The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below.
How many roots of f(x) are rational numbers?

Answer: -5x= -11

Step-by-step explanation:

Final answer:

Subtracting equations to find the value of x.

Explanation:

The result of subtracting the second equation from the first is:

Subtract every corresponding term:

-4x - 2y - (x - 2y) = -2 - 9

-4x - 2y - x + 2y = -11

-5x = -11

x = 11/5 or 2.2

Answer: shameeka sold 20 hamsters to the store.

Step-by-step explanation:

Let x represent the number of hamsters that shameeka sold to the store.

Let y represent the number of hamsters that the pet store had initially.

Shameeka sold her hamsters to a pet store. This doubled the number of hamsters in the store. It means that

x + y = 2y

x = 2y - y

x = y

Then the store got six more hamsters. If the pet store has 46 hamsters now, it means that

2y + 6 = 46

2y = 46 - 6

2y = 40

y = 40/2

y = 20

Since x = y, then

x = 20

Answer:

w=(x-6)

Step-by-step explanation:

x^2-4x-12=(x + 2)(w)

a=wl (area equals width times length)

x^2-4x-12=(x + 2)(w)

(x-6)(x+2)=(x + 2)(w)

(x-6)=w

Answer: La respuesta es cada 132 clientes

Lo que hice fue poner la parte de 33 y 44 sumándose entre si:

33+33=66+33=99+33=132 etc

44+44=88+44=132 etc

Y si te diste cuenta concuerdan los dos en 132

Espero que te sirva

Aplicando el mínimo común múltiplo, se encuentra que a cada 132 clientes se ganan los dos premios es una misma compra, opción D.

Para ver los que ganam ambos, hay que ver lo mínimum común múltiplo de 33 y 44, o sea:

33 - 44|2

33 - 22|2

33 - 11|3

11 - 11|11

1

mcm(33,44) = 2x2x3x11 = 132

O sea, cada 132 clientes se ganan los dos premios es una misma compra, opción D.

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Plane A and Plane B will be approximately 1061.21 miles apart at 5:00 p.m

Given: Speed of plane A is 300 mph and B is 225 mph. Plane A leave at 2 pm and B leaves at 2:30 pm

To find: distance between them at 5 pm

We know that [tex]\text{speed} = \frac {\text{distance}}{\text{time}}[/tex]

So, we can find distance travelled by plane A by 5 pm [tex]= 300 \times 3 = 900[/tex] miles

To calculate distance travelled by plane B we need to find the time plane B has flied between 2:30 and 5 pm. We can see that the plane flew for 2 hours and 30 mins. We can write 2 hours 30 mins as 2.5 hours.

So, distance travelled by plane B by 5 pm [tex]= 225 \times 2.5 = 562.5[/tex] miles

Since plane A is moving in north and plane B is moving in east, it forms a right angled triangle with 900 miles and 562.5 miles as its perpendicular and base.

To find distance between the planes we can use Pythagoras theorem:

[tex]\text{hypotenuse} = \sqrt{ \text{(perpendicular)}^2 + \text{(base)}^2} \\\text{hypotenuse} = \sqrt{ 900^2 + 562.5^2}\\\text{hypotenuse} = \sqrt{810000 + 316406.25}\\\text{hypotenuse} = \sqrt{1126406.25} \approx 1061.21\\[/tex]

Therefore, the planes will be approximately 1061.21 miles apart at 5:00 p.m.

Answer:.5

Step-by-step explanation:

.5

AEC is congruent to DEB should be the answer for 5.

ALSO...

You're proving that EB * EA = EC * ED, so the 7th blank should be "EB * EA = EC * ED"

Otherwise, everything else is good.

Answer: Fraction= 3 3/4kg

Decimal= 3.75kg

Step-by-step explanation:

15 kilograms of rice are separated equally into 4 containers. To get the number of kilograms of rice are in each container, we divide the total kilograms of rice by the number of containers. This will be:

Kilograms of rice in each container=

15/4 =3 3/4kg as a fraction.

To convert the fraction to decimal, we divide 3 by 4 and add to 3. 3/4 equals 0.75. We then add 3 to 0.75. This will be:

Decimal of 3 3/4 = 3+0.75 = 3.75kg

Answer: each candy bars costs 4 dollars

Step-by-step explanation:

subtract 3 from 19 then divide the answer by 4

Each candy bar equalled 4 dollars.

19-3= 16

16 divided by 4 (candy bars) = 4

Answer:

  B. is dependent

Step-by-step explanation:

The denominator determinant will be zero when the coefficients of the variables are dependent. One of the numerator coefficients will be zero when the coefficients involved are dependent. Hence using Cramer's Rule will result in the ratio 0/0 when the system is dependent.

___

The ratio will be 1/0 if the system is inconsistent (has no solution).

Answer:

9 cards

Step-by-step explanation:

he originally had 36 cards before giving 5 away, 36 divided by 4 is 9

Final answer:

Tony originally had 9 cards in each of the 4 equal sets before he gave 5 cards away.

Explanation:

The question asks how many cards were in each set originally when Tony had 4 equal sets of sports cards, gave away 5 cards, and now has 31 cards left. To find the number of cards in each set, we add back the 5 cards Tony gave away to the total number he has left, which gives us 31 + 5 = 36 cards. Since these 36 cards were divided into 4 equal sets, we divide 36 by 4 to find the number of cards in each set. Therefore, each set originally had 36 / 4 = 9 cards.

Answer:

5.5 pieces (it can also be 5 if you dont have 5.5)

Step-by-step explanation:

3 and 2/3 divided by 2/3 is 5 and a half

(please give brainliest if it helps you)

We can call the areas of the squares x and y. x+y=65 and x-y=33.

x would have an area of 49 and y has an area of 16.

Each side of x would be 7 and each side of y would be 4.



Answer:

0.15

Step-by-step explanation:

The only outcome that is divisible by 9 is 9 itself. At this point, the probability is 0.15. Hope this helps!

We have been given that Darren invests $4,500 into an account that earns 5% annual interests. We are asked to find the amount in his account after 10 years, if the interest rate is compounded annually, quarterly, monthly, or daily.

We will use compound interest formula to solve our given problem.    

[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

[tex]5\%=\frac{5}{100}=0.05[/tex]

When compounded annually, [tex]n=1[/tex]:

[tex]A=4500(1+\frac{0.05}{1})^{1\cdot 10}[/tex]

[tex]A=4500(1.05)^{10}[/tex]

[tex]A=4500(1.6288946267774414)[/tex]

[tex]A=7330.025820498\approx 7330.03[/tex]

When compounded quarterly, [tex]n=4[/tex]:

[tex]A=4500(1+\frac{0.05}{4})^{4\cdot 10}[/tex]

[tex]A=4500(1.0125)^{40}[/tex]

[tex]A=4500(1.6436194634870132)[/tex]

[tex]A=7396.28758569\approx 7396.29[/tex]

When compounded monthly, [tex]n=12[/tex]:

[tex]A=4500(1+\frac{0.05}{12})^{12\cdot 10}[/tex]

[tex]A=4500(1.00416666)^{120}[/tex]

[tex]A=4500(1.64700949769)[/tex]

[tex]A=7411.542739605\approx 7411.54[/tex]

When compounded daily, [tex]n=365[/tex]:

[tex]A=4500(1+\frac{0.05}{365})^{365\cdot 10}[/tex]

[tex]A=4500(1.0001369863013699)^{3650}[/tex]  

[tex]A=4500(1.6486648137656943695)[/tex]

[tex]A=7418.9916619456\approx 7419.00[/tex]

Since amount earned will be maximum, when interest is compounded daily, therefore, Darren should use compounded daily interest rate.

Answer:

Option B. 1024(0.5)^x

Step-by-step explanation:

From the question given, we were told that half (1/2) the players are eliminated at the end of each round.

If T is the total number players, then after round one it becomes:

T x (1/2)^1 = T x 0.5

After round x, the the numbers of player remaining will be:

T x (1/2)^x = T x (0.5)^x

From the question given, the total number of players are 1024. Therefore, the above expression can be written as:

T x (0.5)^x => 1024(0.5)^x

Answer:

51

Step-by-step explanation:

Just did it on edgu

Final answer:

Based on the circle graph, 34 percent of the 150 surveyed people completed college, which translates to 51 individuals.

Explanation:

The question asks how many people completed college based on a circle graph showing the education levels of 150 surveyed individuals. To answer this, we use the percentage given for those who completed college and apply it to the total number surveyed. With 34 percent having completed college, we calculate the number of people by multiplying 34 percent (or 0.34 as a decimal) by the total survey number, 150 people.

The calculation is as follows: 0.34 × 150 = 51. Therefore, 51 people surveyed completed college.

Answer:

Step-by-step explanation:

45

Answer:

34

Step-by-step explanation:

1+4=5 2+5=12 3+6=21 5+8= ??

It is noticed that the previous solution is added to the unknowns and the cycle continues.

The previous solution is 5 which is added to 2 and 5 to give 12

5+2+5=12

12 is then added to the next set of unknowns 3+6 to give 21

12+3+6=21

21 is then added to the 5+8 to give 34

21+5+8= 34

Answer:

A

Step-by-step explanation:

just took the quiz on edgen

The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

The property of the logarithm is found as;

[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)}[/tex]

Given equation;

[tex]\rm log_4(x+3) = log_2(2+x)[/tex]

LHS;

[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_4(x+3) \\\\ y_1 = \rm y_1 = \frac{log(x+3)}{log 4}[/tex]

RHS;

[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_2(2+x) \\\\ y_2 = \frac{log(2+x)}{log 2}[/tex]

The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.

Hence, option A is correct.

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The area of a rectangle with dimensions 21 m by 33 m is 693 square meters, calculated by multiplying the length and width.

The area of a rectangle is calculated by multiplying the length by the width. In the case of a rectangle with dimensions 21 m by 33 m, the formula to find the area A is:

A = length x width

So, the area of the rectangle is:

A = 21 m x 33 m

A = 693

Hence, the area of the rectangle is 693 square meters.

Answer:

Contestent K

Step-by-step explanation:

The contestant who was eating at the slowest rate will be in line K.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The three lines represent the number of hot dogs eaten by three contestants at a hot dog eating competition.

The diagram is shown below.

From the diagram, we can observe that for the same run, the rise of line K will be the least.

The contestant who was eating at the slowest rate will be in line K.

The complete question is attached below,

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Answer:

Every value of x.

Step-by-step explanation:

The function is a zero-order polynomial, whose value remains constant for all value of x.

Answer:

Step-by-step explanation:

Area of a parellogram is bh but a parellogram with its adjacent sides equal is a rhombus and rhombuses area us 1/2diagonal1×diagonal2 also diagonal of a parellogram bisect each other so diagonal will be 8cm and 14cm diagonal of a parellogram divides it into two congruent triangle vertically opposite angles are equal all non zero numbers are significant if zero is between two numbers its significant if zero is after decimal and the number less than zero than the zeroes are insignificant like in 0.0820 but the zeroes after decimal are significant

But zeroes after no decimals are not significant like 100 the powers tens are irrelevant like 10^3 has only one significant figure

Sorry don't know answer but hopes this helps so sorry

Final answer:

The circumference of Pluto is 7,232,000 meters, which is represented as 7.232 × 10⁶ meters in scientific notation.

Explanation:

To express the circumference of Pluto in scientific notation, you start by placing the decimal after the first non-zero digit and count the number of places the decimal has moved. The circumference of Pluto is 7,232,000 meters. In scientific notation, this is written as 7.232 × 10⁶ meters.

Here is a step-by-step breakdown of the conversion process:

Remember, scientific notation is useful for expressing very large or very small numbers in a simplified format.

Answer:

Belinda can expect to make $1 more with option B.

Step-by-step explanation:

The expected value for every option is calculated as:

[tex]E(x)=x_1*p(x_1)+x_2*p(x_2)[/tex]

Where [tex]x_1[/tex] and [tex]x_2[/tex] are the posibles money prize and [tex]p(x_1)[/tex] and [tex]p(x_2)[/tex] are their respective probabilities.

Option A:

Belinda has 12 possibilities: 1-3, 1-4, 1-5, 3-1, 3-4, 3-5, 4-1, 4-3, 4-5, 5-1, 5-3 and 5-4

From that 12 possibilities, there are 6 that have a sum greater than 6. That possibilities are: 3-4, 3-5, 4-3, 4-5, 5-3 and 5-4

So, the probability that the sum of the two spins is greater than 6 is:

[tex]P=\frac{6}{12} = 0.5[/tex]

At the same way the probability that the sum of the two spins is lower or equal than 6 is 0.5.

So, the expected value for this option is:

[tex]E_A(x)=(8*0.5)+((-2)*0.5)=3[/tex]

Option B:

Belinda has 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH and TTT

Where T means Tails and H means Heads.

Form that 8 possibilities, there are 4 which heads appear twice. That possibilities are: HHH, HHT, HTH and THH.

So, the probability that head appear twice is:

[tex]P=\frac{4}{8}=0.5[/tex]

At the same way, the probability that head doesn't appear or appear once is equal to 0.5

So, the expected value for this option is:

[tex]E_B(x)=(10*0.5)+((-2)*0.5)=4[/tex]

Finally, Belinda can expect to make $1 more with option B.

[tex]E_A(x)-E_B(x)=4-3=1[/tex]

Belinda can expect to make [tex]\( \frac{9}{8} \)[/tex] more units of currency (dollars) by choosing Option A over Option B.

To find the option with the greater mathematical expectation, we need to calculate the expected value (or mean) for each option.

Option A:

Step 1:

- The spinner has numbers 1, 3, 4, and 5.

- There are a total of 16 possible outcomes when spinning the spinner twice (4 outcomes for each spin).

- We need to find the probability of getting a sum greater than 6 and multiply it by $8, and then find the probability of getting a sum less than or equal to 6 and multiply it by -$2.

Step 2:

Let's calculate the probabilities:

1. Probability of getting a sum greater than 6:

- Possible outcomes: (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5) (total of 8 outcomes)

- Probability: [tex]\( \frac{8}{16} = \frac{1}{2} \)[/tex]

- Winning amount: $8

2. Probability of getting a sum less than or equal to 6:

- Possible outcomes: (1, 1), (1, 3), (1, 4), (1, 5), (3, 1), (4, 1), (5, 1) (total of 7 outcomes)

- Probability: [tex]\( \frac{7}{16} \)[/tex]

- Losing amount: -$2

Step 3:

Now, we calculate the expected value for Option A:

[tex]\[ \text{Expected value (Option A)} = (\text{Probability of winning}) \times (\text{Winning amount}) + (\text{Probability of losing}) \times (\text{Losing amount}) \][/tex]

[tex]\[ \text{Expected value (Option A)} = \left( \frac{1}{2} \right) \times (8) + \left( \frac{7}{16} \right) \times (-2) \][/tex]

[tex]\[ \text{Expected value (Option A)} = 4 - \frac{7}{8} \][/tex]

[tex]\[ \text{Expected value (Option A)} = \frac{29}{8} \][/tex]

Option B:

Step 1:

- There are 2 ways to get heads twice out of 3 coin flips: (HHH, HHT, HTH, THH)

- There are a total of 8 possible outcomes when flipping a coin three times.

- We need to find the probability of getting heads twice and multiply it by $10, and then find the probability of not getting heads twice and multiply it by -$2.

Step 2:

Let's calculate the probabilities:

1. Probability of getting heads twice:

- Possible outcomes: (H, H, T), (H, T, H), (T, H, H) (total of 3 outcomes)

- Probability: [tex]\( \frac{3}{8} \)[/tex]

- Winning amount: $10

2. Probability of not getting heads twice:

- Possible outcomes: (H, H, H), (T, T, T), (T, T, H), (T, H, T), (H, T, T), (H, T, H) (total of 5 outcomes)

- Probability: [tex]\( \frac{5}{8} \)[/tex]

- Losing amount: -$2

Step 3:

Now, we calculate the expected value for Option B:

[tex]\[ \text{Expected value (Option B)} = (\text{Probability of winning}) \times (\text{Winning amount}) + (\text{Probability of losing}) \times (\text{Losing amount}) \][/tex]

[tex]\[ \text{Expected value (Option B)} = \left( \frac{3}{8} \right) \times (10) + \left( \frac{5}{8} \right) \times (-2) \][/tex]

[tex]\[ \text{Expected value (Option B)} = \frac{30}{8} - \frac{10}{8} \][/tex]

[tex]\[ \text{Expected value (Option B)} = \frac{20}{8} \][/tex]

Step 4:

To find out which option has the greater mathematical expectation, we compare the expected values of Option A and Option B:

[tex]\[ \text{Expected value (Option A)} = \frac{29}{8} \approx 3.625 \][/tex]

[tex]\[ \text{Expected value (Option B)} = \frac{20}{8} = 2.5 \][/tex]

Since [tex]\( \frac{29}{8} \)[/tex] is greater than [tex]\( \frac{20}{8} \)[/tex], Belinda should choose Option A.

To find out how much more money she can expect to make by choosing Option A over Option B, we calculate the difference in expected values:

[tex]\[ \text{Difference} = \text{Expected value (Option A)} - \text{Expected value (Option B)} \][/tex]

[tex]\[ \text{Difference} = \frac{29}{8} - \frac{20}{8} \][/tex]

[tex]\[ \text{Difference} = \frac{29}{8} - \frac{20}{8} = \frac{9}{8} \][/tex]

[tex]\[ \text{Difference} = \frac{9}{8} \][/tex]

Belinda can expect to make [tex]\( \frac{9}{8} \)[/tex] more units of currency (dollars) by choosing Option A over Option B.

Answer:

T = sin(6572t)

Step-by-step explanation:

A pure tone is a sine-wave and sine-waves are defined by ω (omega) and t (time)

For a sine model:

Amplitude of wave form = sin(ωt)

A sine model that gives the Tone, T, as a function of time, t, for this key:

T = sin(ωt)

Sin is a mathematical operator in trigonometry

ω = 2πf

π = 3.14

The frequency of the 64th key on a standard 88-key piano is 1046.5 hertz.

f = 1046.5 hertz

ω = 2×3.14×1046.5

ω = 6572.02

T = sin(6572t)

The sine model for the 64th key on a standard 88-key piano with a frequency of 1046.5 Hz is represented as T(t) = A sin(2π(1046.5)t + φ), where A is the amplitude, φ is the phase shift, and t is the time.

The student has asked for a sine model that represents the Tone, T, as a function of time, t, for the 64th key on a standard 88-key piano, which has a frequency of 1046.5 hertz. A sine function that models the tone can be written as:

T(t) = A sin(2πft + φ)

For this example, since frequency (f) is given as 1046.5 Hz and we don't have information about amplitude (A) and phase shift (φ), we can write the model as:

T(t) = A sin(2π(1046.5)t + φ)

This model can be used by piano tuners to ensure that the piano is properly tuned by comparing the accurate frequency with the sound coming from the piano and making adjustments as needed.

Answer:

Expected value=77 people

Standard error=0.0040

Step-by-step explanation:

-Given the proportion is, p=0.67

-The expected value can be calculated as:

[tex]Expected \ Value=np\\\\=120\times 0.637\\\\=76.44\approx 77[/tex]

#The standard deviation is calculated as:

[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.637(1-0.637)}{120}}\\\\=0.0439[/tex]

#We use this calculated standard deviation to calculate the standard error:

[tex]SE=\frac{\sigma_p}{\sqrt{n}}\\\\=\frac{0.0439}{\sqrt{120}}\\\\=0.0040[/tex]

Hence, the sample has an expected value of approximately 77 people and a standard error of 0.0040

La altura inicial del objeto lanzado desde una plataforma es de 60 metros, representando la altura de la plataforma. Esto se obtiene al evaluar h(x) cuando x = 0.

La altura del objeto en el momento del lanzamiento se refiere al valor de la función h(x) cuando x = 0, ya que x representa el tiempo en segundos después del lanzamiento. Para determinar la altura inicial, simplemente sustituimos x = 0 en la función h(x):

h(0) = -5(0)^2 + 20(0) + 60 = 60

Por lo tanto, la altura inicial del objeto en el momento del lanzamiento es de 60 metros.

En términos físicos, esto tiene sentido, ya que el término cuadrático (-5x^2) representa la aceleración debida a la gravedad, y el término lineal (20x) representa la velocidad inicial. Cuando x = 0, no ha pasado tiempo después del lanzamiento, y la altura es simplemente la altura inicial de la plataforma, que es 60 metros.

En resumen, la altura del objeto en el momento del lanzamiento es de 60 metros.

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The object will land on the ground 6 seconds after launch.

To determine when the object will land on the ground, we need to find the time [tex]\( x \)[/tex] when the height [tex]\( h(x) \)[/tex] is zero. The height of the object is given by the equation:

[tex]\[ h(x) = -5x^2 + 20x + 60 \][/tex]

Set [tex]\( h(x) = 0 \)[/tex] to find the time when the object lands on the ground:

[tex]\[ -5x^2 + 20x + 60 = 0 \][/tex]

This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \),[/tex] where [tex]\( a = -5 \), \( b = 20 \),[/tex] and [tex]\( c = 60 \).[/tex] We can solve this using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

Substitute the values of [tex]\( a \), \( b \),[/tex] and [tex]\( c \)[/tex] into the formula:

[tex]\[ x = \frac{-20 \pm \sqrt{20^2 - 4(-5)(60)}}{2(-5)} \][/tex]

Simplify inside the square root:

[tex]\[ x = \frac{-20 \pm \sqrt{400 + 1200}}{-10} \][/tex]

[tex]\[ x = \frac{-20 \pm \sqrt{1600}}{-10} \][/tex]

[tex]\[ x = \frac{-20 \pm 40}{-10} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{-20 + 40}{-10} = \frac{20}{-10} = -2 \][/tex]

[tex]\[ x = \frac{-20 - 40}{-10} = \frac{-60}{-10} = 6 \][/tex]

Since time [tex]\( x \)[/tex] cannot be negative, we discard [tex]\( x = -2 \).[/tex] Therefore, the object will land on the ground [tex]\( 6 \)[/tex] seconds after launch.

So, the object will land on the ground 6 seconds after launch.

The translated question is:

An object is launched from a platform. Its height (in meters), x seconds after the launch, is modelled by:

[tex]h(x)=-5x^2+20x+60[/tex]

How many seconds after launch will the object land on the ground?

Answer:

3

Step-by-step explanation:

3 even numbers 2,4,6

or 1/2

or 50%