Question 28
Find the length of each leg. Leave answer in simplest radical form.

Hello! The interquartile range would be 5°

You must subtract Quartile one from quartile 3 to find iqr

Answer:

y=1/2x-2.5

Step-by-step explanation:

4x-8y=20

Subtract 4x from both sides to get the 8y on on side.

-8y=-4x+20

divide -8 from both sides to get the y by itself.

y=1/2x-2.5

Answer: [tex]\frac{x}{5}+9[/tex]

Step-by-step explanation:

Let be "x" the number mentioned in the given phrase.

"...the quotient of a number and five" indicates a division. In other words, the number "x" is divided by 5. This can represented as:

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

Now,  "Nine more than the quotient of a number and five" indicates that you need to add 9 to the quotient of a number and five ( [tex]\frac{x}{5}[/tex]).

Knowing this, you can conclude that the translation of "Nine more than the quotient of a number and five" into  a math expression is:

[tex]\frac{x}{5}+9[/tex]

Final answer:

The word phrase 'nine more than the quotient of a number and five' translates to the math expression '(x/5) + 9', where 'x' represents the number.

Explanation:

To translate the word phrase 'nine more than the quotient of a number and five' into a math expression, we first identify the quotient of a number and five, which is denoted as ‘x ÷ 5’ or ‘x/5’ where x represents the number. Next, we address the phrase 'nine more than', which indicates that we need to add nine to that quotient. So, the phrase translates to the algebraic expression ‘(x/5) + 9’.

Therefore, as per the above explaination,  the correct answer is (x/5) + 9

Answer:

13,92838827718412‬ft

Step-by-step explanation:

a² + b² = c²

a = 13ft

b = 5ft

169 + 25 = 194

c = √194

c = 13,92838827718412‬ft

Answer:

Final answer is c=-7.

Step-by-step explanation:

Given equation is [tex]0=-x^2+4x-7[/tex].

Now question says that Misha wrote the quadratic equation 0=-x2+4x-7 in standard form. Now we need to find about what is the value of c in her equation.

We know that standard form of quadratic equation is given by [tex]ax^2+bx+c=0[/tex].

compare given equation with the standard form, we find that -7 is written in place of +c

so that means +c=-7

or c=-7

Hence final answer is c=-7.

For this case we must solve the following inequality:

[tex]3x <18[/tex]

Dividing between 3 on both sides of the inequality we have:

[tex]x <\frac {18} {3}\\x <6[/tex]

Thus, the solution of the variable "x" is given by all the numbers smaller than 6.

Answer:

All values of "x" less than 6.

(-∞, 6)

-2^2÷ -2^2=1

(-2)(-2)÷ (-2)(-2)=1

4 ÷4=1

Answer is 1

Answer:

Any number divided by itself is 1.

Step-by-step explanation:

One of the nice parts about algebra is that -- if a number appears more than once -- you can make things a lot cleaner looking by throwing them in a variable. Let's let x = -2² . Our equation then becomes x ÷ x = 1, and it's much clearer here that, since we're dividing x by itself, the answer should clearly be one.

Answer: 17x = 85

Step-by-step explanation:

X is the number in which you'd multiply 17 by to equal 85, therefore x = the number of years.

Answer: Equation would be,

17x = 85

Where, x represents the number of year.

Step-by-step explanation:

Let x represents the number of year after which the cliff erodes 85 centimeters,

Since, the cliff on the seashore is eroding at the rate of 17 centimeters per year,

So, the total eroding of cliff after x years = 17x

[tex]\implies 17x = 85[/tex]

Which is the required equation..

Answer:

C. [tex]\frac{32g^2}{3h^4}[/tex]

Step-by-step explanation:

Answer:

Option C is correct

Step-by-step explanation:

[tex]\frac{\frac{h}{3g^2}}{\frac{h^5}{32g^7}}[/tex]

We need to simplify the above expression.

We can write the above expression as:

[tex]\frac{h}{3g^2}\div\frac{h^5}{32g^7}[/tex]

Changing division sign into multiplication and reciprocating the second term we get,

[tex]\frac{h}{3g^2}*\frac{32g^7}{h^5}[/tex]

Applying the power rule: a^m/a^n = a^{m-n}

Solving:

[tex]\frac{h*32g^7}{3g^2*h^5}\\\\\frac{32g^{7-2}}{3h^{5-1}}\\\frac{32g^5}{3h^4}[/tex]

So, Option C is correct.

Answer:

x verse y on the map

Step-by-step explanation:

It shows what the x and the y cordinates are

20% of the students wore blue shirts

40 x 0.08 = 3.2

3.2% out of the 40 students wore blue shirts.

Let's simplify step-by-step.

2(11(a−2)+12)−(2(5a−3)+a)

Distribute the Negative Sign:

=2(11(a−2)+12)+−1(2(5a−3)+a)

=2(11(a−2)+12)+−1(2(5a−3))+−1a

=2(11(a−2)+12)+−10a+6+−a

Distribute:

=(2)(11(a−2))+(2)(12)+−10a+6+−a

=22a+−44+24+−10a+6+−a

Combine Like Terms:

=22a+−44+24+−10a+6+−a

=(22a+−10a+−a)+(−44+24+6)

=11a+−14

Answer:

=11a−14

Answer:

It would be 7.66 and 7.19 because you can not round downward although I am a little confused on how 7.19 is able to round upwards But I am positive 7.66 rounds up to 8

Step-by-step explanation:

Your problem looks like this

[tex]11\sqrt{45}  - 4\sqrt{5}[/tex]

To make this problem easier, we need to simplify these square roots

[tex]11\sqrt{45}[/tex]    can be simplified

Here's how :

The factors of 45 are 9 and 5

9 is a perfect square root, but 5 is not

Think of the problem like this

[tex]\sqrt{9}     ×     \sqrt{5}[/tex]

The square root of 9 is 3, but 5 has no perfect square root

Now [tex]11\sqrt{45}[/tex] is simplified to [tex]33\sqrt{5}[/tex]

Now let's solve the problem, because we have a common square root of 5

[tex]33\sqrt{5}[/tex] - 4\sqrt{5}[/tex]

Our final answer is

[tex]29\sqrt{5}[/tex]

Feel free to ask questions if you are confused! Hope I helped :)

For this case we must simplify the following expression:

[tex]11 \sqrt {45} -4 \sqrt {5}[/tex]

So, we rewrite 45 as [tex]3 ^ 2 * 5[/tex]:

[tex]11 \sqrt {3 ^ 2 * 5} -4 \sqrt {5} =[/tex]

We have by definition of properties of powers and roots that:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]11 * 3 \sqrt {5} -4 \sqrt {5} =\\33 \sqrt {5} -4 \sqrt {5} =\\29 \sqrt {5}[/tex]

Answer:

[tex]29 \sqrt {5}[/tex]

Answer:

A : x^2 = -12y

Step-by-step explanation:

TO ALL MY EDGE PEOPLE

Answer:

a) x^2=-12y

Step-by-step explanation:

The ratios 4/6 and 8/12 are equivalent ratio of 2/3 which we obtain by multiplying or dividing both numerator and denominator by same number.

To find a ratio that is the same as 2/3, we can multiply or divide both the numerator and the denominator by the same non-zero number.

This will result in an equivalent ratio.

If we multiply both the numerator and denominator of 2/3 by 2, we get:

(2 × 2) / (3 × 2)

= 4/6

Therefore, the ratio 4/6 is the same as 2/3.

Similarly, if we multiply both the numerator and denominator of 2/3 by 2, we get:

8/12

So, the ratio 8/12 is also the same as 2/3.

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Answer:

Shirts = $7

Shorts $17

Step-by-step explanation:

Let:

T - shirts

S - shorts

We can make two equations out of this problem:

4T + 3S = $79

7T + 8S = $185

Through substitution we can solve for one of the unknowns. We make one equation to solve for an unknown

[tex]4T+3S=\$79\\\\3S = \$79-4T\\\\S=\dfrac{\$79-4T}{3}[/tex]

We use the formula of S and insert it into the other equation:

[tex]7T+8(\dfrac{\$79-4T}{3}) = \$185\\\\7T + \dfrac{\$632-32T}{3}=\$185\\\\\dfrac{\$632-32T}{3}=\$185-7T\\\\\$632-32T=3(\$185-7T)\\\\$632-32T=\$555 - 21T\\\\-32T+21T=\$555-\$632\\\\-11T=-\$77\\\\\dfrac{-11T}{11}=\dfrac{-\$77}{11}\\\\T = \$7[/tex]

Thus T-shirts are $7 each.

Now that we know T, we can use it to solve for the other unknown. You can use it on any of the formulas.

[tex]4T+3S=\$79\\\\4(\$7) + 3S = \$79\\\\\$28+3S =\$79\\\\3S=\$79-\$28\\\\3S=\$51\\\\S=\dfrac{\$51}{3}\\\\S = \$17[/tex]

We know then that Shorts are $17 each.

Answer:

b.-1/3

Step-by-step explanation:

Is means equals and of means multiply

W =5/9 * (-3/5)

W = -3/9

W = -1/3

Answer:

1. 40%

2. The theoretical probability is 3% greater than the experimental probability.

Step-by-step explanation:

We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;

(the number of times a 4 was rolled)/(total number of rolls)

8/20 = 0.4

0.4*100 = 40%

The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;

P(HT or TH or TT)

The above events are mutually exclusive, thus;

P(HT or TH or TT) = P(HT) + P(TH) + P( TT)

                               = (22+34+16)/(28+22+34+16)  

                               = 0.72 = 72%

On the other hand, the theoretical probability of obtaining at least one tails,

P(HT or TH or TT) = 3/4

                              = 75%

This is because there is at least one tail in 3 out of 4 possible outcomes.

Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.

Answer:

1. 40%

2. The theoretical probability is 3% greater than the experimental probability.

Step-by-step explanation:

1. Lets define experimental probability first.

Experimental probability is the probability of an event's occurrence when the experiment was conducted.

The number cube is rolled 20 times, so our sample space is 20.

And the number 4 came in result 8 times, so the the event space is 8.

So,

Experimental Probability = 8/20

=> 0.4

Converting into percentage will give:

=> 40%

So the first option is correct.

2. First we have to find the theoretical probability of getting at least one tail when two coins are tossed

The sample space is {HH, HT, TH, TT}

3 out of these 4 outcomes contain at least one tail

So the theoretical probability of getting at least one tail is: 3/4

=> 0.75 or 75%

Now for the experimental probability,

The total sample space is 28+22+34+16 = 100

The number of favorable outcomes are(Which contain at least one tail):

22+34+16 = 72

So, experimental probability of getting at least one tail = 72/100

=> 0.72 or 72%

We can see that the theoretical probability is 3% greater than the experimental probability. So second option is correct..

Answer:

28

Step-by-step explanation:

We can see that all the angles are inside of a triangle and the sum of the interior angle of the triangle is 180 degrees.

Knowing this, we know that the sum of all the angles present is 180 degrees.

1st angle can be seen as 90 degrees, 2nd angle is x+6 and the 3rd is 2x.

The sum can be written as ( 90 + x + 6 + 2x ) and this equals to 180 degrees.

90 + x + 6 + 2x = 180

96 + 3x = 180

( subtract 96 on both sides )

3x = 180 - 96

3x = 84

( divide by 3 on both sides )

x = 84 / 3

x = 28

Answer:

x = 28

Step-by-step explanation:

Consider the lower right triangle

The 2 given angles sum to 90° ( sum of angles in a triangle = 180° )

Hence

x + 6 + 2x = 90

3x + 6 = 90 ( subtract 6 from both sides )

3x = 84 ( divide both sides by 3 )

x = 28

Rotations, translations and reflections are transformations that preserve areas, so they always produce congruent figures.

So, the only way you have to produce a similar but not congruent figure is to use dilation with a scale different than 1.

Answer: Last option

inverse property

Step-by-step explanation:

The property of the inverse sum says that if we have a number b and we add it with its negative -b then

[tex]b - b = 0[/tex]

In this case we have that:

[tex]x = a + bi[/tex]

and

[tex]y = -b - bi[/tex]

Note that

[tex]y = -x[/tex]

Therefore:

[tex]x + y = x -x= a + bi - a - bi = 0[/tex]

the answer is the last option

Answer:

Step-by-step explanation:

f(x) = { 0, x<0; 0 <= x, (x +3) * 1000000 }

(Note the graph ought to flatten to zero for x < 0)

ANSWER:

You need to write it’s piecewise function if

x < -3, the term x+3 becomes negative. So , for all values of x < -3 , the term becomes -(x+3)

Piecewise will be

F(x) = square root of (x+3) when x is greater than or equal to -3

F(x) = square root of -(x+3) when x less than or equal to -3

Answer:

a. [tex]-3x^{5}y^{6}[/tex]

Step-by-step explanation:

We want to multiply and simplify:

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

We rearrange the product to obtain:

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

Recall that:

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

We apply this property to obtain:

[tex]-3x^{2+3}y^{2+4}[/tex]

We simplify to obtain:

[tex]-3x^{5}y^{6}[/tex]

Let Poly = X

Andy gets twice as much as Poly so Andy = 2X

Pheobe gets three times as much as Andy, so she is 3(2x) = 6X

Now add them together to equal 270:

X + 2X + 6X = 270

Simplify:

9X = 270

Divide both sides by 9:

X =  270 /9

X = 30

Poly = X = 30

Andy = 2X = 2(30) = 60

Pheobe = 6X = 6(30) = 180

ANSWER

The hypotenuse is 14√2 units.

EXPLANATION

Let the hypotenuse be x, then we can use the Pythagoras Theorem to find the length of the hypotenuse.

We have from the question that, each leg of the 45-45-90 triangle measures 14 cm.

Then, the Pythagorean Theorem, gives:

[tex] {x}^{2} = {14}^{2} + {14}^{2} [/tex]

[tex] {x}^{2} = 2 \times {14}^{2} [/tex]

Take positive square root to obtain;

[tex]x = \sqrt{ {14}^{2} \times 2} [/tex]

This simplifies to

[tex]x = 14 \sqrt{2} [/tex]

The length of the hypotenuse of the 45-45-90 triangle is 19.796 cm.

In a 45-45-90 triangle, the two legs are congruent (they have the same length) and the length of the hypotenuse is equal to the length of the legs multiplied by the square root of 2.

Given that each leg of the triangle measures 14 cm, the length of the hypotenuse can be calculated as follows:

Length of hypotenuse = Length of leg × √2

Length of hypotenuse = 14 cm × √2

Using a calculator or approximating the square root of 2 to 1.414, we can find:

Length of hypotenuse ≈ 14 cm × 1.414

Length of hypotenuse ≈ 19.796 cm (rounded to three decimal places)

Therefore, the length of the hypotenuse of the 45-45-90 triangle is approximately 19.796 cm.

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[tex]\bf \textit{area of a square}\\\\ A=s^2~~ \begin{cases} s=&sides'\\ &length\\ \cline{1-2} A=&150 \end{cases}\implies 150=s^2\implies \sqrt{150}=s~~ \begin{cases} 150=&2\cdot 3\cdot 5\cdot 5\\ &2\cdot 3\cdot 5^2 \end{cases} \\\\\\ \sqrt{2\cdot 3\cdot 5^2}=s\implies 5\sqrt{2\cdot 3}=s\implies 5\sqrt{2}\cdot \sqrt{3}=s[/tex]

well then, we have a couple of known fellows, √2 and √3.

now, let's bear in mind that 2 and 3 are both prime numbers, a prime number is not divisible by anything but itself or 1, so we will never find two same-values that will give us either 2 or 3, namely, there's no exact root for √2 or √3, which means they're both irrationals, and therefore since they're factors of the answer, the answer is irrational.

Given the low sampling variability, the average annual salary for the other group of the business school graduates is most likely to be close to $96,000. Thus, extreme values, significant higher or lower than $96,000, are less likely.

In the domain of statistics, when the sampling variability is low, it means that most of the samples drawn from a population will have averages (means) that are close to the population mean. The data from the samples will be clustered around a single value.

In this context, given that the average salary of one group was $96,000, the salaries of the other groups are also likely to be around this value given the low sampling variability. Therefore, an average annual salary that is significantly higher or lower than $96,000 for another group would be least likely.

By using the concept of sampling variability, we could reasonably predict that extremes, such as $40,000 or $150,000, would be highly unlikely as average salaries for the other groups if the business school graduates' salaries are distributed normally and the sampling variability is indeed low.

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Answer:

1)center =(-2,3)

2) Vertices = (8,3) and (-12,3)

3) foci =(4,3) and (-8,3)

Step-by-step explanation:

As the general equation of ellipse with center at (h,k) is given by:

(x-h)^2/a^2 +(y-k)^2/b^2 = 1

where a=radius of the ellipse along the x-axis

b=radius of the ellipse along the y-axis

h, k= the x and y coordinates of the center of the ellipse.

Given equation of ellipse:

(x+2)^2/100 + (y-3)^2/64 = 1

1)

Finding center:

comparing with the general formula

h=-2 and k=3

Center of given ellipse is at (-2,3)

2)

Finding vertices:

comparing given equation of ellipse with the general formula:

a^2= 100 and b^2=64

then a = 10 and b=8

As a>b, it means the ellipse is parallel to x-axis

hence vertices along the x-axis are a = 10 units to either side of the center i.e (8,3) and (-12,3)

The co-vertices along the y-axis are b=8 units above and below the center i.e (-2,11) and (-2,-5)

3)

Finding Foci, c:

From equations of general ellipse we have a^2 - c^2=b^2

Putting values of a^2=100 and b^2=64 in above

100-c^2=64

c^2=100-64

     = 36

taking square root on both sides

c=6

foci of given ellipse is either side of the center (-2,3) that is (4,3) and (-8,3)!

It’s either d or A but I’m sure it’s A