2.
What is the slope of the line passing through the points (9,16) and
(3, 4)?

The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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A p-value of 0.23 in the context of a clinical trial testing a vaccine's effectiveness suggests that the observed reduction in the percentage of individuals catching the virus, when comparing the vaccine group to the control group, is not statistically significant at conventional levels of significance (such as 0.05 or 0.01).

The p-value represents the probability of obtaining the observed data, or data more extreme, under the assumption that the null hypothesis is true.

In this case, the null hypothesis would typically state that there is no difference in the percentage of virus cases between the vaccine and control groups. A p-value of 0.23 indicates that there is a 23% chance of observing the reported reduction in cases or an even more substantial reduction if the null hypothesis were true.

Therefore, based solely on the p-value of 0.23, the best interpretation is that the observed reduction in virus cases could plausibly be due to random variation or chance, rather than a true effect of the vaccine. However, it is important to consider other factors, such as the study design, sample size, and clinical significance of the observed reduction, before drawing final conclusions about the vaccine's effectiveness.

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There is not sufficient evidence to conclude that the average calorie content of chocolate chip cookies is greater than 110 calories at the 0.01 level of significance.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable.

We will use a one-sample t-test to test the hypothesis.

Null hypothesis: The mean calorie content of chocolate chip cookies is 110 calories.

Alternative hypothesis: The mean calorie content of chocolate chip cookies is greater than 110 calories.

We will use a significance level of α = 0.01.

We first calculate the sample mean and sample standard deviation:

\($\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i = \frac{1780}{15} = 118.67$\)

\($s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2} = \sqrt{\frac{1}{14} \sum_{i=1}^{n} (x_i - 118.67)^2} = 26.899$\)

The test statistic is calculated as:

\($t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} = \frac{118.67 - 110}{26.899/\sqrt{15}} = 1.84$\)

Using a t-distribution table with 14 degrees of freedom and a one-tailed test at the 0.01 level, the critical value is 2.977.

Since the test statistic (1.84) is less than the critical value (2.977), we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to conclude that the average calorie content of chocolate chip cookies is greater than 110 calories at the 0.01 level of significance.

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The three numbers that are in both sequences between 20 and 40 would be 25 , 31 , and 37 .

When given the sequence of 2 n - 1, the terms between 20 and 40 would be : 21 , 23 , 25 , 27 , 29 , 31, 33, 35, 37, 39.

For the sequence 3 n + 1 , the terms between 20 and 40 are : 22, 25, 28, 31, 34 , 37 .

The three numbers that are in both sequences would therefore be :

25 , 31 , and 37 .

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The estimated length of the board to the nearest hundredth of a meter is 2.49 meters. Therefore, Option A  is the correct choice.

To estimate the length of the board to the nearest hundredth of a meter, we need to look at the digit in the thousandth place, which is the fourth decimal place. In this case, the digit in the thousandth place is 3.

If the digit in the thousandth place is less than 5, we round down. In this case, 3 is less than 5. Therefore, we keep the digits up to the hundredth place as they are, and the estimated length of the board becomes 2.49 meters.

Option A, 2.49m, is the correct choice as it represents the estimated length of the board to the nearest hundredth of a meter.

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The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

The logarithmic properties of a linear system are used to solve the equation.

The x-value of the intersection is x =46.

It is a system of an equation in which the highest power of the variable is always 1.

A one-dimension figure that has no width.

It is a combination of infinite points side by side.

Given

The pond can hold 400 water liters.

\(\rm y = 3.915(1.106)x\) is an expression.

Let x be the day and y be the hold of water.

When pond can hold 400 liters of water the x will be;

400 = 3.915(1.106)ˣ

(1.106)ˣ = 400/3.915    

(1.106)ˣ = 102.17

Taking logarithm on both sides, we get

log (1.106)ˣ = log (102.17)

x log (1.106) = log (102.17)                       [log aˣ = x loga] x = [log (102.17)/log (1.106)]    

x = 45.92

x = 46

Thus, the x-value of the intersection is x =46.

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Answer:

Graphing y = 3.915(1.106)x and y = 400, then finding the x-value of the intersection

Step-by-step explanation:

Answer:

\(c^6h^3\)

Step-by-step explanation:

         \(hhh=h^3\\c^3c^2h^3c\\c^3c^2c\\ccc = c^3\\=c^{3 \cdot 2}\\=c^6\\=c^6h^3\)

After considering the given data we conclude that the probability of choosing a triangle card can be evaluated applying t × r.

Here we have to apply the principle of  multiplication to derive the satisfactory answer.
Let us consider that the probability of picking a triangle card is t whereas the probability of picking a red card is r. Hence, the probability of picking a triangle card and a red card can be evaluated as follows:
The probability of picking a triangle card from the first box is t.
The probability of picking a red card from the second box is r.
Finally, the probability of picking a triangle card and a red card is t × r.

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Answer:

Step-by-step explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Tony's points can be described by ...

  p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

  p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

  p = p

  12 +10t = 0 +14t . . . . substitute for p in both cases

  12 = 4t . . . . . . . . . . subtract 10t

  3 = t . . . . . . . . . . divide by 4

  p = 14·3 = 42 . . . . the scores after 3 turns

Answer:

if you meant x times y...

15 x 20 is 300.

if you meant x + y...

15 + 20 is 35.

if you meant anything else, please let me know

the way it was written confused me but I tried.

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

(9,3)

Step-by-step explanation:

Use elimination to solve.

-2 (-3x + 3y = -18)

6x - 6y = 36

-6x - 3y = -63

The 6x and -6x are eliminated and you are left with -9y = -27 when you combine -6y and -3y, and 36 - 63.

y = 3

Then, substitute 3 into either equation to find x

-3x + 3(3) = -18

-3x + 9 = -18

-3x = -27

x = 9

Step-by-step explanation:

£22.25 pls mark brainliest thanks

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Answer:

x = 7

Step-by-step explanation:

2(3x-9)=2x+10

6x - 18 = 2x + 10

4x = 28

x = 7

Answer:

x = 7

Step-by-step explanation:

In order to find the value of x, isolate it in the equation.

1) First, distribute the 2 to the terms inside the set of parentheses.

\(2 (3x - 9) = 2x + 10 \\6x - 18 = 2x + 10 \\\)

2) Next, move all the x terms to one side and all the other terms to the other side. Subtract both sides by 2x and add both sides by 18.

\(6x - 18 = 2x + 10 \\4x = 28\)

2) Divide both sides by 4 to finally isolate x.

\(4x = 28 \\x = 7\)

Thus, x = 7.

The minimum value of the product is -8.

The minimum value is the y value of the lowest point on the graph.

The function y = 2x-8 and we have to find the minimum value of the XY.

Plugging the value of y in the product;

\(\rm f(x)=x(2x-8)\\\\f(x)=2x^2-8x\)

f(x) represents an upward parabola and we know that for an upward parabola, the minimum point is the vertex.

So in order to find the minimum value, we find the y coordinate of the vertex of the parabola.

The x-coordinate of the parabola is given by;

\(\rm = \dfrac{-b}{2a}\\\\=\dfrac{-8}{2\times 2}\\\\ =\dfrac{-8}{4}\\\\=-2\)

The y -coordinate of the parabola is;

\(\rm f(x)=2x^2-8x\\\\f(2)=2(2)^2-8(2)\\\\f(2)=2\times 4-16\\\\ f(2)=8-16\\\\ f(2)=-8\)

The vertex is (2,-8)

Hence, the minimum value of the product is -8.

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Answer:

z = 4

Step-by-step explanation:

-6 + 3z = 6

+6.           +6

3z = 12

/3.      /3

z = 4

Answer:

\(x^2-6x-13\)

Step-by-step explanation:

\(\frac{-b+-\sqrt{b^2-4ac} }{2a} \\a=1\\b=-6\\c=-13\)

A) The corresponding unit rate for each package is,

For Cannie cakes;

⇒ $1.85

Bark bits;

⇒ $2.25

Woofy Waffles;

⇒ $1.9

B) The best buy by the units rates is, Cannie cakes.

We have to given that;

Jeremiah needed dog food for his new pippy.

Now, We get;

A) The corresponding unit rate for each package is,

For Cannie cakes;

⇒ 74/40

⇒ $1.85

Bark bits;

⇒ 27/12

⇒ $2.25

Woofy Waffles;

⇒ 76 / 40

⇒ $1.9

Hence, We get;

B) The best buy by the units rates is, Cannie cakes.

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The solution of the expression is x = (-1 ± i√3)/2 and the domain of the expression is all values of x l x ≥ 0 (option c).

The given equation is -x² = √x. To solve this equation, we need to isolate x on one side of the equation. We begin by squaring both sides of the equation to eliminate the radical:

(-x²)² = (√x)²

x⁴ = x

Now we have a quartic equation, which we can solve by factoring:

x(x³ - 1) = 0

We can further simplify this equation by factoring the cubic term using the difference of cubes formula:

x(x - 1)(x² + x + 1) = 0

From this factorization, we can see that the solutions are x = 0, x = 1, and the solutions of the quadratic factor x² + x + 1 = 0. To find the solutions of the quadratic, we can use the quadratic formula:

x = (-1 ± √1 - 4(1)(1))/2(1)

x = (-1 ± i√3)/2

Therefore, the solutions to the equation -x² = √x are x = 0, x = 1, and x = (-1 ± i√3)/2.

Now let's consider the domain of the solutions, which is determined by the inequality x ≥ 0. This inequality means that the solutions must be greater than or equal to 0. We can see that x = 0 and x = 1 satisfy this inequality.

For the solution x = (-1 ± i√3)/2, we can see that it does not satisfy the inequality x ≥ 0 because it is negative. Therefore, the solutions to the equation -x² = √x in the domain x ≥ 0 are x = 0 and x = 1.

Finally, let's consider the inequality x ≤ 0. This inequality means that the solutions must be less than or equal to 0. We can see that x = 0 satisfies this inequality. However, x = 1 and x = (-1 ± i√3)/2 do not satisfy this inequality. Therefore, the solutions to the equation -x² = √x in the domain x ≤ 0 are x = 0.

Hence the correct option is (c).

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Complete Question:

Solve the expression -x² = √x . And identify the domain of the expression,

A. all values of x

B. all values of x l x ≥ 1

C. all values of x l x ≥ 0

D. all values of x l x ≤ 0

9514 1404 393

Answer:

Step-by-step explanation:

Let 'a' represent the number of adult tickets sold. Then (200-a) is the number of child tickets sold. The total revenue is ...

  8.50a +3.50(200 -a) = 1500

  5a = 800 . . . . . . . . . . . . . . . . . . . subtract 700 and collect terms

  a = 160

  (200-a) = 40

160 adults and 40 children paid to see the movie.

Answer:

160 adults and 40 children saw the movie on the first night.

Step-by-step explanation:

Total number of tickets sold = 200

Let the total number of adults be 'x'

So, Total number of children = 200 - x

Cost of adult tickets = $8.50

Cost of child tickets = $3.50

Total sum made on first night = $1,500

Total sum made on first night is equal to total cost of adult tickets + total cost of child tickets

\( \longrightarrow \) 8.50x + 3.50(200 - x) = 1500

\( \longrightarrow \) 8.5x + 700 - 3.5x = 1500

\( \longrightarrow \) 8.5x - 3.5x = 1500 - 700

\( \longrightarrow \) 5x = 800

\( \longrightarrow \) x = \( \sf \dfrac{800}{5} \)

\( \longrightarrow \) x = 160

\( \therefore \) Total number of adults = 160

Total number of children = 200 - 160 = 40

Answer:

Eight times ten plus six times one plus two times one-tenth plus seven times one-thousandth.

Step-by-step explanation:

(8 x 10) = eight times ten

(6 x 1) = six times one

(2 x 0.1) = two times one-tenth

(7 x 0.001) = seven times one-thousandth

I am not always the best with the equations to words stuff, so please comment if I am wrong!

Answer:

I am 100% sure its 4.03 x 10^7

Step-by-step explanation: