer:

remainder: 504

Step-by-step explanation:

x³ – 2x² + ax +18 = x²(x-2) - 9*(x-2)

a = -9

(x³ – 2x² - 9x +18) / (x-9) = (x² +7x + 54)(x-9) + 504   ... long division

From the given i) and v) are discrete metric and ii), iii), iv) and vi) are continuous metric.

What distinguishes discrete from continuous data?

i)  'X' :  is discrete   because Number of automobile accidents per year is countable  (45, 78, 90) and cannot be fraction (4.5)

ii) 'Y'   : is continuous   because it could take any time to play 18 holes of golf.  (15.10 min)

iii) 'M'  :   is continuous because volume measured can be in fraction. Like 15.6 liters of milk produced by a cow

iv) 'N'  :  is  discrete  because eggs are countable . no half eggs or broken eggs are counted.  example: 30 eggs per month by a hen.

v) 'P'   : is discrete because permits issued are in countable amount and cannot go beyond or like half permit.

vi) 'Q':    is continuous because weight can be less or more and can be in fraction. 20 AND HALF OR 56,6 Kg.

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Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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7

a full rotation is 360°

divide 2520 by 360 it gives u 7.

7×360=2520

There are 7 complete rotations at 2520 degrees. Then the correct option is C.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

A rotation by 2520°.

Then the number of the rotations will be

⇒ 2520° / 360°

⇒ 7 rotation

Thus, the correct option is C.

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Given:

Distance traveled for upstream = 60 km

Time taken for upstream = 5 hours

Distance traveled for downstream = 60 km

Time taken for downstream = 3 hours

Required:

The rate of the boat in the still water.

Explanation:

Let x be the speed of the water and y be the speed of the current.

For upstream , the speed is given as

For downstream, the speed is given as,

Now,

Therefore,

Answer:

30000

Step-by-step explanation:

60×1000=60000

60000×3=180000

Answer:

the mean is 65

Step-by-step explanation:

Using the normal distribution, the area underneath the shaded region between the two z-scores is given by:

C. 0.6766.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Hence, for this problem, the area is the p-value of z = 0.75 subtracted by the p-value of z = -1.3.

Looking at the z-table, the p-values are given as follows:

Then:

0.7734 - 0.0968 = 0.6766.

Which means that option C is correct.

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An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Answer:

y=-1/3x-5

Step-by-step explanation:

Using slope formula, -7+3/6+6=-1/3

The Y Intercept is -5