If i= -1, what is the value of i3?
O-1
Ο i
O 1
O -i

Answer:

\(P = 48 in\),\(A= 120in^2\)

Step-by-step explanation:

Again we can use Pythagorean theorem to find the missing side

x^2 + 15^2 = 17^2

x^2 + 225 = 289

Subtract 225 from both sides

x^2 = 64

Find the square root of both sides

√x^2 = √64

x = 8

So

l = 15in, w = 8in

P=2(15) + 2(8)

P = 30 + 18

P = 48 in

A= 15(8)

A= 120in^2

Answer:

It depends

Step-by-step explanation:

Planet Fitness offers 10 bucks a month but they suck (Lunk alarm + pizza nights? really?) If they offer good services like 24 hour fitness or good equipment then go for it my guy!

Answer:

6

Step-by-step explanation:

I solved the equation, but you can't simplify 6.

Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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Answer:

The  interval is  \(0.7187 < p < 2.421\)

Step-by-step explanation:

From the question we are told that

      The  sample size is  \(n = 100\)

       The  population  proportion is \(p = 0.81\)

       The  confidence level is  C =  98%

The level of significance is mathematically evaluated as

     \(\alpha = 100 -98\)

    \(\alpha = 2%\)%

    \(\alpha = 0.02\)

Here this level of significance represented the left and the right tail

The degree of  freedom is evaluated as

     \(df = n-1\)

substituting value  

    \(df = 100 - 1\)

     \(df = 99\)

Since we require the critical value of one tail in order to evaluate the  98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2

The  critical value of  \(\frac{\alpha}{2}\) and the evaluated degree of freedom is  

      \(t_{df , \alpha } = t_{99 , \frac{0.02}{2} } = 2.33\)

this is obtained from the critical value table  

The standard error is mathematically evaluated as

             \(SE = \sqrt{\frac{p(1-p )}{n} }\)  

substituting value  

           \(SE = \sqrt{\frac{0.81(1-0.81 )}{100} }\)  

           \(SE = 0.0392\)  

The 98%  confidence interval is evaluated as

      \(p - t_{df , \frac{\alpha }{2} } * SE < p < p + t_{df , \frac{\alpha }{2} }\)

substituting value  

     \(0.81 - 2.33 * 0.0392 < p < 0.81 +2.33 * 0.0392\)

      \(0.7187 < p < 2.421\)

The result of the given formula P(1 + r)^n is equal to: D. 148.02.

Mathematically, compound interest can be calculated by using this mathematical expression:

A(n) = P(1 + r)^{n}

Where:

Substituting the given parameters into the compound interest formula, we have;

A(10) = 100(1 + 0.04)^{10}

A(10) = 100(1.04)^{10}

A(10) = 100 × 1.4802

A(10) = 148.02

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The range is greater for the girls and the mean is greater for the girls. So, correct option is B.

A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.

Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.

B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:

(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours

To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:

(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours

Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".

So, correct option is B.

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The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

it could be 32 if im correct

Step-by-step explanation:

Answer:

32 is correct........

After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We are given that the factored form of 30.8n+8.4 is a(11n+3).

To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.

Expanding a(11n+3), we get:

a(11n+3) = 11an + 3a

Equating this to 30.8n+8.4, we have:

11an + 3a = 30.8n + 8.4

We can factor out an "a" from the left-hand side:

a(11n + 3) = 30.8n + 8.4

Now we can see that this is the same as the given factored form, so we can equate the two expressions:

a(11n + 3) = a(11n + 3)

This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):

a = 30.8/(11n+3)

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Answer:

x=3

y=5

Step-by-step explanation:

3x+2y=19

- 2x+2y=16

_____________

x=3

3(3)=9

19-9=10

10÷2=5

y=5

Answer:

x=3

y=5

Step-by-step explanation:

Method 1 ; Substitution Method

\(3x + 2y =19\\2x+2y=16\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:3x+2y=19:\\\quad x=\frac{19-2y}{3}\\\\\mathrm{Subsititute\:}x=\frac{19-2y}{3}\\\begin{bmatrix}2\times \frac{19-2y}{3}+2y=16\end{bmatrix}\\\\Simplify\\\begin{bmatrix}\frac{38+2y}{3}=16\end{bmatrix}\\\mathrm{Isolate}\:y\:\mathrm{for}\:\frac{38+2y}{3}=16:\quad y=5\\\\\mathrm{For\:}x=\frac{19-2y}{3}\\\\Substitute\:y\:= \:5\\x=\frac{19-2\times\:5}{3}\\\\\frac{19-2\times\:5}{3}=3\\\\x=3,\:y=5\)

Method 2 : Elimination method

\(\begin{bmatrix}3x+2y=19\\ 2x+2y=16\end{bmatrix}\\\\\mathrm{Multiply\:}3x+2y=19\mathrm{\:by\:}2\:\\\mathrm{:}\:\quad \:6x+4y=38\\\\\mathrm{Multiply\:}2x+2y=16\mathrm{\:by\:}3\:\\\mathrm{:}\:\quad \:6x+6y=48\\\\\begin{bmatrix}6x+4y=38\\ 6x+6y=48\end{bmatrix}\\\\6x+6y=48\\-\\\underline{6x+4y=38}\\2y=10\\\\\begin{bmatrix}6x+4y=38\\ 2y=10\end{bmatrix}\\\\\mathrm{Solve}\:2y=10\:\mathrm{for}\:y:\quad y=5\\\mathrm{For\:}6x+4y=38\mathrm{\:plug\:in\:}y=5\)

\(\mathrm{Solve}\:6x+4\times\:5=38\:\mathrm{for}\:x:\quad x=3\\\\x=3,\:y=5\)

Answer:

third chord length is 27.8088 cm

Between III and I chord is \(27^\circ57'30''\)

Between III and II chord is \(37^\circ36'30''\)

Step-by-step explanation:

The calculation of measurements of the triangle is shown below:-

By Cosine rule

\(BC^2 = (14.32)^2 + (18.64)^2 - 2\times 14.32 \times 18.64 cos\114^\circ26'\\\\ BC^2 = 773.330156\\\\ BC = \sqrt{773.330156}\)

BC = 27.8088 (it is the length of third chord)

By Sin rule

\(\frac{Sin A}{BC} = \frac{Sin B}{14.32} \\\\ \frac{Sin114^\circ26'}{27.8088} = \frac{Sin B}{14.32} \\\\ Sin B = \frac{14.32114^\circ26}{27.8088}\)

After solving this we will get

Sin B = 0.468829

\(<B = Sin^{-1} 0.468829\\\\ <B = 27^\circ 57'30''\)

Therefore

\(<A + <B + <C = 180^\circ\)

\(<C = 180^\circ - 114^\circ26'-27^\circ57'30''\\\\ <C = 37^\circ36'30''\)

Now,

third chord length is 27.8088 cm

Between III and I chord is \(27^\circ57'30''\)

Between III and II chord is \(37^\circ36'30''\)

The same is to be considered

Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.

Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

The maximum value of the original data set is 109.

To determine the maximum value of the original data set from the given stemplot, we need to look at the rightmost digits in each stem and identify the highest value.

Looking at the stemplot:

O 10 | 0 0 8 9 8 9 0 0 0

0 20 | 5 4 7 9 6

0 30 | 1 4 6 7 7 9 7

0 40 | 0 0 2 5 5 7 7 9 9 8

0 50 | 1 2 2 2 3 4 5 5 7 8 9 9

0 60 | 0 0 0 3 3 3 3 6 8

The rightmost digits in each stem represent the original data values. We can see that the highest value occurs in the stem "10" with a rightmost digit of "9".

Therefore, the maximum value of the original data set is 109.

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Answer:

-------------------------

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

The length of FG is approximately 15.3 cm.

To calculate the length of FG using Pythagoras' theorem, we need to find the length of the hypotenuse (FG) of a right triangle. Let's denote the length of FG as x.

According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

\(FG^2 = GH^2 + FH^2\)

Given that GH = 8 cm and FH = 13 cm, we can substitute these values into the equation:

\(x^2 = 8^2 + 13^2\)

\(x^2 = 64 + 169\)

\(x^2\) = 233

To find x, we take the square root of both sides:

x = √233 ≈ 15.26 cm (rounded to 1 decimal place)

Therefore, the length of FG is approximately 15.3 cm.

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Step-by-step explanation:

ig this is 29 .............

Answer:

13 1/8 -9 6/7 = 3 15/56

Step-by-step explanation:

13 1/8 -9 6/7 = ?

convert to a common denominator:

56 works in this case

13 7/56 - 9 48/56 = ?

it's complicated to subtract 48/56 from 7/56 so let's convert 13 7/56 to 12 63/56

12 63/56 - 9 48/56 = 3 15/56

Answer:

• a=0

• a=2

• a=2

Step-by-step explanation:

factorise a³-4a²+4a=0

thus,a(a-2)²=0

Answer:

y - (-4) = 3(x - (-1)

Step-by-step explanation:

Answer:

y−4=−3(x+1)

Step-by-step explanation:

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Answer:

11

Step-by-step explanation:

\(61 {}^{2} - {60 }^{2} = 121\)

\( \sqrt{121} = 11\)

Answer:

11 x 2^3 =11 x 2 x 2 x 2 = 88

Step-by-step explanation:

88

11 8

   2 4

      2 2

Use a factor tree it helps a lot :0).

Answer: Consider me the brainiest. The answer is... Decimal form =4.083

Exact form= 49/12

The mixed number form=4 1/12

How do we solve fractions step by step?

Conversion a mixed number 2  1/3 to a improper fraction: 2 1/3 = 2  1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator

A;   Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one-third are seven-thirds.

Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.

Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It

is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions.  The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12.  It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling.  In other words - seven thirds plus seven quarters is forty-nine twelfths.

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

a e f and g I think this because it has to be then they say that then ya

Answer:

c

Step-by-step explanation:

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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The number of possible arrangements of pictures she can hang on her wall is 120.

The number of possible arrangements can be determined by dividing the factorial of 6 by the factorial of 3.

Number of possible arrangements = 6! / 3!

( 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 6 x 5 x 4 = 120

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