William is planning to create a rectangular mosaic which measures 120 cm by 144 cm. The mosaic will be covered completely with square pieces of colored glass. William has decided that he will purchase only one size of glass squares, and he does not plan to cut any of the pieces. If the art supply store only sells the glass squares in whole-number side lengths (measured in centimeters), find the smallest number of squares which William could use for his mosaic.

Step-by-step explanation:

In the first three, the probability of success (or failure) is constant, so those distributions have binomial distributions.

The problem says nothing about doses, which most likely wouldn't be independent events anyways.

So the answer is indeed the first three.  Good job!

Answer: A . When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

Step-by-step explanation:

From all the given options, option A, B and C has trials that have same probability of success for the given event X .

But option D shows event X is the number of doses each patient needs to take which varies depending on the patient.

Hence, the trials do not have same probability of success .

C. randomly select from all residents.

Answer:

Sorry if i'm late but i think the answer is C. Randomly select from all of the town residents

im 97% sure

Answer:

The sum is equal to 5

Step-by-step explanation:

we know that

The algebraic expression of the phrase "  the sum of negative two squared plus one" is equal to

[tex](-2)^{2}+1\\=4+1\\=5[/tex]

Answer:

5

Step-by-step explanation:

(-2)^2 +1

Since the quantity is squared, it becomes a positive number

4+1

5

look at the picture not my text lol

Answer:

B

Step-by-step explanation:

Look at the other guys box and whisker plot

Answer:

your answer is a

Step-by-step explanation:

The correct inequality and number line that model the situation above is:

             10 ≤ weight of boxes ≤ 20

  and the correct graph is:  Graph A

The desired weight of raisins is:  15 ounces.

As the weight of the raisins packed differs by a maximum of 5 ounces.

This means that the weight of the raisins packed could either be less by 5 ounces or more by 5 ounces.

i.e.  Weight of raisins could be minimum= 15-5=10 ounces.

and weight of raisins could be maximum= 15+5=20 ounces.

Hence, the inequality that will hold true is:

               10 ≤ weight of boxes ≤ 20

and the graph that describe this situation is attached to the answer.

Answer:

  see below

Step-by-step explanation:

21) The law of sines can be used, since you have a side and its opposite angle.

  sin(F)/DE = sin(D)/EF

  F = arcsin(DE/EF·sin(D)) = arcsin(20/31·sin(95°)) ≈ 39.994°

  E = 180° -95° -39.994° ≈ 45.006°

  DF = sin(45.006°)/sin(95°)·31 ≈ 22.006

__

22) The remaining two problems can be solved using the law of cosines:

  c^2 = a^2 + b^2 - 2ab·cos(C)

Of course, c is the square root of the expression on the right.

  EF = √(19^2 +35^2 -2(19)(35)cos(61°)) ≈ √(941.203) ≈ 30.679

Then an angle can be found using the law of sines

  E ≈ arcsin(35/30.679·sin(61°)) ≈ 86.203°

  F ≈ 180° -61° -86.203° ≈ 32.797°

__

23) As in 22 …

  RS = √(20^2 +28^2 -2(20)(28)cos(91°)) ≈ √(1203.547) ≈ 34.692

  R ≈ arcsin(20/34.692·sin(91°)) ≈ 35.199°

  S ≈ 180° -91° -35.199° ≈ 53.801°

the answer is.... no solution

An equation is formed of two equal expressions. For the given equation 64³ˣ=512²ˣ⁺¹² no solution for x exists.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The above equation 64³ˣ=512²ˣ⁺¹² can be solved in the following manner as stated below,

64³ˣ = 512²ˣ⁺¹²

(8²)³ˣ=(8³)²ˣ⁺¹²

8⁶ˣ = 8⁽⁶ˣ⁺³⁶⁾

6x = 6x +36

6x - 6x = 36

0 = 36

As the value of x can not be defined, it can be concluded that the equation has no solution.

Hence, for the given equation no solution for x exists.

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False

As indicated in Figure A below, Plane S contains only point B (remarked in red). Point E (remarked in blue) lies on plane R.

True

As indicated in Figure B below, the line containing points A and B lies entirely in plane T. That line has been remarked in red and it is obvious that lies on plane T.

False

As indicated in Figure C below, line v intersects lines x and y, but line x in intersected at point B while line y (remarked in red) is intersected at point A (remarked in blue), and they are two different points, not the same.

True

As indicated in Figure D below, line z that has been remarked in yellow, intersects plane S at point C that has been remarked in blue.

True

As indicated in Figure E below, planes R and T intersect at line y. The line of intersection has been remarked in red.

Answer:

The Monday ratio was equal to the Tuesday ratio.

The Tuesday ratio was greater than the Wednesday ratio.

The Wednesday ratio was less than the Monday ratio.

Step-by-step explanation:

Using the ratio and Proportion concept, The true statements are:

The Monday ratio was equal to the Tuesday ratio.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.

What is Proportion?

Ratio and fractions are the main bases on which proportion is discussed. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a percentage. In this case, a and b can be any two numbers. Ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics.

So, According to the question:

The ratio on Monday = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]

The ratio on Tuesday = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]

The ratio on Wednesday = [tex]\frac{6}{6}[/tex] = [tex]\frac{1}{1}[/tex]

So, from the above fraction, we can easily conclude that The Monday ratio was equal to the Tuesday ratio.

Hence, The Monday ratio was equal to the Tuesday ratio.

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Answer:

19

Step-by-step explanation:

If C is the midpoint of KN, then KC = CN

So we can equate the expressions

[tex]KC= 2x+10[/tex]

[tex]CN= 4x+1[/tex]

KC = CN

[tex]2x+10=4x+1[/tex]

Subtract 2x on both sides

[tex]2x-2x+10=4x-2x+1[/tex]

[tex]10=2x+1[/tex]

Subtract 1 on both sides

[tex]9=2x[/tex]

Divide both sides by 2

[tex]x=4.5[/tex]

Now we find out KC

[tex]KC= 2x+10[/tex]

[tex]KC= 2(4.5)+10[/tex]

[tex]KC= 19[/tex]

Answer:

the new pyramid in terms of b and h.

Step-by-step explanation:

the new pyramid

Answer: The radius

Step-by-step explanation:

The radius is the distance between the center point of the circle and a edge, it is half of the diameter which is the straight line passing through the center point.

Answer:

an exponential function

Step-by-step explanation:

Use a function of the same form as the compound amount formula:

A = P(1+r)^5, where r is the appreciation or depreciation rate and P is the initial value.  This is definitely an exponential function.

The given function could model the value of the car as an exponential function.

We have given that,

Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year.

We have to determine which type of function could model the value of the car.

Use a function of the same form as the compound amount formula

A = P(1+r)^5,

where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.

Therefore the given function could model the value of the car as an exponential function.

Therefore the option A is correct

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Answer:

(x − 4)2 + ( y + 6)2 = 49

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is                                (x − h)2 + (y − k)2 = r2.

Define h, k and r using the given values. So, h = 4, k = −6 and r = 7.

Substitute the values into the equation of a circle:

(x − 4)2 + (y − (−6))2 =72

Simplify.

(x − 4)2 + (y + 6)2 = 49

Therefore, the equation of the circle B with center B(4, -6) and radius 7 is   (x − 4)2 + (y + 6)2 = 49.

The equation of the circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the corrcet option is B.

A circle can be represented as;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where h and k are the centers of the circle and r is the radius of the circle.

The equation of circle B with center B(4,−6) and radius 7.

Substitute all the values in the equation

[tex]\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-4)^2+(y-(-6))^2=7^2\\\\\rm (x-4)^2+(y+6)^2=49[/tex]

Hence the equation of circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the correct option is B.

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Answer:

N⊥M

Step-by-step explanation:

If N║ P and P⊥M then N⊥M

Answer:

The answer is (d) ⇒ cscx = √3

Step-by-step explanation:

∵ sinx + (cotx)(cosx) = √3

∵ sinx + (cosx/sinx)(cosx) = √3

∴ sinx + cos²x/sinx = √3

∵ cos²x = 1 - sin²x

∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M

∴ (sin²x + 1 - sin²x)/sinx = √3

∴ 1/sinx = √3

∵ 1/sinx = cscx

∴ cscx = √3

Answer:

d. [tex]\sqrt{3}[/tex]

Step-by-step explanation:

see attachment, it's correct :))

Answer:

Correct choice is (C). [tex]4z^5[/tex].

Step-by-step explanation:

Given expression is [tex]-3z^5-\left(-7z^5\right)[/tex].

Now we need to simplify that then select the correct difference value from the given choices.

[tex]-3z^5-\left(-7z^5\right)[/tex]

negative times negative is positive

[tex]=-3z^5+7z^5[/tex]

Combine like terms because variable z has same exponent.

[tex]=(-3+7)z^5[/tex]

[tex]=4z^5[/tex]

Hence correct choice is (C). [tex]4z^5[/tex].

Answer:

2

Step-by-step explanation:

It is not 7, although that looks possible. The 7 is a coefficient (in my day we called it a numerical coefficient).

The constant is not d either.  That is a variable.

The constant is the 2

Step-by-step explanation:

y = ⅓x − 2

y = -3x − 12

The first line has a y-intercept of -2 and a slope of ⅓.

The second line has a y-intercept of -12 and a slope of -3.

The graph looks like this: desmos.com/calculator/raouxrikbg

From the graph, we see they intersect at (-3, -3).

Answer:The length is 13/2, while the width is 15/4, after combination. Ratio of length to width is then (13/2)/(15/4) = 26/15.

Answer:

[tex]\frac{b+3}{3}[/tex]

Step-by-step explanation:

[tex]\frac{b+3}{b} \div\frac{3}{b}[/tex]

We need to solve the above equation.

We replace the division sign by multiplication and reciprocated the second term

[tex]=\frac{b+3}{b} *\frac{b}{3}[/tex]

Multiplying both fractions:

[tex]=\frac{(b+3)*b}{3b}[/tex]

Cancelling b from numerator and denominator.

[tex]=\frac{(b+3)}{3}[/tex]

So, answer is:

[tex]\frac{b+3}{3}[/tex]

ANSWER

[tex]\frac{b + 3}{3}[/tex]

EXPLANATION

The given expression is

[tex] \frac{b + 3}{b} \div \frac{3}{b} [/tex]

We multiply the first fraction by the multiplicative inverse of the second fraction.

[tex]\frac{b + 3}{b} \times \frac{b}{3}[/tex]

We now cancel out the common factors to get:

[tex]\frac{b + 3}{3} [/tex]

Therefore simplified form is:

[tex]\frac{b + 3}{3} [/tex]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

[tex]\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}[/tex].

[tex]\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}[/tex].

[tex]\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}[/tex].

Note that the inverse sine function here [tex]\sin^{-1}()[/tex] is also known as arcsin.

By the law of cosine,

[tex]c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}[/tex],

where

For triangle ABC:

Therefore, replace C in the equation with A, and the law of cosine will become:

[tex]a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}[/tex].

[tex]\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}[/tex].

For triangle ABC:

Start by finding the cosine of angle B. Apply the law of cosine.

[tex]b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}[/tex].

[tex]\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}[/tex].

[tex]\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree[/tex].

For triangle DEF:

Apply the law of sine:

[tex]\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}[/tex]

[tex]\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9[/tex].

Answer:

24°

Step-by-step explanation:

The sum of the ratios is 30.  We know that the degree measure of a triangle is 180, so if we divide 180 by 3 we get increments of 6°.  That means that 4 parts algebraically can be expressed as 4(6°); 12 parts as 12(6°); 14 parts as 14(6°).  That gives us angles of 24°, 72°, 84°.  If we add those up we do indeed get 180°, so the smallest angle measure in that extended ratio is 24°

Answer:

B. -9a+2

Step-by-step explanation:

You are given the sequence

[tex]t_1=2a,\\ \\t_2=3a-1,\dots\\ \\t_n=2t_{n-1}-3t_{n-2}+1,\ n\ge 3[/tex]

According to the given rule, find [tex]t_3,\ n=3[/tex]

[tex]t_3=2t_2-3t_1+1=2\cdot (3a-1)-3\cdot 2a+1=6a-2-6a+1=-1[/tex]

and [tex]t_4,\ n=4[/tex]

[tex]t_4=2t_3-3t_2+1=2\cdot (-1)-3(3a-1)+1=-2-9a+3+1=-9a+2[/tex]

Answer:

D. x > -4 or x < -8

Step-by-step explanation:

For this case we must indicate the solution of the following inequalities:

[tex]4x> -16[/tex]

We divide both sides of the inequality by 4:

[tex]x> - \frac {16} {4}\\x> -4[/tex]

On the other hand we have:[tex]6x\leq - 48[/tex]

We divide between 6 on both sides of the inequality:

[tex]x\leq - \frac {48} {6}\\x\leq- 8[/tex]

Thus, the solution will be:

[tex]x>-4[/tex] or [tex]x\leq-8[/tex]

ANswer:

Option D

The probability would be 50 because 25+25=50

Answer:

$11,250

Step-by-step explanation:

Yvonne earns a fixed amount of $1,850 per month and want to earn $2,300. The difference is

[tex]\$2,300-\$1,850=\$450.[/tex]

This difference is her commission. If she earns the commission of 4% on the amount of goods that she sells, then

$x - 100%

$450 - 4%

Make a proportion:

[tex]\dfrac{x}{450}=\dfrac{100}{4}\Rightarrow 4x=45,000\\ \\x=\dfrac{45,000}{4}\\ \\x=\$11,250[/tex]

Yvonne must sell $11,250

Answer:

The predicted GPA is then y = 0.149(15) + 0.89 = 3.125

Step-by-step explanation:

Although you don't specifically say so, the equation you provide here is probably a "best fit" equation based upon data:  GPA versus number of hours of study per week.

Here, y = 0.149x + 0.89 and the number of study hours of interest is 15.

The predicted GPA is then y = 0.149(15) + 0.89 = 3.125

The GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a line of best fit:

y = 0.149x + 0.89

Plug x = 15 hours

y = 0.149(15) + 0.89

y = 3.125

Thus, the GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89

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For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following line:

[tex]2x-3y = 12\\2x-12 = 3y\\y = \frac {2} {3} x-4[/tex]

If the line we wish to find is perpendicular to the one given, then its slope is given by:

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = - \frac {3} {2}[/tex]

Then the line is:

[tex]y = - \frac {3} {2} x + b[/tex]

We substitute the point:

[tex]6 = - \frac {3} {2} (2) + b\\6 = -3 + b\\b = 6 + 3\\b = 9[/tex]

Finally, the equation is:

[tex]y = - \frac {3} {2} x + 9[/tex]

Answer:

[tex]y = - \frac {3} {2} x + 9[/tex]