Math true or false

Septima investing money into two different accounts at the same time. the system of inequalities represent the balance of each account where x represents the number of years the money has been invested.
Math! Please help! Please explain your answers.

Answer:

p = 1/12 = p(o1) = p(o3) = p(o5)

3p = 1/4 = p(o2) = p(o4) = p(o6)

Step-by-step explanation:

p(o1) +p(o2) +... +p(o6) = 1 . . . . the condition on the sum of probabilities

... p +3p +p +3p +p +3p = 1 . . . . substitute values

... 12p = 1 . . . . simplify

... p = 1/12 . . . . divide by 12

Then ...

... 3p = 3/12 = 1/4

Final answer:

The probabilities of rolling each face of a loaded six-sided die, where even numbers are three times more likely than odd numbers, are 1/9 for odd numbers (1, 3, 5) and 1/3 for even numbers (2, 4, 6), satisfying the condition that the total probability sums to 1.

Explanation:

The student is dealing with a probability question involving a "loaded" die. To find the probabilities for each face of the die, we assign a variable p to represent the probability of rolling an odd-numbered face and 3p for an even-numbered face. The sum of all probabilities must equal 1 because one of the outcomes must occur when the die is rolled. We can set up the following equation: p + 3p + p + 3p + p + 3p = 1.

Combining like terms gives us 9p = 1, so p = 1/9. Thus, the probabilities of rolling each face are as follows:

This system satisfies the condition that all probabilities sum to 1, making it the correct distribution for this loaded die.

Answer:

A. 36°

Step-by-step explanation:

Same-length chords subtend same-measure arcs. Arc YZ has the same measure as its central angle (∠YOZ) and the same measure as arc XY (36°).

the measure of angle YOZ is 36°, which corresponds to option A. Therefore, the correct answer is option b.

The measure of an angle formed by two chords in a circle is half the measure of the arc intercepted by the angle.

If chord XY is congruent to chord YZ, it means that the arcs intercepted by these chords are also congruent.

So, if the measure of arc XY is "x" degrees, then the measure of arc YZ is also "x" degrees.

Now, the angle YOZ is formed by these two congruent arcs. Therefore, the measure of angle YOZ is half the measure of the arcs XY and YZ.

Angle YOZ = 0.5 * (x + x) = 0.5 * 2x = x degrees.

Now, if you're given the measure of arc XY (or YZ), you can substitute that value into the formula to find the measure of angle YOZ.

The answer choices you provided are in degrees, so the correct answer is A. 36°, assuming you have the measure of the arc XY (or YZ) in the problem.

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Answer:

The table A contains a set of non-linear ordered pairs.

Step-by-step explanation:

To answer this question we have to recall what is the meaning of a linear ordered pair. As you can see, in every table there are 4 values for x, and 4 values for y. In every case, the set of values for x are

[tex]x=\{0, 1, 2, 3\}[/tex]

but in every table, the values for y varies. Now, the key is to calculate the variation of these values, and in order to have a linear relation between x and y, the variation must be the same quantity for every y value that depend of each x value.

For example, in table B, the variation is +3, as from the first y value to the second, 3 is added... and this +3 variation must be the same for each new value of y (and as you can see, 4+3 is 7, 7+3 is 10, 10+3 is 13).

Keeping this in mind, the variation in table C is -2, and the variation in table D is +1, so tables B, C and D contains sets of linear ordered pairs.

To answer the question, we just have to realise that table A has differents variations in the values of y, and this means that it contains a set of non-linear ordered pairs, wich is the correct answer to the question.

We have the triangle 30° - 60° - 90°.

The sides are in proportion: 2 : √3 : 1

(look at the picture).

[tex]2a=14[/tex]       divide both sides by 2

[tex]a=7[/tex]

[tex]a\sqrt3=7\sqrt3[/tex]

The area of a trinagle AFD:

[tex]A_{\Delta}=\dfrac{1}{2}(7)(7\sqrt3)=\boxed{\dfrac{49\sqrt3}{2}}[/tex]

The area of a triangle ADF is 42.46 square units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, in ∆ADF, m∠F=90°, AD = 14 and m∠D=30°

We know that, sinθ= Perpendicular/Hypotenuse

Now, sin A=FD/AD

sin60°=FD/14

⇒ √3/2 = FD/14

⇒ FD=7√3

sin30°=FA/AD

⇒ 1/2 =FA/14

⇒ FA=7

We know that, area of a triangle is 1/2 ×Base×Height

Area of ∆ADF

= 1/2 ×FD×FA

= 1/2×7√3×7

= 42.46 square units

Therefore, the area of a triangle ADF is 42.46 square units.

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Answer:

So, our rate of exponential growth is is 6.93 %

Step-by-step explanation:

The formula for exponential growth rate is

A = P[tex]e^{rt}[/tex] .... (1

Here

P = is the initial investment

A = amount after certain time

As we are given after 10 years (t = 10) the investment doubles

so plugging A=2P and t= 10 into equation (1)

2P = P[tex]e^{10r}[/tex]

cancelling P on both sides

2 = [tex]e^{10r}[/tex]

taking natural log on both sides

ln (2) = ln ([tex]e^{10r}[/tex]

ln(2) = 10r(lne)

as ln(e) = 1

ln (2) = 10r

r = [tex]\frac{ln(2)}{10}  [/tex]

solving the natural log

r = 0.0693

or

r =6.93 %

So, our rate is 6.93 %

Combine the left hand side, then write both sides as powers of 6:

[tex]\log_64x^2-\log_6x=\log_6\dfrac{4x^2}x=2\implies6^{\log_6\frac{4x^2}x}=6^2[/tex]

[tex]\implies\dfrac{4x^2}x=36[/tex]

[tex]\implies x^2=9x[/tex]

[tex]\implies x^2-9x=x(x-9)=0[/tex]

[tex]\implies x=0,x=9[/tex]

However, for any base [tex]b[/tex], [tex]\log_bx[/tex] is undefined if [tex]x=0[/tex], so the only solution is [tex]x=9[/tex].

Answer:

D. x=9

Step-by-step explanation:

The recursive formula

[tex] a_n = 2a_{n-1}+5 [/tex]

means that, to compute the next value, you have to double the previous one and then add 5.

So, we start with 5. To get the second term, we double it and add five, so we have

[tex] a_2 = 2\cdot 5+5 = 10+5 = 15 [/tex]

Next, we will double 15 and add 5:

[tex] a_3 = 2\cdot 15 + 5 = 30+5 = 35 [/tex]

So, the answer is B, because it's the only option starting with 5,15,35.

Just to check, let's compute the last step:

[tex] a_4 = 2\cdot 35 + 5 = 70+5 = 75 [/tex]

Which confirms option B

The amount borrowed is $84,000. The annual interest rate is 6%. There are 12 payments per year for 21 years at a monthly payment amount of $587.

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In the loan scenario, the person borrowed $84,000 at an annual interest rate of 6%. They will make 12 payments of $587 each year for a term of 21 years.

In the provided loan scenario, the following key components can be identified:

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Answer: the angle is 1°+n×120°

1°, 121°, 241°

Step-by-step explanation:

Angles are taken modulo 360°, so 363° = 3°.

Angle plus supplement gives 180°.

Let a be angle, s be supplement of a.

So s = 180-a. Given a = 3 + 2s

a = 3 + 2(180 - a)

a = 3 + 360 - 2a = 363 - 2a

3a = 363° or 3° or 723°

a = 121° or 1° or 241°

a = 1°

s = 179°

2s = 358°

2s+3 = 361° = 1° (modulo 360)

a = 121°

s = 180-121 = 59°

2s = 118°

2s + 3 = 121°, as required.

a = 241°

s = 360+180-241 = 540-241 = 299

2s = 598

2s + 3 = 601 = 241 (modulo 360)

Answer:

Step-by-step explanation:

This is a system of inequalities such that:

[tex]\left \{ {{2x+3y\geq 2} \atop {3x-4y\leq 3}} \right.[/tex]

Let's start by solving for y for both equations:

Equation 1:

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

Equation 2:

[tex]3x-4y\leq 3\\\\-4y\leq -3x+3\\\\y\geq -\frac{(-3x+3)}{4}[/tex]

Now if we substitute the 2nd y into the first equation we obtain:

[tex]2x+3(\frac{3x-3}{4}) \geq  2\\\\2x+\frac{9x-9}{4}\geq 2\\\\\frac{8x+9x-9}{4}\geq 2\\\\17x-9\geq 8\\\\17x\geq 17\\\\x\geq 1[/tex]

Now we will solve for the second equation using the first result of y and we obtain:

[tex]3x-4(\frac{-2x+2}{3}\leq 3\\\\3x+\frac{8x-8}{3}\leq 3\\\\\frac{9x+8x-8}{3}\leq 3\\\\17x-8\leq 9\\\\17x\leq 17\\\\x\leq 1[/tex]

And so our solution for the system of equations is:

[tex]x \leq 1\\and \\y\geq \frac{-2x+2}{3}[/tex]

As well as:

[tex]x>1\\and\\y\geq \frac{3x-3}{4}[/tex]

D) 10.2 ft

The mnemonic SOH CAH TOA reminds you that

... Sin = Opposite/Hypotenuse

You want to find the length of the side Opposite the 50° angle, given the Hypotenuse is 12 ft. Then the relation is ...

... sin(50°) = height/(12 ft)

Multiplying by 12 ft gives

... height = (12 ft)·sin(50°) ≈ 9.2 ft

The height of the platform is 1 ft up from this value:

... 9.2 ft + 1 ft = 10.2 ft

Final answer:

Ramona rode rides at a rate of 2 rides per hour during her visit to the theme park.

Explanation:

Ramona's Rate of Riding Rides:

Rate = Number of rides ÷ Number of hours

Rate = 14 rides ÷ 7 hours

Rate = 2 rides per hour

Answer:

[tex]h^{24}[/tex]

Step-by-step explanation:

[tex](\frac{h^{12}}{h^4})^3\\ (h^8)^3\\h^{24}[/tex]

When dividing two exponents (of the same bases) you subtract the exponents.  When there is an exponent to an exponent, you multiply the to exponents.

[tex]\left(\dfrac{h^{12}}{h^4}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\left(h^{12-4}\right)^3=\left(h^8\right)^3\\\\\text{use}\ (a^n)^m=a^{n\cdot m}\\\\=h^{8\cdot3}=h^{24}\\\\Answer:\ \boxed{\left(\dfrac{h^{12}}{h^4}\right)^3=h^{24}}[/tex]

The midpoint between (-1+9i) and B=(5-3i) is (2+3i).

The midpoint between (-1+9i) and B=(5-3i) can be found by taking the average of the real and imaginary parts separately.

For the real part, we take the average of -1 and 5 which is 2. For the imaginary part, we take the average of 9i and -3i which is 3i.

Therefore, the midpoint between (-1+9i) and B=(5-3i) is (2+3i).

Sarah: 18

Brother: 24

The difference in ratio units is 4-3 =1. The difference in years is 6, so 1 ratio unit stands for 6 years.

Multiplying by 6, we have ...

... Sarah : Brother = 3·6 : 4·6 = 18 : 24

Sarah is 18; her brother is 24.

Answer:

10.8 units

Step-by-step explanation:

As the equation represents the area of a rectangle

i.e.

length * width = Area

Now area is 285.12 units square

while length is 26.4

and width is represented by w

now putting in the formula it will become

26.4 * w = 285.12

dividing both sides by 26.4

[tex]\frac{26.4w}{26.4}=\frac{285.12}{26.4}[/tex]

this will become

w = 10.8 units

Which is the required width of the Rectangle

so answer is 10.8 units

Answer:

option 2

Step-by-step explanation:

in the given triangle,

tan45° = 8/x

=> 1 = 8/x

=>x = 8

for y,

cos45° = 8/y

=>1/√2 = 8/y

=>y = 8√2

Answer:

x=8, [tex]y=8 \sqrt2[/tex]

Step-by-step explanation:

Consider the given right triangle,

As, [tex]\tan \Theta = \frac{Perpendicular}{Base}[/tex]

Consider [tex]\tan 45^{\circ}=\frac{x}{8}[/tex]

[tex]1=\frac{x}{8}[/tex]

So, x=8

As, [tex]\sin \Theta = \frac{Perpendicular}{Hypotenuse}[/tex]

Consider [tex]\sin 45^{\circ}=\frac{8}{y}[/tex]

[tex]\frac{1}{\sqrt2}=\frac{8}{y}[/tex]

So, [tex]y=8 \sqrt2[/tex]

Therefore, x = 8 and [tex]y=8 \sqrt2[/tex]

96 necklaces

To find out how many necklaces Camilla can make, we need to see how many times the required number of beads "goes into" the available number of beads.

Silver: 8160/85 = 96

Black: 2880/30 = 96

Camilla has enough beads to make 96 necklaces.

_____

Comment on this answer

Obviously, if one of the quotients is smaller than the other, Camilla can only make as many necklaces as are supported by the constraining resource.

Even if she had 3000 black beads (way more than 2880), she could still only make 96 necklaces (for example) because she would run out of silver beads making that 96th necklace. (There would be 120 black beads left over in that scenario.)

A graph is attached

The equation is in slope-intercept form:

...  y = mx + b

Here, the value of m (the slope) is 1/2, and the value of b (the y-intercept) is -3.

This means that point (0, -3) is a point on the graph. This point is on the y-axis, 3 units below the x-axis.

Slope is sometimes referred to as "rise over run." The slope of 1/2 means the line will rise 1 unit for each 2 units to the right. That is, for some point (x, y) on the ine, another point will be found at (x+2, y+1).

Given a point at (0, -3), another point will be (0, -3) +(2, 1) = (2, -2), and another point will be (2, -2) +(2, 1) = (4, -1).

You can plot as many points as you like, then draw the line through them.

Answer:

24.5

Step-by-step explanation:

A calculator or spreadsheet is good for doing this sort of computation.

_____

You add up the magnitudes of the differences between the given y-value and the corresponding value you get from the equation. For the first couple of points, these values are ...

... |3 - (0.1·1 +2.9)| = 0

... |2.5 -(0.1·6 +2.9)| = |2.5 -3.5| = 1

The computation proceeds like this for the remaining 6 points, and the numbers added. The result is 24.5.

Answer:

It is rational

Step-by-step explanation:

2 * sqrt(3) * sqrt(12)

2 * sqrt(3) sqrt(4) * sqrt(3)

2 sqrt(3) 2 sqrt(3)

4 sqrt(3)^2

4 *3

12

Multiplying 3 by a smaller number gives a smaller product.

1/10 is smaller than 10, so 3·(1/10) is smaller than 3·10.

Answer:

0.9885   (98.85%)

Step-by-step explanation:

Since sample is less than 10% of the population, we can use binomial distribution to approximate the probability.

So we want to calculate P( X < 20 ).

We can calculate the probability of complement event P( X = 20 ).

Use binomial formula b(x; n, p) = C( n, x ) p^(x) (1-p)^(n-x)

b( 20; 20, 0.8 )

= C( 20, 20 ) (0.8)^(20) (0.2)^0

= (0.8)^20 ≈ 0.0115

So since P( X < 20 ) = 1 - P( X = 20 ), we have

P( X < 20 ) ≈ 1 - 0.0115 = 0.9885

The required value of probability for the given sample is given as 0.9885.

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Total number of students are given as 800.

The probability of students riding the school bus is 80% = 0.8.

Then,  probability of students not riding the school bus is 1 - 0.8 = 0.2.

The probability of finding at least one student out of 20 not riding the bus is given as,

1 - P(All of the students ride bus)

It can be solved using binomial distribution as follows,

⇒ 1 - ²⁰C₂₀(0.8)²⁰(0.2)⁰

⇒ 1 - 0.0115 = 0.9885

Hence, the probability that at least one of the students doesn't ride the bus is given as 0.9885.

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Answer:

B

Step-by-step explanation:

• Parallel lines have equal slopes

calculate the slope m of the given line using the gradient formula and compare to the slope of the equations given

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (1,1) ← 2 points on the line

m = [tex]\frac{1+1}{1+1}[/tex] = 1 ← slope of graph

consider the slope of the given equations

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

(A)

y = 2x + 1 has slope = 2 → not parallel

(B)

x - y = - 3 ( subtract x from both sides )

- y = - x - 3 ( multiply through by - 1 )

y = x + 3 with slope = 1 → thus parallel to graph

(C)

x + y = 2 ( subtract x from both sides )

y = - x + 2 with slope = - 1 → not parallel

(D)

y = - x + 1 with slope = - 1 → not parallel

An equation of a line that is parallel to the line r shown in the graph include the following: B. x - y = -3.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

[tex]y - y_1 = m(x - x_1)[/tex]

Where:

First of all, we would determine the slope for this line by using these points (1, 1) and (0, 0);

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope (m) = (0 - 1)/(0 - 1)

Slope (m) = 1

For the line to be parallel to the line r, it must have the same slope as line r. At data point (0, 0) and a slope of 1, an equation for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

y - 0 = 1(x - 0)  

y = x

Based on the answer options, we have;

y = 2x + 1 ⇒ slope is 2 (not parallel).

x - y = -3

y = x + 3 ⇒ slope is 1 (parallel).

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To find the area of a circle given its diameter's endpoints, determine the diameter length, radius, and then calculate the circle's area using the radius.

The area of a circle can be found using the distance formula between two points representing the diameter's endpoints. Given points P(3,2) and Q(7,10), the diameter length is calculated as sqrt((7-3)^2 + (10-2)^2) = sqrt(4^2 + 8^2) = sqrt(16+64) = sqrt(80).

Knowing that the radius is half the diameter, the radius, r = sqrt(80)/2 = 4*sqrt(5).

Finally, the area of the circle is A = pi*r^2 = pi*(4*sqrt(5))^2 = 80*pi square units.

Answer:

(16 + 8√3) in²

Step-by-step explanation:

The ratio of side dimensions for a 30°-60°-90° triangle are 1 : √3 : 2. If we call the horizontal dimension of the triangle its base, then its height (vertical dimension) will be √3×4 in. Of course the area of the triangle is ...

... A = (1/2)bh = (1/2)(4 in)(4√3 in) = 8√3 in²

The total sod area is the sum of the square area (16 in²) and the triangle area, so is ...

... area to cover = (16 +8√3) in²

_____

Comment on problem dimensions

The area involved here is not much larger than the size of your hand. It would make more sense for the dimensions to be in feet or yards or meters, rather than inches.

Answer: 29.9 in.

Step-by-step explanation:

16+(8*√3)

Answer:

d. 13.5, 20.25

Step-by-step explanation:

An exponential function is monotonic and does not change sign. On this basis alone, the first three choices can be eliminated.

The common ratio is 6/4 = 3/2.

The term in the sequence after 9 is 9·(3/2) = 27/2 = 13.5.

The term in the sequence after 27/2 is (27/2)·(3/2) = 81/4 = 20.25.

Final answer:

The missing values for the exponential function table with an increasing common factor of 1.5 are 13.5 for x=1 and 20.25 for x=2, making the correct answer Option D.

Explanation:

The student's question pertains to finding the missing values for the exponential function represented by the table with given x and y values. Given the nature of an exponential function, we expect that as x increases by 1, the value of y is multiplied by the same factor each time. We can observe this behavior in the initial y-values: 4, 6, and 9. To find this constant multiplier, we can divide 6 by 4 and 9 by 6, which both give us 1.5. This constant factor, which we'll call base of the exponential function, indicates that for every increase of 1 in x, the value of y is multiplied by 1.5.

To find the missing y-values for x=1 and x=2, we just continue multiplying by the base 1.5. Thus, when x=1:

y = 9 × 1.5 = 13.5

When x=2:

y = 13.5 × 1.5 = 20.25

Hence, the completed table should read as follows:

x=-2, y=4

x=-1, y=6

x=0, y=9

x=1, y=13.5

x=2, y=20.25

The correct answer is therefore Option D: 13.5, 20.25.

Answer:

8x2 or (8)(2)

Step-by-step explanation:

The value of 1 hour is 2 widgets, in 8 hours simplified would lead to 8x2 which is 16 widgets.

This leaves you with 16 widgets made in 8 hours.

Frank can make 16 widgets by working 8 hours a day.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that at Frank's work he can produce 2 widgets every hour.

Thus if he produce 2 widgets in one hour, using Unitary method

In 1 hour Frank can make 2 widgets.

Thus in 8 hour work, Frank can make (2 * 8) widgets.

In 8 hour work, Frank can make 16 widgets.

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Answer:

b

Step-by-step explanation:

Final answer:

Point P divides the distance from A to B into a ratio of 3:5, with P being 3/8 of the way from A to B. The correct option is c.

Explanation:

If point P is 3/8 of the distance from A to B, we can understand this situation by imagining the entire distance from A to B as being divided into 8 equal parts, and point P lies at the end of the third part when moving from A to B. Since P is 3 parts away from A, it leaves the remaining 5 parts to reach B. This sets up a partition of the segment into two parts: one from A to P and the other from P to B. The ratio of these distances is the number of parts from A to P to the number of parts from P to B. Therefore, the ratio of AP to PB is 3:5. Option c is accurate.

Answer:

Your answer is Taylor

Step-by-step explanation:

Answer:

Taylor

Step-by-step explanation:

her answer is 0.09 greater then suki who is 2nd biggest

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