The Waves swim team has a ratio of 14 boy: 12 girls. If there are 39 athletes,How many girls are there?


If 7 more boys join the Waves team, how many girls should be added to the team to maintain the same ratio of boys and girls.

Answer:

(x - 4)

Step-by-step explanation:

Given

x² + 2x - 24

Consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (+ 2)

The factors are + 6 and - 4, since

6 × - 4 = - 24 and 6 - 4 = + 2, thus

x² + 2x - 24 = (x + 6)(x - 4) ← in factored form

Thus the other factor is (x - 4)

The solution is Option D.

The equation x² + 2x - 24 = 0 has the factors as ( x + 6 ) and ( x - 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x² + 2x - 24 = 0   equation (1)

The equation can be factorized as

x² + 6x - 4x - 24 = 0

Taking x as the common factor , we get

x ( x + 6 ) - 4 ( x + 6 ) = 0

So , the equation will be

( x + 6 ) ( x - 4 ) = 0

Therefore , the factors of x are -6 and 4

Hence , the factors of the equations are ( x + 6 ) and ( x - 4 )

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#SPJ6

First you graph "y = 2x +2." You shade in the region below it, because it's y "LESS THAN" and you keep the line solid (not dotted) because it's "equal to" 2x+2 too.

Answer:

The correct answer is C) The elevation changes from 635 to 600 at the picnic area.

Answer:

(5x+2)(2x-3)

Step-by-step explanation:

this is the answer

Answer:

Step-by-step explanation:

prime: 3 5 7 11 13

P(notprime) = (12-5)/ 12 = 7/12

Answer:

1. 10.64

2. 6.45

Step-by-step explanation:

Hope this helps and can u mark me brainliest?

Answer:

The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this question, we have that:

[tex]n = 1200, p = 0.3[/tex]

So

[tex]\mu = E(X) = np = 1200*0.3 = 360[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.3*0.7} = 15.8745[/tex]

The probability that less than 348 possess that characteristic is

Using continuity correction, this is P(X < 348 - 0.5) = P(X < 347.5), which is the pvalue of Z when X = 347.5. So

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

[tex]Z = \frac{347.5 - 360}{15.8745}[/tex]

[tex]Z = -0.79[/tex]

[tex]Z = -0.79[/tex] has a pvalue of 0.2148.

The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.

The population follows a normal distribution.

The probability that less than 348 possess that characteristic is 0.2248

The given parameters are:

[tex]\mathbf{n = 1200}[/tex]

[tex]\mathbf{p = 30\%}[/tex]

Start by calculating the mean:

[tex]\mathbf{\mu =np}[/tex]

[tex]\mathbf{\mu =1200 \times 30\%}[/tex]

[tex]\mathbf{\mu =360}[/tex]

Calculate the standard deviation

[tex]\mathbf{\sigma = \sqrt{np(1 - p)}}[/tex]

[tex]\mathbf{\sigma = \sqrt{360(1 - 30\%)}}[/tex]

[tex]\mathbf{\sigma = \sqrt{252}}[/tex]

[tex]\mathbf{\sigma = 15.87}[/tex]

Calculate the z-score

[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]

Where:

x = 348

So, we have:

[tex]\mathbf{z = \frac{348 - 360}{15.87}}[/tex]

[tex]\mathbf{z = -\frac{12}{15.87}}[/tex]

[tex]\mathbf{z = -0.7561}[/tex]

So, the probability is represented as:

[tex]\mathbf{P(x < 348) = P(z < -0.7561)}[/tex]

From the z-table of probabilities, we have:

[tex]\mathbf{P(x < 348) = 0.2248}[/tex]

Hence, the probability that less than 348 possess that characteristic is 0.2248

Read more about probabilities at:

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Answer:

A =78.5

Step-by-step explanation:

We need the radius to find the area of a circle

r = d/2 = 10/2 =5

The area of a circle is given by

A = pi r^2

A = 3.14 (5)^2

A =3.14 (25)

A =78.5

Answer:

Well, as it turns out, when two figures are similar or congruent, they have certain properties, and these properties can be used to prove relationships between the figures. When two figures are similar figures, they have the following properties: Corresponding angles have equal measure.

Step-by-step explanation:

Answer:

The largest possible number is 28.

Step-by-step explanation:

Sophie has to choose seven different numbers whose mean is 7, this means that the sum of the numbers is 49. (since the mean is the sum of them all divided by 7 and if we want the mean to be 7, then the sum would need to be 49).

We are asked what is the largest possible number she could choose, so therefore, the other six numbers should be non-zero and the smallest ones so she would have to choose the numbers from 1 to 6 first.

Let's see how much they sum up: [tex]1+2+3+4+5+6=21[/tex]

So now, she needs one more number to sum up to 21 and that will give her 49 in total, this number is 28 (since 28 + 21 =49).

Thus, 28 is the largest number she could choose because if she chose any other greater number the mean would be bigger than 49.

Answer:

116.6

Step-by-step explanation:

100^2 + 60^2 = c^2

1360 = c^2

square root of 1360 is 116.6

Answer:

Shortcut = 116.62

Step-by-step explanation:

Hypotenuse = [tex]\sqrt{a^{2} +b^{2} } = \sqrt{60^{2} +100^{2} } = 116.61904 = 116.62[/tex]

Answer:

57

Step-by-step explanation:

Firstly, we will need to calculate what x is.

To calculate this, the important property of the parallelogram to use is that adjacent angles are supplementary.

This means A and B are supplementary while B and C are also supplementary

what we are trying to say is that they add up to be 180

Thus,

5x + 18 + 3x -6 = 180

8x +12 = 180

8x = 180-12

8x = 168

x = 168/8

x = 21

Thus, the measure of angle B is 3x-6 = 3(21) -6 = 63-6 = 57

Now, another important property of parallelograms is that opposite angles are equal. This means that angle B= C = 57

Answer:

Step 2

Step-by-step explanation:

Michelle's step in trying to solve the equation is given below:

[tex]\begin{aligned} t-\dfrac35&=\dfrac45\\\\ t-\dfrac35+\dfrac35&=\dfrac45+\dfrac35&\green{\text{Step } 1}\\\\ t&=1&\blue{\text{Step } 2} \end{aligned}[/tex]

Michelle made a mistake in Step 2.

The right hand side of Step 1:  [tex]\dfrac45+\dfrac35\neq 1[/tex]

Rather, the correct sum is:

[tex]\dfrac45+\dfrac35=\dfrac75\\\\=1\dfrac25[/tex]

Answer:

Its 1/5

Step-by-step explanation:

Khan

Answer:

Tyson had the better deal

Step-by-step explanation:

We simply want to know who paid less for the ticket.

Tyson bought 8 tickets for the members of his basketball team and it cost it $168 in total.

The cost of each ticket is therefore:

168 / 8 = $21

He paid $21 for each ticket.

The parent bought her son's ticket for $24.

Therefore, Tyson had the better deal because he paid $3 less than the woman.

Answer:

We have to questions here where we need to find the distance from the origin to each given point.

The formula for distance is

[tex]s=\sqrt{x^{2}+y^{2} }[/tex]

[tex]s_{(3,4)}=\sqrt{3^{2}+4^{2} } =\sqrt{9+16}=\sqrt{25}\\ s_{(3,4)}=5[/tex]

Therefore, the value s that yields the coordinate (3,4) is 5 units.

[tex]s_{(9,1)}=\sqrt{9^{2}+1^{2} } =\sqrt{81+1}=\sqrt{82}\\ s_{(9,1)} \approx 9.05[/tex]

Therefore, the value s that yields the coordinate (9,1) is 9.05 units, approximately.

The values of s that yield the coordinates (3.4) and (9,1) are: 5 and 9.1, respectively

The coordinates are given as:

(3,4) and (9,1)

The single value that yields the coordinates is calculated as:

[tex]s = \sqrt{x^2 + y^2}[/tex]

For (3,4), we have:

[tex]s = \sqrt{3^2 + 4^2} = 4[/tex]

For (9,1), we have:

[tex]s = \sqrt{9^2 + 1^2} = 9.1[/tex]

Hence, the values of s that yield the coordinates (3.4) and (9,1) are: 5 and 9.1, respectively

Read more about coordinates at:

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Answer:

The solution to the equation are [tex]5+\frac{\sqrt{42} }{2\\} \ and \ 5-\frac{\sqrt{42} }{2\\}\\[/tex]

Both of his values are positive real numbers

Step-by-step explanation:

The general formula of a quadratic equation is expressed as [tex]ax^{2}+bx+c = 0\ where;\\x = -b\±\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

Given the expression  0 = x² – 5x – 4 which can be rewritten as shown below;

x² – 5x – 4 = 0

Comparing this to the general equation; a = 1, b = -5, c= -4

To get the solution to the quadratic equation, we will use the general formula above;

[tex]x = -b\±\frac{\sqrt{b^{2}-4ac } }{2a}\\x = -(-5)\±\frac{\sqrt{(-5)^{2}-4(1)(-4) } }{2(1)}\\\\x = 5\±\frac{\sqrt{25+16 } }{2}\\x =5\±\frac{\sqrt{41} }{2}\\x = 5+\frac{\sqrt{42} }{2}\ and \ 5-\sqrt{42} /2\\[/tex]

Both of his values are positive real numbers

Answer: D.–0.7

Step-by-step explanation: hope this helps :)

Answer:

448in^2

Step-by-step explanation:

The area of a trapezoid is the bases added divided by two times the height.

(32+24)/2*16=28*16=448 in^2

Hello!

[tex]\boxed{ \bf The~degree~of~the~polynomial~is~B.~5}[/tex]

___________________________________________

The term with the greatest exponent determines the degree of the polynomial.

Let's list all the terms:

Out of all of these terms, the first one has the greatest exponent (5).

Answer:

A. 4

Step-by-step explanation:

leading zeros not included and the sig figs start from the first 1 so 4 sig figs

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 - 2x = 5x - 9x + 10  {add the like terms}

6 - 2x = - 4x + 10        {add (-6) to both side}

6 - 2x - 6 = - 4x + 10 - 6

-2x = - 4x + 4         {add 4x to both sides}

-2x + 4x = -4x + 4 + 4x

2x = 4           {divide both sides by 2}

2x/2x = 4/2

x = 2

Answer:

(0, 5)

Step-by-step explanation:

To solve for the y-intercept, plug in 0 for all x values and solve.

Answer:

33.165

Step-by-step explanation:

Answer:

33.165

Step-by-step explanation:

4.95*6.7= 33.165

hope this helps

Answer:

2.275%

Step-by-step explanation:

The first thing to do here is to calculate the z-score

Mathematically;

z-score = (x-mean)/SD

from the question, x = 12,300 hours , mean = 11,500 hours while Standard deviation(SD) = 400 hours

Plugging the values we have;

z-score = (12,300-11,500)/400 = 800/400 = 2

Now, we want to calculate P(z ≤ 2)

This is so because we are calculating within a particular value

To calculate this, we use the z-score table.

Mathematically;

P(z ≤ 2) = 1 - P(z > 2) = 1 - 0.97725 = 0.02275

To percentage = 2.275%

Answer:

1000/10x12= answer

Step-by-step explanation:

Part A:

Divide the number of lightning strikes to the number of seconds to find the average rate.

1000 / 10 = 100 strikes per second

Now, multiply by 12 to find the number of strikes that occurred.

100 * 12 = 1200 strikes in 12 seconds

Part B:

Divide the number of seconds to the number of lightning strikes to find the average rate.

10 / 1000 = 0.1 seconds per strike

Now, multiply by 7250 to find the number of seconds that passed.

0.1 * 7250 = 72.5 seconds in 7250 strikes

Best of Luck!

Answer:

Step-by-step explanation:

Given the intensity, or loudness, of a sound  measured in decibels (dB), according to the equation [tex]I (dB)= 10log(\frac{I}{Io} )[/tex] where;

I is the intensity of a given sound and

[tex]Io[/tex] is the threshold of hearing intensity

To get I(dB) when [tex]I=10^{32} Io[/tex]

We will substitute the value of I = [tex]I=10^{32} Io[/tex] into the equation above to have;

[tex]I (dB)= 10log(\frac{10^{32}Io }{Io} )\\I(dB)=10log10^{32}\\ I(dB)=32*10log10\\[/tex]

Since log10 = 1;

[tex]I(dB)=32*10(1)\\I(dB)=320[/tex]

The intensity in decibel is 320 decibel

Answer:

Its D or 80

Step-by-step explanation:

I=10^8 (I subscript 0) can be written as I/I subscript 0, and you can plug that right into the log to get 80.

Complete question is:An orange is shot up into the air with a catapult. The function h given by h(t) = 15 + 60t - 16t² models the orange’s height, in feet, t seconds after it was launched.

Select all the true statements about the situation.

Options:

1. The domain of function h only contains values greater than or equal to 0.

2. The orange is at the same height 1 second after launch and 2 seconds after launch.

3. After 3 seconds, the orange has hit the ground.

4. The orange is 15 feet above the ground when it is launched.

5. The value t = 10 does not belong to the domain of h.

Answer:

Option 1 - True

Option 2 - False

Option 3 - False

Option 4 - True

Option 5 - True

Step-by-step explanation:

Looking at the options,

-The domain is the x or t value and it is time. Now, time can only be positive or greater than or equal to zero i.e. t ≥ 0. Thus, option 1 is true.

- At t = 1 second;

h = 15 + 60(1) - 16(1)²

h = 15 + 60 - 16 = 59 ft

Also, at t = 2 seconds;

h = 15 + 60(2) - 16(2)²

h = 15 + 120 - 64 = 71 ft

So,value of h is not the same at t = 1 and t = 2. Thus, option 2 is not true.

- The orange will hit the ground when h(t) = 0.

However, at t = 3;

h(t) = 15 + 60(3) - 16(3)²

h(t) = 51 ft

h(t) is not equal to zero at t = 3, so option 3 is false

- when the orange is launched it is at time t = 0.

Thus,

h(0) = 15 + 60(0) - 16(0)²

h(0) = 15 ft

So option 4 is true.

- At t=10, h(t) = 15 + 60(10) - 16(10)²

h(10) = -985

This means the orange would be below ground level and thus doesn't belong to the domain of h, so option 5 is true.

Answer:

1 true 4 true and 5 true the rest are false

Step-by-step explanation:

Answer:

= 99/32

Step-by-step explanation:

2 3/4 1 1/8

= 11/4 * 9/8

= 99/32