Bush Middle school is selling spirit sticks, 4 for $5.00. What is the cost of one spirit stick? *

Answer: 49/50

Step-by-step explanation:

81 + 17 + 2 = 10

98/100 = 49/50

The probability as a fraction in simplest form is 49/50.

Answer:

m<2 = 73

Step-by-step explanation:

Since <1 and <2 are complementary (which means that they equal 90), all you have to do is subtract 17 from 90 to find your answer:

90 - 17 = 73

thus, m<2 = 73

Answer:

73

Step-by-step explanation:

Answer:

-8 i think

Step-by-step explanation:

Answer:

  one solution: (1, 4)

Step-by-step explanation:

You want the graphs and number of solutions to the system of equations ...

The graph is attached. The first equation has a y-intercept of +1 and a slope of 3. The second equation has a y-intercept of +2 and a slope of 2.

The different slopes mean there is exactly one solution. The graph shows that solution to be (x, y) = (1, 4).

__

Additional comment

The slope is the x-coefficient when the equations are written in this "slope-intercept" form. It is the "rise/run" for the line on the graph. A slope of 3, for example, means the line has a rise of 3 grid squares for a run of 1 square (to the right). Knowing the y-intercept and slope makes it easy to graph the line.

The linear inequality in open-sentence form are

An open sentence is a mathematical statement that contains at least one blank or unknown and that becomes true or false when the blank is filled or a quantity is substituted for the unknown.

Now, since we have the expressions,

First, we note that there are 3 open sentences and only two of them are inequalities.

The 3 open sentences are

The two inequalities are

So, the linear inequality in open-sentence form are

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The required equation that represent or approximate the population is:

\(\mathrm P(t) = 1,500 \times 3^{(1/7)}^t\)

To represent the population, P, as a function of time in days, t, we need to find an exponential growth equation.

Since the population grows exponentially by a factor of 3 every week, we need to convert the weekly growth to daily growth.

Let's break down the problem step by step:

Now, we can represent the population, P, as a function of time, t, using the exponential growth equation:

\(\mathrm P(t) = \mathrm{Initial \ Population} \times \mathrm {Growth \ Factor}^t\)

where:

Initial Population (Po) = 1,500 (given)

Growth Factor per day = \(3^{(1/7)\)

So, the equation representing the population as a function of time in days is:

\(\mathrm P(t) = 1,500 \times 3^{(1/7)}^t\)

Hence the required equation that represent or approximate the population is:

\(\mathrm P(t) = 1,500 \times 3^{(1/7)}^t\)

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Answer:

B

Step-by-step explanation: Differences between squares.

9x^2-4

(3^2) (x^2) -(2^2)

(3x-2)(3x+2)

SOLUTION

The given function is:

Recall the rule of rational zero theorem

From the given function

The contant term is 7

Factors of the constant term are

The leading coefficient is 3

Factors of the leading coefficient are

Using the the rational zero theorem

The posible zeros are

This gives

Substitute the possible zeros into the equation to get the actual zeros

The roots are

Factorizing the given function gives

Answer:

x=3

Step-by-step explanation:

● -3 (-4x+4) = 15 + 3x

Multiply -3 by (-4x+4) first

● (-3) × (-4x) + (-3)×(4) = 15 + 3x

● 12 x - 12 = 15 +3x

Add 12 to both sides

● 12x - 12 + 12 = 15 + 3x +12

● 12 x = 27 + 3x

Substract 3x from both sides

● 12x -3x = 27 + 3x - 3x

● 9x = 27

Dividr both sides by 9

● 9x/9 = 27/9

● x = 3

The algebraic expression for the statement the product 7 and the square of a number is 7x²

Algebraic expressions are described as mathematical expressions that consist of arithmetic terms, factors, constants, variables and coefficients.

These expressions are also composed of arithmetic operations which may include;

From the information given, we have that;

The product 7 and the square of a number

Now, let the number be x

The square of x is x²

This statement is expressed as;

7x²

Thus, the expression is 7x²

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The complete question:

The product 7 and the square of a number. Write the algebraic expression

Answer:

for this we need 90 percent 5410

so we multiply 5410*0.9=4869

Hope This Helps!!!

Answer:

O The ranges of g(x) and f(x) are the same, but their domains are not the same.

Step-by-step explanation:

The statement that best describes g(x) and f(x) is:

The domains of g(x) and f(x) are the same, but their ranges are not the same.

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The function g(x) is obtained by taking the parent function f(x) = ∛x and performing a series of transformations:

- shifting the graph horizontally 6 units to the left

- shifting it vertically 8 units downward.

Since the cube root function is defined for all real numbers, both g(x) and f(x) have the same domain, which is the set of all real numbers.

However, the transformations applied to f(x) change the shape of the graph and the range of the function.

In particular,

g(x) is shifted 8 units downward, so its range is shifted down by 8 units compared to the range of f(x).

Therefore,

The domains of g(x) and f(x) are the same, but their ranges are not the same.

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The product of 325 and some power of 10 is 32,500. 325 is multiplied by the exponent 10² to get the value as 32,500.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The product of 325 and some power of 10 is 32,500.

Let the power value be = x

The statement converted into expression is -

325 × 10^x = 32500

Use the arithmetic operation of division -

10^x = 32500/325

10^x = 100

Express right-hand side in exponential or power form -

10^x = 10^2

Since, the base of LHS and RHS is same, so -

x = 2

Therefore, the value of x is obtained as 2.

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Answer: A

Step-by-step explanation: You're Welcome

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

Fire animals = 36 * 1/4 = 9

Water animals = 36 * 1/6 = 6

Grass animals = 36 - (9 + 6) = 21

There are 21 - 9 = 12 more grass animals than fire animals

Answer:

(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Step-by-step explanation:

i literally just learned this today so here we go:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:

(x - (-7))^2 + (y - (-4))^2 = r^2

(x + 7)^2 + (y + 4)^2 = r^2

We also know that the circle contains the point (-1, -8).

We can substitute these values for x and y, and solve for r:

(-1 + 7)^2 + (-8 + 4)^2 = r^2

36 + 16 = r^2

r^2 = 52

Substituting this value of r^2 into the equation for the circle, we get:

(x + 7)^2 + (y + 4)^2 = 52

Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Answer:

it would be 74

Step-by-step explanation:

8(10)-6=74

Answer:

74

Step-by-step explanation:

8a - b is actually 8 X 10 - 6 which is 74

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

The coordinates of the image of vertex F after a reflection across the line y=-x is (3,-1)

From the question, the coordinates of the vertex F are:

F = (1,3)

When reflected across the line y = -x, the coordinates become

F' =  (3,-1)

Hence, the coordinates of the image of vertex F after a reflection across the line y=-x is (3,-1)

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Answer:

The answer is Ahope this helps

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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Answer:

5x+48=130

Step-by-step explanation:

5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.

Answer:

11/15 of  the trail

Step-by-step explanation:

Step one:

given data

She ran 2/5 of the trail on Monday

Then ran a different 1/3 of the trail on Tuesday

Required

The total distance covered for Monday and Tuesday

Step two:

Total= 2/5+1/3

lcm= 15

Total= 6+5/15

Total= 11/15

Answer:

15-9-2.65-1.35-1.74 which is a negative number meaning he doesnt have enough money

Step-by-step explanation:

9(1) + 2.65(1) + 1.35(1) + 1.74(2) = 16.48

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

From the question, we have the following function that can be used in our computation:

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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