The president of a company that packages almonds releases a report to the media. The report shows that people who eat a handful of almonds each day have 10% fewer cavities.

Which statement describes the most likely reason the president releases the report?




A. The president wants people to understand the importance of taking care of their teeth.

B. The president wants people to believe that almonds are good for one's teeth so that they buy more almonds.

C. The president wants people to know that it is possible to reduce the number of cavities they may get in the future.

D. The president wants people to believe that they should not eat more than a handful of almonds each day.

the point estimate typically is in the middle of the interval, so it would be at (1/2)(0.52+0.80) or 0.66.

Answer:

see explanation

Step-by-step explanation:

Using the coefficients of the polynomial and evaluating for h = - 3

- 3 | 1   - 4   - 9   36

      ↓   - 3   21   - 36

      -------------------------

       1   - 7   12   0 ← remainder

Since remainder is 0 then (x + 3) is a factor, so

y = (x + 3)(x² - 7x + 12)

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (- 7)

The factors are - 4 and - 3, since

- 4 × - 3 = + 12 and - 4 - 3 = - 7, then

x² - 7x + 12 = (x - 4)(x - 3), and

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

Answer:

Option B.

Step-by-step explanation:

we have

[tex](x-3)^{2}=5[/tex]

take square root both sides

[tex](x-3)=(+/-)\sqrt{5}[/tex]

[tex]x=3(+/-)\sqrt{5}[/tex]

11125 ft2. I hope i got it right

Answer:

180π cm³

Step-by-step explanation:

The formula for the area of an ellipse with major axis a and minor axis b is

A = π·a·b.

Here, that area is A = π(6 cm)(4 cm) = 24π cm².

Multiplying this base area by the altitude, 7.5 cm, results in the volume:

V = (24 cm²)·π·(7.5 cm) = 180π cm³

Answer:

565,5 cm³

Step-by-step explanation:

To calculate the volume of a cylinder we have to found the area of the base and multiply by the altitude of the cylinder. As the base is elliptical, the area is given by:

[tex]A = a*b*\pi[/tex], where a is the major axis and b the minor axis. Thus:

[tex]A=6*4*\pi =75.39 cm^2[/tex]

And,

[tex]V = A*h = 75.39*7.5 = 565.48 cm^3[/tex].

Rounding to the nearest tenth: 565.5 cm³

(9/18)(9/18) = 81/324. The probability that Amy takes out pink chips in both draws is 81/324.

In this example we will use the probability property P(A∩B), which means given two independent events A and B, their joint probability P(A∩B) can be expressed as the product of the individual probabilities P(A∩B) = P(A)P(B).

The total number of chips of different colors in Amy's bag is:

8 blue chips + 9 pink chips + 1 white chip = 18 color chips

Amy takes out a chip from the bag randomly without looking, she replaces the chip and then takes out another chip from the bag.

So, the probability that Amy takes out a pink chip in the first draw is:

P(A) = 9/18 The probability of takes out a pink chip is 9/18 because there are 9 pink chips in the total of 18 color chips.

Then, Amy replaces the chip an takes out another which means there are again 18 color chips divide into 8 blue chips, 9 pink chips, and 1 white chip. So, the probability of takes out a pink chip in the second draw is:

P(B) = 9/18  The probability of takes out a pink chip is 9/18 because there are 9 pink chips in the total of 18 color chips.

What is the probability that Amy takes out a pink chip in both draws?

P(A∩B) = P(A)P(B)

P(A∩B) = (9/18)(9/18) = 81/324

Probability of taking out pink chip in both draws is equal to [tex]9[/tex] over [tex]18[/tex]multiplied by [tex]9[/tex] over [tex]18[/tex] equals [tex]81[/tex] over [tex]324[/tex].

" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes."

Formula used

Probability [tex]= \frac{n(F)}{n(T)}[/tex]

[tex]n(F)=[/tex] Number of favourable outcomes

[tex]n(T)=[/tex] Total number of outcomes

For independent events

[tex]P(A\cap B) = P(A) \times P(B)[/tex]

According to the question,

Given,

Total number of chips [tex]= 18[/tex]

Number of pink chips [tex]= 9[/tex]

[tex]'A'[/tex] represents the event of taking out pink chip first time

[tex]'B'[/tex] represents the event of taking out pink chip second time

Probability of taking out pink chip first time [tex]'P(A)' = \frac{9}{18}[/tex]

After replaces the chips again number of chip remain same

Probability of taking out pink chip second time [tex]'P(B)' = \frac{9}{18}[/tex]

Both the events are independent to each other

Substitute the value in the formula of probability of independent event we get,

Probability of taking out pink chip in both draw

[tex]P(A \cap B) = \frac{9}{18} \times \frac{9}{18}[/tex]

               [tex]= \frac{81}{324}[/tex]

Hence, probability of taking out pink chip in both draw is equal to [tex]9[/tex] over [tex]18[/tex]multiplied by [tex]9[/tex] over [tex]18[/tex] equals [tex]81[/tex] over [tex]324[/tex].

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[tex] - 4 \sqrt{3} x - 2 + 6 = 22 \\ - 4 \sqrt{3}x + 4 = 22 \\ - 4 \sqrt{3}x = 18 \\ x = \frac{18}{ - 4 \sqrt{3} } = \frac{ - 18 \sqrt{3} }{12} = \frac{ - 3 \sqrt{3} }{2} = - 1.5 \sqrt{3} [/tex]

HOPE THIS WILL HELP YOU

The solution depends on the argument of the square root. Please be more precise and less ambiguous when writing your questions.

You could either mean:

[tex]-4\sqrt{3}x-2+6=22,\quad -4\sqrt{3x}-2+6=22,\quad -4\sqrt{3x-2}+6=22[/tex]

In the first case, we have

[tex]-4\sqrt{3}x-2+6=22 \iff -4\sqrt{3}x= 18 \iff x = -\dfrac{18}{4\sqrt{3}}[/tex]

In the second case, we have

[tex]-4\sqrt{3x}-2+6=22 \iff \sqrt{3x}=-\dfrac{9}{2}[/tex]

which has no solution, because a square root can't be negative

In the third case, we have

[tex]-4\sqrt{3x-2}+6=22 \iff -4\sqrt{3x-2}=16 \iff \sqrt{3x-2}=-4[/tex]

which again has no solution, for the same reason.

Answer:

see below

Step-by-step explanation:

The opposite of 2 is -2. The opposite of that is -(-2) = 2. The graph shows 2 on the number line.

Answer:

-2

Step-by-step explanation:

When it comes to negatives and positives, both are the opposite of each other because they are on the opposite sides on the number line. For example, the opposite of 9 would be -9. Or, the opposite of -9 is 9.

Answer:

(- 5, 0) and (3, 0)

Step-by-step explanation:

Given

f(x) = x² + 2x - 15

To find the x- intercepts let f(x) = 0, that is

x² + 2x - 15 = 0 ← in standard form

(x + 5)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 ← left x- intercept

x - 3 = 0 ⇒ x = 3 ← right x- intercept

Answer:

Left-most x-intercept: (-5, 0)

Right-most x-intercept: (3, 0)

Answer:

the answer should be f(x)=-4

Substitute x=-3 in the equation

F(x)= -2(-3)^2 -3(-3) +5

-18+9+5=-4

The answer is -4

Answer:

A [tex]\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.[/tex]

Step-by-step explanation:

The equation [tex]12x^3-5x=2x^2+x+6[/tex] have in both sides expressions [tex]12x^3-5x[/tex] and [tex]2x^2+x+6.[/tex]

Therefore, the system of two equations

[tex]\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.[/tex]

has the solution (x,y), where x is the solution of the equation above.

ANSWER

[tex]y = 12 {x}^{3} - 5x[/tex]

{

[tex]y= 2 {x}^{2} + x + 6[/tex]

EXPLANATION

The given equation is

[tex]12 {x}^{3} - 5x = 2 {x}^{2} + x + 6[/tex]

To find the system of equations, we just have to equate each side of the equation to y and form two different equations.

The left sides gives one equation,

[tex]y = 12 {x}^{3} - 5x[/tex]

The right side also gives,

[tex]y= 2 {x}^{2} + x + 6[/tex]

Hence the correct choice is A

Find the volume of the lake:

37 x 30 x 2 = 2,220 cubic miles.

Now find 65% of the total volume:

2,220 x 0.65 = 1,443 cubic miles

Divide the number of fish by the volume of the lake:

115, 200 fish / 1,443 cubic miles = 79.83 fish per cubic mile.

Rounded to the nearest fish = 80 fish per cubic mile.

Answer:

80 fish per cubic mile.

Answer:

  B.  s = 0.85r

Step-by-step explanation:

The sale price is 15% off the regular price. In equation form, that is ...

  s = r - 15%×r

  s = r(1 - 0.15) = 0.85r

The equation that can be used to calculate the sale price is s = 0.85r.

Answer:

(x - 8)² + (y - 13)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre is located at the midpoint of the endpoints of the diameter.

Use the midpoint formula to find the centre

[[tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex] ]

with (x₁, y₁ ) = (5, 9) and (x₂, y₂ ) = (11,17)

centre = ( [tex]\frac{5+11}{2}[/tex], [tex]\frac{9+17}{2}[/tex] ) = (8, 13)

The radius is the distance from the centre to either end of the diameter

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 13) and (x₂, y₂ ) = (5, 9)

r = [tex]\sqrt{(5-8)^2+(9-13)^2}[/tex]

  = [tex]\sqrt{(-3)^2+(-4)^2}[/tex]

  = [tex]\sqrt{9+16}[/tex] = [tex]\sqrt{25}[/tex] = 5 ⇒ r² = 25

Hence

(x - 8)² + (y - 13)² = 25

The force used by Randy is 40 N.

When a force moves anything over a distance, it is said to be doing work.

Work = Force * Displacement

Work done given in the question = 200 N.m

Distance moved by the piano = 5m

W = F * d

200 = F * 5

F = 40N

Hence, the force used by randy is 40N.

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Answer:

It is unlikely

Step-by-step explanation:

The probability of a sticky dart landing in the green section of the board, assuming that it lands on the board is possible but very unlikely.

The green section of the board has the least area compare to an other section of the board. Therefore, the dark is unlikely to land in this section.

Answer:

it is unlikey

Step-by-step explanation:

the possibility of the sticky dart landing on the green part is unlikley

Answer:

Step-by-step explanation:

Please, share the possible answer choices next time.

The graph of a parabola y = x^2 has its vertex at the origin, (0, 0), and opens up.  By replacing x with (x - 3), we translate the graph 3 units to the right.

Answer:

the answer is c

Step-by-step explanation:

For this case we have that by definition of trigonometric relations of a rectangular triangle, that the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle. While the tangent of the same angle is given by the leg opposite the angle on the leg adjacent to the angle.

Then, according to the figure we have:

[tex]sin (B) = \frac {7} {25} = 0.28\\tg (B) = \frac {7} {24} = 0.2917[/tex]

Answer:

[tex]sin (B) = \frac {7} {25}\\tg (B) = \frac {7} {24}[/tex]

Answer:

[tex]\text{sin}(B)=\frac{7}{25}[/tex]

[tex]\text{tan}(B)=\frac{7}{24}[/tex]

Step-by-step explanation:

We have been given a right triangle. We are asked to find the [tex]\text{sin}(B)[/tex] and [tex]\text{tan}(B)[/tex] for our given triangle.

We know that sine relates opposite side of right triangle to its hypotenuse.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

We can see that AC is opposite side to angle B and  AB is hypotenuse of the given triangle.

[tex]\text{sin}(B)=\frac{AC}{AB}[/tex]

[tex]\text{sin}(B)=\frac{7}{25}[/tex]

We know that tangent relates opposite side of right triangle to its adjacent.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

We can see that AC is opposite side to angle B and  BC is adjacent side of the angle B.

[tex]\text{tan}(B)=\frac{AC}{BC}[/tex]

[tex]\text{tan}(B)=\frac{7}{24}[/tex]

Answer:

9% + 5%

Step-by-step explanation:

Answer:

$1644.

Step-by-step explanation:

We have been a typical household in the United States has an average after-tax income of $41,100. We are asked to find how much more is spent on insurance/pensions than on health care.

We have been given that 5% is spent on health care and 9% is spent on insurance/pensions. This means that 4% (9%-5%) is more on insurance/pensions than on health care.

Now, we need to find 4% of $41,100.

[tex]\text{Amount more spent on insurance/pensions than on health care}=\frac{4}{100}\times \$41,100[/tex]

[tex]\text{Amount more spent on insurance/pensions than on health care}=4\times \$411[/tex]

[tex]\text{Amount more spent on insurance/pensions than on health care}=\$1644[/tex]

Therefore, $1644 is more spent on insurance/pensions than on health care.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x-4y=4\\x+2y=18&\text{multiply both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x-4y=4\\2x+4y=36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=40\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=8}\\\\\text{Put the value of x to the second equation:}\\\\8+2y=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}[/tex]

[tex]\text{Put the values of x and y to the expression}\ x^2+y^2+xy:\\\\8^2+5^2+(8)(5)=64+25+40=129[/tex]

Answer:

I think its C) 43. Let me know what you get

Answer:

it's 43

Step-by-step explanation:

i got the answer right

ANSWER

405m

EXPLANATION

We know the opposite side of of the right triangle to be 4629m and the given angle is 85°.

Since we want to find the adjacent side which is x units, we use the tangent ratio to obtain,

[tex] \tan(85 \degree) = \frac{opposite}{adjacent} [/tex]

[tex] \tan(85 \degree) = \frac{4629}{x} [/tex]

Solve for x.

[tex]x = \frac{4629}{\tan(85 \degree)} [/tex]

x=404.985

To the nearest meter, x=405m

Answer: 405m

Step-by-step explanation:

When you raise something to the power of -1, all that happens is that thing turns upside down.

For example: (x^3 / y^4)^-1 will become (y^4 / y^3), basically the same fraction but just swap the numerator and denominator.

In your example, the first exponent is 4 and the second exponent is 3.

Answer: y^4 and x^3

Answer:

d is your answer

Step-by-step explanation:

Answer:

Option D.

Step-by-step explanation:

The given system of equations is

[tex]y=2x[/tex]         ....(i)

[tex]y=x^2-15[/tex]         ...(ii)

From (i) and (ii) we get

[tex]x^2-15=2x[/tex]

[tex]x^2-2x-15=0[/tex]

[tex]x^2-5x+3x-15=0[/tex]

[tex]x(x-5)+3(x-5)=0[/tex]

[tex](x-5)(x+3)=0[/tex]

Using zero produc property we get

[tex]x-5=0\Rightarrow x=5[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

If x=5, then

[tex]y=2(5)=10[/tex]

If x=-3, then

[tex]y=2(-3)=-6[/tex]

The solutions of the given system of equations are (-3,-6) and (5,10).

Therefore, the correct option is D.

well the intercepts are  (8,0) and (-4,0) its a lot of math so you need to find it i would show you but i have a quiz

im not sure tho soo

Answer:

The x-intercepts of the quadratic function are 8 and -4.

Step-by-step explanation:

The given function is

[tex]f(x)=x^2-4x-32[/tex]

Equate the function f(x) equal to 0, to find the x-intercepts of the quadratic function.

[tex]f(x)=0[/tex]

[tex]x^2-4x-32=0[/tex]

The middle term can be written as -8x+4x.

[tex]x^2-8x+4x-32=0[/tex]

[tex]x(x-8)+4(x-8)=0[/tex]

Take out the common factors.

[tex](x-8)(x+4)=0[/tex]

Using zero product property,

[tex]x-8=0\Rightarrow x=8[/tex]

[tex]x+4=0\Rightarrow x=-4[/tex]

Therefore the x-intercepts of the quadratic function are 8 and -4.

Answer:

He correctly determines that she has 300 nickels and 330 dimes.

Step-by-step explanation:

I'll first explain how Mark got that system of equations. Then I'll solve the system of equations to find the numbers of coins.

Moira has a collection of nickels and dimes. We don't know the number of nickels and the number of dimes she has.

First, we define two variables to represent the unknowns in this problems, the numbers of coins.

Let n = number of nickels.

Let d = number of dimes.

The sum of the numbers of coins is n + d. We are told she has 630 coins, so the first equation is

n + d = 630

Since we have two unknowns, we need two equations. Now we write an equation based on the values of the coins. A nickel is worth $0.05. A dime is worth $0.1. n nickels are worth 0.05n, and d dimes are worth 0.1d. The total value of the coins is 0.05n + 0.1d. We are told the value of the coins is $48. Now we can write the second equation.

0.05n + 0.1d = 48

Our system of equations is:

n + d = 630

0.05n + 0.1d = 48

These are the same equations Mark got.

Now we solve the system of equations. We will use the substitution method. First, we solve one equation for one variable. Then we substitute that into the other equation.

Let's solve the first equation for n:

n + d = 630

Subtract d from both sides:

n = 630 - d

Now that we know that n is the same as 630 - d, we replace n of the second equation with 630 - d.

0.05n + 0.1d = 48

0.05(630 - d) + 0.1d = 48

Distribute the 0.05:

31.5 - 0.05d + 0.1d = 48

Combine the terms in d:

0.05d + 31.5 = 48

Subtract 31.5 from both sides.

0.05d = 16.5

Divide both sides by 0.05.

d = 330

Now that we know d is 330, we substitute d with 330 in the first original equation and solve for n.

n + d = 630

n + 330 = 630

Subtract 330 from both sides.

n = 300

Since we let n = the number of nickels, and d = the number of dimes, now we can fill in the blanks.

n = number of nickels = 300

d = number of dimes = 330

Answer: He correctly determines that she has 300 nickels and 330 dimes.

*******************************************************************

The question is already answered, but we can check with the given information to confirm that our answer is correct.

We check the number of coins:

300 nickels + 330 dimes = 630 coins (the number of coins checks out.)

Now, we check the value of the coins:

300 * $0.05 + 330 * $0.1 = $15 + $33 = $48 (the value of the coins checks out.)

Since both the number of coins and the value of coins check correctly, our answer, 300 nickels and 330 dimes, is correct.

To find the number of nickels and dimes Moira has, start by simplifying the system of equations and solve for the variables. The solution to the given system of equations reveals that Moira has 300 nickels and 330 dimes.

The subject of this question is about solving a system of equations. The system in this case is given as {n+d=630 & 0.05n+0.10d=48}, where n represents the number of nickels Moira has and d represents the number of dimes she has.

First, we clear the decimals in the second equation by multiplying every term by 100, which gives us 5n + 10d = 4800. This can be simplified to n + 2d = 960 after dividing each term by 5.

Now, we have a new system of equations: {n + d = 630 & n + 2d = 960}. Subtraction of the first equation from the second will give us d = 330. Substituting d = 330 into the first equation will give us n = 300. Therefore, Moira has 300 nickels and 330 dimes.

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Answer:

The graph  attached below is for r=2+ 2sin θ where θ=pi

Step-by-step explanation

The coordinates in a polar equation are written as (r,θ)

r= radius and θ is the angle

⇒⇒⇒ so this mean we rotate θ radians and of the size r units

In our case assume θ=[tex]\pi[/tex] where 0≤θ≤2[tex]\pi[/tex]

Answer:

336

Step-by-step explanation:

The average rate of change is Δy/Δx.

On the interval [5, 7]:

(1469 - 549) / (7 - 5) = 460

On the interval of [2, 4]:

(287 - 39) / (4 - 2) = 124

The difference is:

460 - 124

336

ANSWER

[tex]x = 2 \: \: or \: \: x = 15[/tex]

Or

[tex]x = - 2 \: \: or \: \: x = - 15[/tex]

EXPLANATION

The given polynomial is

[tex] f(x) = {x}^{2} + kx + 30[/tex]

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

[tex]m + n = - \frac{b}{a} = -k [/tex]

and the product of roots is

[tex]mn = \frac{c}{a} = 30[/tex]

The square difference of the zeroes is given by the expression.

[tex]( {m - n})^{2} = {(m + n)}^{2} - 4mn [/tex]

From the question, this difference is 169.

This implies that:

[tex]( { - k)}^{2} - 4(30) = 169[/tex]

[tex]{ k}^{2} -120= 169[/tex]

[tex] k^{2} = 289[/tex]

[tex] k= \pm \sqrt{289} [/tex]

[tex]k= \pm17[/tex]

We substitute the values of k into the equation and solve for x.

[tex]f(x) = {x}^{2} \pm17x + 30[/tex]

[tex]f(x) = (x \pm2)(x \pm 15)[/tex]

The zeroes are given by;

[tex] (x \pm2)(x \pm 15) = 0[/tex]

[tex]x = \pm2 \: \: or \: \: x = \pm 15[/tex]

Hence  margin of error for population proportion is option c which is 0.6

MoE refers to estimated point value that tells us how much difference is there from actual value.

critical value * SD of population

Given max sample proportion =0.28 and min sample proportion=0.16

Hence we can directly calculate MOE by subtracting both = 0.28=0.16=0.6

which is option no. c

Hence option c is 0.6 which is correct.

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Answer:

0.6 is the answer