Lucia draws a square and plots the center of the square. She claims that any rotation about the center of the square that is a multiple of 45" will carry the square onto itselt Which statement best describes Lucia's claim? a. Lucia's claim is incorrect since not all rotations that carry a square onto itself are multiples of 45
b. Lucia's claim is incorrect slace not all rotations that are multiples of 45' carry a square onto itself c. Lucia's daim is correct since any rotation that is a multiple of 45 canles a square onto tselt d. Lucia's calm is correct since any rotation that comes a square onto itself is a multiple of 45

The linear function that relates your distance to the number of seconds is y = Sx, and the graph is attached below.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

The formula for distance covered is given by,

[tex]Distance = Speed \times time[/tex]

Assume the speed is constant,

D = S × t

Assume distance is in y direction and time is in x direction, the equation can be written as,

y = Sx

Suppose my speed of mine is 5 m / s and the speed of my friend's is 10 m/s then the function of distance for my friend,

Y = 10X

And for me

y = 5x

The graph of this is attached below, the red line in the graph is my distance equation and the green line is of my friend.

Therefore, the linear function that relates your distance to the number of seconds is y = Sx.

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Answer:

-21.5b - 16

Step-by-step explanation:

Simplify the expression

3(−5.5b − 3) − (5b + 7)

-16.5b - 9 - 5b - 7  [Expand the parentheses]

-21.5b - 16              [Add like terms]

This matches the third option.

Step-by-step explanation:

as percent means per 100

So we can say 0.54 or 54100 is the same as 54%.

hope understand

The measure of the required angle of the given rhombus ABCD is m∠ADC = 64°.

The given rhombus has four angles as

∠ADC, ∠DCB, ∠CBA, and ∠BAD

It has two diagonals that bisect each other at point E.

And we have ∠ABD = 32° and ∠ACD = 58°

Here, the angles ∠ABD and ∠BDC are alternate angles. Since we know that, the alternate angles are equal in measure, we can write

∠ABD = ∠BDC

⇒ 32° = ∠BDC

Since we know that the diagonals of a rhombus bisect the angles, we get

∠ADC = 2∠BDC

⇒ ∠ADC = 2 × 32° = 64°

Therefore,  the required angle of the rhombus is ∠ADC = 64°.

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The buyer concludes that there is not a significant difference between the observed t-shirt sales and the expected t-shirt sales.

Given :

goodness of fit 5. a buyer for a t-shirt shop wants to compare the proportion of t-shirts of each size that are sold to the proportion that were ordered. the buyer counts the number of t-shirts of each size that are sold in a week.

Test :

Test             Contribution

Category     Observed  Proportion  Expected  to Chi-Square

Small              25                  0.1           22.5       0.277778

Medium          41                  0.2           45.0       0.355556

Large              91                  0.4           90.0       0.011111

Extra Large    68                  0.3           67.5       0.003704

The overall chi-square statistic is 0.648 and has a p-value of 0.885. Because the p-value is greater than the significance level of 0.05, the buyer fails to reject the null hypothesis.

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The numbers which are greater than 1 are 2 ÷ 1/3 and 3/4 ÷ 2/3 so options (B) and (D) are correct.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

As per the given fractions,

2 ÷ 1/3 = 2 x 3/1 = 6 > 1

3/4 ÷ 2/3 = 3/4 x 3/2 = 9/8 > 1

Hence "The numbers which are greater than 1 are 2 ÷ 1/3 and 3/4 ÷ 2/3".

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The complete question below,

Here is sufficient evidence that revenue and the number of downloads are linearly related.

A computer software developer would like to use the number of downloads for the trial version of his new shareware to predict the amount of revenue.

The Null hypothesis is the common statistical theory that asserts that no statistical relationship or significance exist between two sets of observed data and measure phenomena based on a single observed variable.

Therefore the null hypothesis become,

H₀ : ρ₁ = 0

and the adjacent hypothesis will become,

H₁ : ρ ≠ 0

Now we will calculate test statistic,

t = r × [tex]\sqrt{\frac{n-2}{1-r^{2} } }[/tex]

 = (0.8691) × [tex]\sqrt{\frac{30 - 2}{0.1309^{2} } }[/tex]

t = 9.2974

we know that degree of freedom = n - 2 = 28

p-value at t = 9.2974 is 0.00

α = 0.05

since p-value < α

so null hypothesis will be rejected.

Hence we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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The u(1, 1, 2), v(2, 3, 1), and w(4, 5, 5) supplied vectors are linearly dependent.

A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.

As per the given information in the question,

The given vectors are:

u = (1, 1, 2)

v = (2, 3, 1) and,

w = (4, 5, 5)

If there are three scalars that are not all zero and that are dependent on a set of vectors (u, v, and w), they have been shown to be linearly dependent.

au + bv + cw = 0

⇒ a(1, 1, 2) + b(2, 3, 1) + c(4, 5, 5) = (0, 0, 0)

⇒ (a + 2b + 4c, a + 3b + 5c, 2a+ b + 5c) = (0, 0, 0)

So,

a + 2b + 4c = 0    (i)

a + 3b + 5c = 0    (ii)

2a+ b + 5c = 0     (iii)

From equation (i) and (ii)

b = -c

From equation (i)

a - 2c + 4c = 0

⇒ a = -2c

Let's assume that c = 1

So,

a = -2 and,

b = -1

Then, from the obtained values,

-2u - v + w = 0

As a result, there is a set of non-zero values for a, b, and c such that:

au + bv + cw = 0

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0.65  is the probability that the chosen student eats neither fish nor eggs.

What are examples and probability?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.                  

                                      The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

We know that there is sample of 275 MHS Students

20 are vegetarians

      9 eat both fish and eggs

      3 eat eggs but not fish

      8 eat neither

Total 20

In a table

           FISH FISHc TOTAL

EGGS     9        3       12

EGGSc   1         7        8

TOTAL    10       10      20

P(F U E) = 9 + 3 + 1 / 20 = 13/20 = 0.65

Or

P(F U E) = 10/20 + 12/20 -9/20 = 13/20 = 0.65

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Answer: Mr.Jones have to drive 420 miles more to get to his destination

Step-by-step explanation:

Find 70 percent of 600

70 percent is the same as 0.7

Mutiply 600 by 0.7 to find the remaining miles

600*0.7=420

(2, 1,985.5) is not a solution of the equation y = 2200(0.95)x.

What is solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Consider, the given equation

y = 2200(0.95)x

And the point given is, (2, 1985.5).

From this x = 2, y = 1985.5

Plug x = 2 in the above equation,

y = 2200(0.95)(2)

y = 4180 ≠ 1985.5

Hence, the given point (2, 1985.5) is not a solution to the equation

y = 2200(0.95)x.

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Answer:

all the above

Step-by-step explanation:

examples of undefined term are point line and plane

90 miles per hour is 132 feet per second. To convert multiply it by 5,280, then divide by 3,600. The foot per second is a speed and velocity unit.

Mile per hour is a speed unit defined in the Imperial and US customary systems of measurement. It calculates how many miles an object travels in an hour. The international mile [mi] is a length unit that is equivalent to 5280 feet and precisely defined as 1609.344 metres. The abbreviation mph is more commonly used on signs and labels, but in science and engineering contexts, mi/h may be more convenient for unit arithmetic.

The Imperial and US customary systems of units define the foot per second as a unit of speed. It calculates the distance an object travels in one second. The foot [ft] is a length unit that is precisely defined as 0.3048 metres.

To convert a speed value from miles per hour to feet per second, multiply it by 5,280, then divide by 3,600.

Speed in miles per hour = 90 miles per hour

Speed in feet per second = 90 * 5,280 / 3600 = 132 feet per second

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The measures of the missing angles are:

1. x = 41°

2. x = 100°

3. x = 42°

4. x = 47°

5. x = 65°

6. x = 73°

7. x = 70°

8. x = 43°

To find the missing measures of each of the angles given, we need to apply one of the property of isosceles triangles which states that the base angles of an isosceles triangle has the same measure.

1. x = 41° [base angles]

2. x = 180 - 2(40) = 100°

3. x = 180 - 2(69) = 42°

4. x = 1/2(180 - 86) = 47°

5. x = 65° [base angles are equal]

6. 2x = 146

2x/2 = 146/2

x = 73°

7. x = 180 - 2(180 - 125)

x = 70°

8. 2x = 86

2x/2 = 86/2

x = 43°

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Probability that jim will not be accepted at either university is 0.42

He has applied to two different universities.

the acceptance rate for applicants with similar qualifications is 30% for university x

the acceptance rate for applicants with similar qualifications is 40% for university Y

Here, getting accepted into the two different universities are two independent events.

P(A or B) = P(A) x P(B)

Probability of not getting accepted in university X is 1 - 0.30

Probability of not getting accepted in university Y is 1 - 0.40

Probability that jim will not be accepted at either university

P'(X or Y) = P'(X) x P'(Y)

=(1 - 0.30) x(1 - 0.40) = 0.70 x 0.60 = 0.42

Therefore, Jim will not be accepted at either university has a probaility of 0.42 or 42%

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For the linear factors of the cubic, which are (x - 2)(x - 3)(x – 5), the function will be f(x)=1/6x³–5/3x²+31/6x–5.

The first-degree equations that make up a polynomial's linear factors serve as the foundation for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. A linear factor model establishes a linear equation-based relationship between the return on an asset (such as a stock, bond, mutual fund, or other type of investment) and the values of a small number of factors.

Here,

The linear factors of the cubic are  

=(x – 2)(x – 3)(x – 5)

To solve for the leading coefficient, use  

–5 = a(0 – 2)(0 – 3)(0 – 5)

a = 1/6

f(x)=1/6x³–5/3x²+31/6x–5

The function will be f(x)=1/6x³–5/3x²+31/6x–5 for the the linear factors of the cubic that is (x – 2)(x – 3)(x – 5).

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Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.

What is independent events?

Winning a hockey game and scoring a goal is dependent because if we score a goal then only we can win the game.

Hence, Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.

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Using the given information, the city's next year population will be 69,840

From the question, we are to determine what the population of the city will be the following year

From the given information,

"The population of a city decreases by 3.3% per year"

and

This year's population is 72,000

Thus,

The population of the following year will be

72000 - 3% of 72000

Next year population = 72000 - 3% of 72000

Next year population = 72000 - 3% × 72000

Next year population = 72000 - 0.03 × 72000

Next year population = 72000 - 2160

Next year population = 69,840

Hence, the population will be 69,840

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The answers to each part are as follows -

a. n refers to the number of bought tickets. p is representative of the probability that I will win some prize after taking a single ticket.

b. The values of X will be in the range 0 to 5. It is indicative of number of won tickets. Hence, values that are possible are 0, 1, 2, 3, 4 and 5.

c. The probability of each value of x will be calculated using Binomial formula. The formula is-

P(x) = (n choose x) × [tex] {p}^{x} [/tex] × [tex] {(1 - p)}^{n - x} [/tex]

In this formula, n is the number of trials, p is probability of success and x is number of successes.

Keep the values in formula for calculation -

P(0) = (5 choose 0) * 0.256^0 * (1-0.256)^(5-0)

P(0) = 0.326

P(1) = (5 choose 1) * 0.256^1 * (1-0.256)^(5-1)

P(1) = 0.410

P(2) = (5 choose 2) * 0.256^2 * (1-0.256)^(5-2)

P(2) = 0.219

P(3) = (5 choose 3) * 0.256^3 * (1-0.256)^(5-3)

P(3) = 0.062

P(4) = (5 choose 4) * 0.256^4 * (1-0.256)^(5-4)

P(4) = 0.011

P(5) = (5 choose 5) * 0.256^5 * (1-0.256)^(5-5)

P(5) = 0.001

d. For the probability histogram stating the distribution of x, the x-axis will have x values and y-axis will have the probability of each x value. The mean of distribution will be calculated by the formula -

mean = n × p

mean = 5 × 0.256

mean = 1.28

Further, the standard deviation will be calculated by the formula -

Standard Deviation = [tex] \sqrt{n × p × (1-p)} [/tex]

Keep the values in formula -

Standard Deviation = [tex] \sqrt{5 × 0.256 × (1-0.256)} [/tex]

Standard Deviation = 0.995

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If we reject the null hypothesis, we conclude that there is not enough statistical evidence to infer that the null hypothesis is true.

In hypothesis testing, the researcher makes a claim about the population and then uses a sample of the population to determine whether or not the claim is accurate. Before the sample is drawn, the degree of significance—or the predicted error—must be determined. The validity of a claim is determined by the value of a test statistic.

The researcher rejects the provided null hypothesis if the test statistic's value is significant. When the null hypothesis is rejected, there is no discernible difference between the hypothesized value and the sampled observations. If the null hypothesis is rejected, it is determined that there is insufficient statistical support to draw the conclusion that it is true.

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Step-by-step explanation:

Liz is baking cookies. a single batch uses ¾ teaspoons of vanilla. if Liz is mixing the ingredients for five batches at the same time, how many tablespoons of vanilla will she use?

3/4 = 0.75 teaspoons

0.75 teaspoons  * 5 batches = 3.75 teaspoons

There are 3  teaspoons in a tablespoon so:

Liz will use:

1 1/4 tablespoons

if you need in decimal form: 1.25 tablespoons

Answer:  [C]:  " 46 units ."
______

Step-by-step explanation:

The question (and corresponding image) asks:
 " If B is the midpoint of AC, find the length of AC. "

Note:  
    The midpoint refers to the point in the middle of the line [segment].

In this particular question:
⇒ The line segment; AC  is divided into 2 (two) equal segments of the same length:
  AB = (x + 13) ;  and:

  BC = (2x + 3) ;  {as per 'posted image'} ;
We  are asked to find the length of AC.

[length of AB] + [length of BC] = [length of AC].

            (x + 13) +  (2x + 3)  = [length of AC; for which we solve] :

We shall solving for x ; & then plug in the value to solve.
Note:
   [length of AB] =  [length of BC] ;  Plug in our known values:
⇒ that is;  (x + 13) = (2x + 3) ;

So, we have:  " x + 13  = 2x + 3 "

_____________________

 " x  +  13  =    2x  +  3    "  ;

− x   −  3   =   − x   −  3   "   ;

_____________________
  0  +   10  =     x   +  0 ;

  →  "  10 = x  " ;

       ↔  {Note: According to the "symmetric property" algebra:
                "a = b " ; then " b = a"};

  →  " x = 10 " ; {according to the "symmetric property of alm
__________________
Another method:
 When we have:
 " x  +  13  =   2x  +  3  " ;

→ Subtract each side of the equation by x ; & subtract each side of the equation by 3 ;  

to isolate x on one side of the equation —
  [in this case, the 'right-hand' side of the equation];

and to solve for x ; as follows:
  " x  +  13  =  2x + 3 ";

Now; for each side of the question—on a separate 'left-hand' side; and: on a separate 'right-hand' side basis; we can combine the 'like terms' and simply:
 For the left-hand side:
   "  x  +  13  − x − 3 " : Combine the 'like terms":
   + x −  x  =  0 ;  [that is: " +1x − 1x = 0"];
  + 13 − 3 = + 10 ;  We have:  " 0 + 10 = + 10 ".    

Now, For the right-hand side:
  " 2x  +  3  − x − 3 " :  Combine the 'like terms'; as follows:

     " + 2x  − x  = x " ; {that is:  " +2x − 1x = 1x = x "} ;

     " + 3  − 3  " =  0 " .   " x + 0 = x "    

        So: [left-hand side = right-hand side] ;

             →    10 =  x ;  ↔ " x = 10 ."

Both methods result in the same value for x ; that is:  x = 10 ; which happens to suggest credibility.

Now, to find the length of AC ; which equals:
 →   " x + 13 + 2x + 3 " ;
Then, we plug in our calculated value; 10 —for the values of x ;
 and solve!

→  " 10 + 13 + (2*10) + 3 "  =  " 10 + 13 + 20 + 3 "  =  " 46 units ".

⇒ which corresponds to the correct answer:  [C]:  " 46 units."

_______
Hope this answer with explanation is helpful.

 Best wishes!
_______

3 of 7 in percentage with rounding is 42.86%

Percentage is a way of expressing a number as a fraction of 100. It is often used to express how much of something there is compared to the total amount.

For example, if you have 20 apples and the total number of apples is 100, you can express the fraction of the total number of apples you have as a percentage. That is 20/100 = 0.2, which is equal to 20%.

In order to write 3 of 7 as a percent, we can say:

3/7 × 100 = 42.86%

Thus, with rounding 3 of 7 is 42.86%

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Complete Question

3 of 7 percent with rounding  =  ___ %

A. y = - (4/3)x + 4.

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

No solution.

B. y = 4x - 5.

y = - 2x + 7.

one solution.

C. 2x + 3y = 8

4x + 6y = 17.

No solution.

D. y = 5x - 15.

y = 5(x - 3).

Infinitely many solutions.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

We'll graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.

y = - (4/3)x + 4.

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

These are parallel lines no solution.

y = 4x - 5.

y = - 2x + 7.

These lines intersect at (2, 3) one solution.

2x + 3y = 8

4x + 6y = 17.

They are parallel to each other.

y = 5x - 15.

y = 5(x - 3).

These are coinciding lines if we distribute the terms hence infinitely many solutions.

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Answer:

around 8,000 or 100,000 is the answer

The expression which is equivalent to −10.75(20x +15.2) is -215x - 163.4.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical terms.

As per the given expression,

−10.75 (20x +15.2)

By multiplying or opening the bracket,

When a bracket opens then the outer number will multiply with all inner variables as,

⇒ (-10.75 × 20x) + (- 10.75 × 15.2)

⇒ -215x - 163.4

Hence "The expression which is equivalent to −10.75(20x +15.2) is -215x - 163.4".

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Based on the permutation concept, the allowed final result is 20

Permutation method

In statistics, permutation means a mathematical calculation of the number of ways a particular set can be arranged.

Given

Here we need to find how many bit strings of length 5 do have 3 consecutive zeros such that the remaining two bits are not not equal.

Let us consider T denote the number of bit strings of length  containing 3 consecutive 0's.

Total no. of bit strings of length = 5

And the no. of bit strings of length  not containing 3 consecutive 0's = 3

Then the possible combination of permutation is calculated as,

=> T = 5!/3!

=> T = 20

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Answer: 8 + i

Step-by-step explanation:

The complex number 8/1+i can be written in standard form as 8 + i. In standard form, a complex number is written as a+bi, where a is the real part and bi is the imaginary part. In this case, the real part is 8 and the imaginary part is i. Therefore, the standard form of the complex number 8/1+i is 8 + i.

Answer: 4-4i

Step-by-step explanation:

[tex]\displaystyle\\\frac{8}{1+i} =\\\\\frac{8(1-i)}{(1+i)(1-i)}=\\\\\frac{8(1-i)}{1^2-i^2} =\\\\\frac{8(1-i)}{1-(\sqrt{-1})^2 }=\\\\\frac{8(1-i)}{1-(-1)}=\\\\\frac{8(1-i)}{1+1} =\\\\\frac{8(1-i)}{2} =\\\\4(1-i)=\\\\4-4i[/tex]