If there are 48 students in a school play the ratio of boys to girls is 5:7 how many more girls than boys are in the play?

Answer:

Area of ΔDEF is [tex]45\ cm^2[/tex].

Step-by-step explanation:

Given;

ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Length of AB = [tex]2\ cm[/tex] and

Length of DE = [tex]6\ cm[/tex]

Area of ΔABC = [tex]5\ cm^2[/tex]

Solution,

Since, ΔABC and  ΔDEF is similar and ∠B ≅ ∠E.

Therefore,

[tex]\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}[/tex]

Where triangle 1 and triangle 2 is  ΔABC and  ΔDEF respectively.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

[tex]\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2[/tex]

Thus the area of  ΔDEF is [tex]45\ cm^2[/tex].

The total number of college students was 17.94 million.

Step-by-step explanation:

Percentage of part time students = 34%

Number of part time students = 6.1 million

Let,

x be the total number of students

According to statement,

34% of x = 6.1 million

[tex]\frac{34}{100}x=6.1\ million\\0.34x=6.1[/tex]

Dividing both sides by 0.34

[tex]\frac{0.34x}{0.34}=\frac{6.1}{0.34}\\x=17.94\ million[/tex]

The total number of college students was 17.94 million.

Keywords: percentage, division

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Answer:

40 and 50

Step-by-step explanation:

We know that River's mom drove for 45 minutes. Furthermore, at x miles per hour for a time amount y, she drove 10 miles, and at x+10 miles per hour for time amount z, she drove 25 miles. We can set up the equations like this:

x*y = 10

(x+10)*z = 25

y+z = 0.75

I knew to include time as the variable because time was given at the end, and is the only way possible to solve this. Furthermore, we can multiply x and y because we drive for x miles per hour for y hours, so

[tex]\frac{x miles}{hours}  * \frac{yhours}{1}  = xmiles*y[/tex]

I turned 45 into 0.75 as 45 is 3/4 of an hour, and y and z are in hours.

We're kind of stuck here, so it would be nice if we could limit the variables in an equation. One way to do this would be to solve for y in the first equation, so x=10/y. Then, we can plug that into the second equation to get

(10/y+10)*z=25

Combining that with the third equation, we can solve for z in the second equation to get that 25/(10/y+10)=z, and then plug that into the third to get that

y+25/(10/y+10) = 0.75

Multiplying both sides by 10/y+10 to get rid of the denominator, we get

10+10y+25=7.5/y+7.5

Then we multiply by y to get rid of the denominator

10y+10y²+25y=7.5+7.5y

Subtracting 7.5+7.5y to get everything on one side for a quadratic equation

10y²+27.5y-7.5=0

Plugging this into the quadratic equation, we get than y either equals -3 or 0.25. It's clear that you can't have negative time, so y = 0.25

Then, 0.75-0.25=0.5=z, and 10/0.25=40, so x=40, and x+10=50 for the 2 driving speeds

Answer: 838% to the nearest percent

Step-by-step explanation:

225 - 24 =201

=201/24 * 100

= 838% to the nearest percent

After solving for x1, we get

[tex]x_1 = 2M-x_2[/tex]

Step-by-step explanation:

Given formula is:

[tex]M = \frac{x_1+x_2}{2}[/tex]

In order to solve for x1, we have to isolate x1 on one side of the equation

So,

Multiplying the whole equation by 2:

[tex]2M = \frac{x_1+x_2}{2} * 2\\2M = x_1+x_2[/tex]

Subtracting x2 from both sides

[tex]2M-x_2 = x_1+x_2-x_2\\2M-x_2 = x_1[/tex]

so,

After solving for x1, we get

[tex]x_1 = 2M-x_2[/tex]

Keywords: Formulas, Solving for a variable

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Answer:

[tex]\displaystyle y = 7[/tex]

Step-by-step explanation:

Since the rate of change [slope] is zero, that automatically makes our equation set equal to the y-coordinate of the ordered pair, which in this case is the y-intercept.

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Answer:

From what I can tell from the image, b is equivalent to B.) 50°

Step-by-step explanation:

So to start off 2a=80° there is 2 a's. so  you subtract 80° from 180° to get 100°.

now b=c and their is 100° left over. So 100°/2 is 50° because if b=50° and c=50° both angles equal 100°.

Answer : The correct option is, (B) 50

Step-by-step explanation:

As we are given :

2a = 80

b = c

As we know that:

The sum of interior angles of a triangle is equal to [tex]180^o[/tex].

That means,

[tex]\angle A+\angle B+\angle C=180^o[/tex]

[tex]80^o+\angle B+\angle C=180^o[/tex]

and, [tex]\angle B=\angle C[/tex]

So,

[tex]80^o+2\angle B=180^o[/tex]

[tex]2\angle B=180^o-80^o[/tex]

[tex]2\angle B=100^o[/tex]

[tex]\angle B=\frac{100^o}{2}[/tex]

[tex]\angle B=50^o[/tex]

Thus, the value of 'b' is [tex]50[/tex]

If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

For the values you've given:

- The slope (m) is 35.
- The y-intercept (b) is 550.

From these pieces of information, you can conclude:

1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.

2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.

With these conclusions, you can write the equation of the line in slope-intercept form:

\[ y = 35x + 550 \]

This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.

Answer:22/24 or 11/12

Step-by-step explanation:

Answer:

Six books are removed from the shelves, so $24-6=18$ books remain. Of these, $10-2=8$ are math books. Therefore, $8/18=\boxed{4/9}$ of the books remaining are math books.

Step-by-step explanation:

4/9

Answer:

Y = - 2

Step-by-step explanation:

Put your finger at x= 0 or (0,0) and go down until you hit the black line, thats your y

Answer:

(0,2.5), (-1.25,0) and (3,8.5)

Step-by-step explanation:

we have

[tex]-4x+2y-5=0[/tex]

This is a linear equation (equation of a line)

If a ordered pair is a solution of the linear equation, the the ordered pair must satisfy the linear equation

1) Find the y-intercept

The y-intercept is the value of the y when the value of x is equal to zero

For x=0

substitute the value of x in the linear equation and solve for y

[tex]-4(0)+2y-5=0[/tex]

[tex]2y=5[/tex]

[tex]y=2.5[/tex]

The ordered pair is (0,2.5)

2) Find the x-intercept

The x-intercept is the value of the x when the value of y is equal to zero

For y=0

substitute the value of y in the linear equation and solve for x

[tex]-4x+2(0)-5=0[/tex]

[tex]-4x=5[/tex]

[tex]x=-1.25[/tex]

The ordered pair is (-1.25,0)

3) Assume any value of x or y and solve for the other variable

For x=3

[tex]-4(3)+2y-5=0[/tex]

[tex]-12+2y-5=0[/tex]

[tex]2y=17[/tex]

[tex]y=8.5[/tex]

The ordered pair is (3,8.5)

Answer:

[tex]15x^7y^5[/tex]

Step-by-step explanation:

Given

[tex]5x^3y^2\times 3x^4y^3[/tex]

Rewrite it as

[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)[/tex]

Use power property:

[tex]a^m\cdot a^n=a^{m+n},[/tex]

so

[tex]x^3\cdot x^4=x^{3+4}=x^7\\ \\y^2\cdot y^3=y^{2+3}=y^5[/tex]

Then

[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)=15\times x^7\times y^5=15x^7y^5[/tex]

Answer:

3

Step-by-step explanation:

To solve this you have to work backwards with what you are given.

16-7=9

Then we know that a number has to be multiplied by itself to equal nine the only number that follows that criteria is 3

3*3=9+7=16

Answer:

3

Step-by-step explanation:

Work backwards. 16 Subtract 7. Take square root. We take the square root because that is how to undo a number that was multiplied by itself.

16-7=9 √(9)=3

Check this by going through the same steps listed in the question:

A positive number is multiplied by itself. then 7 is added. the answer is 16

3×3=9

9+7=16

Answer:

There can be 180 apples in that box.

Step-by-step explanation:

1. Let's review the information given to answer the question correctly:

Number of apples in a box < 200

2. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?

The answer is that the number of apples that can be in the box is the highest multiple of 2, 3, 4, 5, and 6 that is close to 200.

The common multiples for this set of numbers are 60, 120, 180, 240, 300 and so on with 60 as the constant.

Therefore, the highest number that is multiple for this set of numbers and at the same time lower than 200 is 180.

There can be 180 apples in that box.

Answer:

120 or 180 apples

Step-by-step explanation:

It hasd to be divisible by 5 so it can only end in fives and zeroes next it has to be divisible by 2 so that narrows it tdown to only number that end in zero the it has to be divisible by 3 once yo find that you have two answers

120 or 180 and that is how many apples can be in the box

Answer:

C = 8 + 3x

The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.

The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.

Step-by-step explanation:

Let the admission cost of the fair is $x and each game is $3.

Now, Steven went to the state fair, played  4 games and spent a total of $20 on  admission and games.

So, we can write 20 = x + 4 × 3 {As the relation is linear}

⇒ x = $8

Therefore, the admission cost in the fair is $8.

Therefore, the equation that models the situation is  

C = 8 + 3x ............ (1)

Where C is the total cost and x is the number of games played.

So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.

Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)

The right answer is Option D.

Step-by-step explanation:

Given equations are;

2x+4y=3    Eqn 1

x+3y=13    Eqn 2

When we use subtraction-addition method, we make one of the variables same with opposite signs so that only one variable remains after addition or subtraction.

In the given problem, we will multiply Eqn 2 with "-2" so that the x variables become equal and then we can add both the equations and solve for y.

Therefore,

The first step will be to multiply the second equation by -2 to solve the linear system of equations.

The right answer is Option D.

Keywords: linear equations, subtraction

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Answer:

It's D.

Step-by-step explanation:

It was correct on my unit test review.

The solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]

To find the solutions for [tex]\( \csc^2x - 5\csc x = 0 \)[/tex], we can factor the expression:

[tex]\[ \csc x (\csc x - 5) = 0 \][/tex]

This equation is satisfied when either [tex]\(\csc x = 0\) or \(\csc x - 5 = 0\)[/tex].

1. For [tex]\(\csc x = 0\)[/tex], we know that [tex]\(\csc x\)[/tex] is the reciprocal of the sine function, and sine is 0 at multiples of [tex]\(\pi\)[/tex]. Therefore, [tex]\(x = n\pi\)[/tex] where n is an integer.

2. For [tex]\(\csc x - 5 = 0\)[/tex], solving for [tex]\(\csc x\)[/tex] gives [tex]\(\csc x = 5\)[/tex], and the sine of an angle is the reciprocal of its cosecant. Therefore, [tex]\(x = \sin^{-1}(1/5)\).[/tex]

In summary, the solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]

The complete question is probably:

What are the solutions for \( \csc^2x - 5\csc x = 0 \)?

Answer:

Step-by-step explanation:

50% of 60? 0.5*60=30

10% of 60? 0.1*60=6

75% of 60? 0.75*60=45

50percent of 60 minutes is 30 minutes, 10percent of 60 minutes is 6 minutes, and 75percent of 60 minutes is 45 minutes.

50percent of 60 minutes: 50percent of 60 minutes is half of 60, which equals 30 minutes.

10percent of 60 minutes: 10percent of 60 minutes is 6 minutes (10percent of 60 is 6).

75percent of 60 minutes: 75percent of 60 minutes is 45 minutes (75percent of 60 is 0.75 * 60 = 45).

Answer:

It goes up my $1.80

Step-by-step explanation:

You multiply $4.50 by 0.40 and you get 1.80 and that’s how much it goes up by

Answer:

I think it would be either (-10, 5) or (35, -20)

Step-by-step explanation:

Answer:

It Is C

Step-by-step explanation:

Edg 2020

Answer:   using t - test value is 1.37<2.08( At 0.05 level of significance)

        The mean of the sample was drawn from the population.

Step-by-step explanation:

Here sample size n=22

Given sample mean =530

Given population mean   =500

[tex]t=\frac{sample mean-µ}{\frac{S}{\sqrt{n-1} } }[/tex]

given sample standard deviation s=100

a) null hypothesis:-  The mean of the sample was drawn from the population   µ =500

Alternative hypothesis:-

The most powerful test you can use is t - distribution.

The test statistic is  

[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }  

here S is the standard deviation of the sample

b)  The value of the test statistic

           [tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }  

substitute given values sample size n=22

sample mean =530

sample standard deviation s =100

mean of the population µ =500

the calculated value of t =[tex]\frac{530-500}{\frac{100}{\sqrt{22} } }[/tex]

                      the calculated value=1.3748

c) The degrees of freedom =n-1 = 22-1 = 21

     The table value of t are 0.05 level of significance with 21 degrees of freedom is 2.08

       The calculated value 1.37<2.08

∴ we accept null hypothesis at 0.05 level of significance

conclusion:-

The mean of the sample was drawn from the  population.

A t-test is the most powerful test for this hypothesis. The test statistic value is calculated using t = (X - µ) / (s / √n). Based on a significance level of 0.05, we can conclude by comparing the calculated t-value with the critical t-value from t-distribution table.

The subjects of this question are hypothesis testing and statistics.

To answer your question: a) The most powerful test to use to test your hypothesis is the t-test for single mean. This is because you have one sample mean, one hypothesized population mean, and the population standard deviation is not known.

b) The value of the test statistic can be calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size. Plugging in your values, the formula becomes t = (530 - 500) / (113/ √22).

c) With a = 0.05, we conclude by comparing the calculated t-value with t-distribution table (df = 22-1 = 21). If the calculated t-value exceeds the critical t-value from the t-distribution table, we reject the null hypothesis.

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Explanation:

Simply pair each value given in the sequence with a0,a1,a2,etc like so

a0 = 4

a1 = 11

a2 = 18

a3 = 25

a4 = 32

a5 = 39

Answer:

20 cups of broth are needed to make 30 servings of the soup.

Step-by-step explanation:

This is a typical proportion math problem.

Just set up the proportion and solve for the unknown variable, let it be x, because it's simple to use.

12/8=30/x

simplify 12/8 to 3/2,

3/2=30/x

cross product,

2*30=3*x

60=3x

x=60/3

x=20

Number of cups of broth needed for making 30 servings is 20.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

We have,

Cups of broth needed for 12 servings of soup = 8 cups

Let cups of broth needed for 30 servings of soup = x cups

Using the concept of proportion,

12 / 8 = 30 / x

Doing the cross multiplication,

12x = 8 × 30

12x = 240

x = 240 / 12

x = 20

Hence 20 cups of broth are needed to make 30 servings of the soup.

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The y-intercept is 1/3

I'll assume the function is the following:

[tex]f(x)=-\frac{2}{9}x+\frac{1}{3}[/tex]

As you can see, this is the equation of a line written in Slope-intercept form. The general rule of writing lines in this form is:

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

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, which is the point at which [tex]x=0[/tex]. By comparing our function with the written rule, we can say that the y-intercept is:

[tex]\boxed{b=\frac{1}{3}}[/tex]

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Answer:

[tex]b=\frac{1}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=-\frac{2}{9}x +\frac{1}{3}[/tex]

This given function is a linear function, because its variables have one as exponent, we can also say that its variables are linear.

This function, as a linear one, it's represented as a line.

Additionally, the form of this function is called slope-intercept form as

[tex]f(x)=mx+b[/tex]

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

So, in this case

[tex]m=-\frac{2}{9}[/tex] and [tex]b=\frac{1}{3}[/tex]

Therefore, the y-intercept of the given function is

[tex]b=\frac{1}{3}[/tex]

Answer:

[tex] \frac{5}{2} \\ [/tex]

Step-by-step explanation:

[tex] \frac{ - 5 - 5}{ - 8 - - 4} [/tex]

Y - Y divided by X - X, the Y is 5 and the X is 2 (Rise over Run)

Answer:

[tex]\displaystyle 2\frac{1}{2} = m[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 5}{4 - 8} = \frac{-10}{-4} = 2\frac{1}{2}[/tex]

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Answer:

0.6 ounces

Step-by-step explanation:

Answer:

[tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex]

Step-by-step explanation:

Given:

Dividend = [tex](-15)^{-1}[/tex]

Quotient =  [tex](-15)^{-1}[/tex]

We notice that the dividend and the quotient are equal. This means the divisor is 1.

By identity property of 1, any number divided by 1 is equal to the same number or the quotient of a number divided by 1 is equal to the number itself.

So, we can write this as:

[tex]\frac{(-15)^{-1}}{1}=(-15)^{-1}[/tex]

Thus [tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex] (Answer)

Final answer:

The simplified expression for 3.4m + 2.4m is 5.8m. You simply add the coefficients of like terms.

Explanation:

To simplify the expression 3.4m + 2.4m, we need to combine like terms. The term 'like terms' refers to terms that have the exact same variable raised to the same power. In this case, both terms have 'm' as the variable, and it's not raised to any power (which is the same as being raised to the power of 1).

Combine the coefficients (numerical parts) of the like terms:

3.4m + 2.4m = (3.4 + 2.4)m

Add the coefficients: 3.4 + 2.4 = 5.8

Therefore, 3.4m + 2.4m = 5.8m.

There were 980 student desks originally before the purchase was made.

Step-by-step explanation:

Total desks purchased = 295

As 50 new desks are for teachers, therefore, we will subtract this amount from total;

Desks purchased for students = 295-50 = 245

Let,

x be the number of original student desks, therefore,

[tex]\frac{1}{4}\ of\ x=245\\\frac{x}{4}=245[/tex]

Multiplying both sides by 4

[tex]4*\frac{x}{4}=245*4\\x=980[/tex]

There were 980 student desks originally before the purchase was made.

Keywords: subtraction, fractions

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