it cost $5.25 for a bottle of 150 vitamins. if the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?

Could you please give me the equation and show me how you got it please so I could understand... thanks.

Step-by-step explanation:

f(x)=x^3+7

y=x^3+7

x=y^3+7

y^3=x-7

y=cube root (x-7)

f(x) inverse=cube root of x-7

The inverse function of the given function is \(y=\sqrt[3]{(x-7)}\).

The given function is f(x)=x³+7.

Inverse function is represented by \(f^{-1\) with regards to the original function \(f\) and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

Now, f(x)=x³+7 can be written as y=x³+7

⇒ x=y³+7

⇒ y³=x-7

⇒ \(y=\sqrt[3]{(x-7)}\)

Therefore, the inverse function of the given function is \(y=\sqrt[3]{(x-7)}\).

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Answer: Y: 2/3 X: 3/2

Step-by-step explanation:

Y rise: 2 run: 3

2/3= Is about 0.6666

And

X: rise: 3 run:2

3/2= 1.5

Answer:

I don't know what the person above put but the slope is 2/3 abd y intercept is -2 so the answer is A on edge

Step-by-step explanation:

IT IS A ON EDGE

Answer:

22m

Step-by-step explanation:

You're welcome, just trust me it's right.

In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Answer:

A

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

Answer:

The sum Bello deposited was #750.

To calculate this, we use the formula for simple interest:

I = Prt

Where I is the interest, P is the principal (the amount deposited), r is the rate of interest (8% per annum), and t is the time (3 years).

We can rearrange the formula to solve for P:

P = I/rt

Substituting the given values, we get:

P = 806/0.08(3)

P = 750

Therefore, the sum Bello deposited was #750.

Answer:

Subtraction property of inequality

Step-by-step explanation:

Step 1: Definition of Subtraction property

Subtraction property of equality refers to balancing an equation by using the same mathematical operation (minus) on both sides.

Step 2: Relate the definition above with the given question.

It can be seen from the statements in the question that 3 was subtracted from both sides of the initial equation to get:

\(x + 3 = 17 \\ x + 3 - 3 = 17 - 3 \\ x = 14\)

a. Expenses: Books and supplies, Housing and food, Tuition and fees, Transportation and Personal expenses. Funding: Savings,

Scholarships, Grants and Student loans.

b. Total estimated expenses are $29,400

(a) Below is an estimate of all her expenses and sources of funding for her 2-year college education.

Expense:

Books and supplies: $1700

Housing and food: $14,020

Tuition and fees: $11,660

Transportation: $2040

Personal expenses: $2980

Funding:

Savings: $7800

Scholarships: $10,240

Grants: $11,600

Student loans: $6200

(b) What is the total of her estimated expenses?

To find the total estimated expenses, we need to add up all the expenses mentioned:

$1700 + $14,020 + $11,660 + $2040 + $2980 = $29,400

Therefore, the total estimated expenses for Nicole's 2-year college education is $29,400.

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The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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The length of the curve segment y = 4x^2 from x = 0 to x = 1 can be calculated by evaluating the definite double integral over the region of the x-y plane bounded by the curve y = 4x^2 and the x-axis,

The square root of the sum of the squares of the partial derivatives of x and y with respect to the arclength parameter.

To evaluate this integral, we first note that

y = 4x^2, so dy/dx = 8x.

Thus, the integral with respect to x is:

s = ∫_0^1 sqrt(1 + (8x)^2) dx

To evaluate this integral,

we can use the substitution

u = 8x,

which gives us

du = 8 dx.

Thus,

the integral becomes:

s = (1/8) ∫_0^8 sqrt(1 + u^2) du

This can be evaluated using trigonometric substitution.

Letting v = arctan(u),

we have

dv = du / sqrt(1 + u^2),

and the integral becomes:

s = (1/8) ∫_{arctan(0)}^{arctan(8)} sqrt(1 + tan^2(v)) dv

This can be evaluated using the substitution

v = tan(v),

which gives us

dv = sec^2(v) dv.

Thus, the integral becomes:

s = (1/8) ∫_0^{arctan(8)} sec(v) dv

This can be evaluated using the substitution

u = tan(v),

which gives us

du = sec^2(v) dv.

Thus, the integral becomes:

s = (1/8) ∫_0^8 1 / sqrt(1 + u^2) du

This can be evaluated using the substitution

u = sinh(v),

which gives us

du = cosh(v) dv.

Thus, the integral becomes:

s = (1/8) ∫_0^8 cosh(v) dv

This can be evaluated using the identity

cosh(v) = (exp(v) + exp(-v)) / 2,

giving us:

s = (1/8) [exp(v) / 2 - exp(-v) / 2]

evaluated from 0 to 8

Finally, evaluating this expression gives us:

s = (1/8) [exp(8) / 2 - exp(-8) / 2]

This is the length of the curve segment y = 4x^2 from x = 0 to x = 1.

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Answer: To find the inverse of the function f(x), we need to switch the roles of x and y, so that x becomes the dependent variable and y becomes the independent variable. Then, we need to solve for x in terms of y.

Let y = √x - 5, then x = y^2 + 5.

To find f^-1(2), we need to substitute 2 for y in the equation x = y^2 + 5:

x = 2^2 + 5 = 9

So f^-1(2) = 9.

This means that the inverse of f(x) at 2 is 9. In other words, if f(x) = 2, then x = 9.

Step-by-step explanation:

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

Hii!

We need to multiply so

3×2.75= 8.25

So she paid $8.25

Brainliest!=

The union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.

The ordered pair is the pair of two numbers which represented in a manner that it provides a particular order.

In an order pair, the first term indicates the x-coordinate, while the second term indicate the y coordinates. The ordered pair are written in close bracket in the following way.

\((x,y)\)

The given set is U(a,e,i,o,u), in which,

\(X=(a,i,o)\\Y=(o,e,u)\\Z=(i,o,u)\)

For the union, write all the terms of  X and Y set.

\(X\cup Y=(a,e,i,o,u)\)

For the intersection, write all the common terms of  X and Z set.

\(X\cap Z=(i,o)\)

For the intersection, write all the common terms of  X , Y and Z set.

\(X\cap Y\cap Z=(o)\)

Hence, the union of X and Y is {a,e,i,o,u}, the intersection of X and Z is {i,o} and the intersection of all the three is {o}.

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Answer:

2,88$

Step-by-step explanation:

36$=100%

1%=36:10

1%=0,36

8%=0,36×8=2,88$

Answer:

There is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.

Step-by-step explanation:

In this case we need to test whether the mean starting salary of a graduate with a bachelor in economics is $48,500.

The information provided are:

\(\bar x=\$43350\\s=\$15000\\n=50\\\alpha =0.01\)

The hypothesis for the test can be defined as follows:

H₀: The mean starting salary of a graduate with a bachelor in economics is $48,500, i.e. μ = 48500.

Hₐ: The mean starting salary of a graduate with a bachelor in economics is different from $48,500, i.e. μ ≠ 48500.

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 \(t=\frac{\bar x-\mu}{s/\sqrt{n}}\)

   \(=\frac{43350-48500}{15000/\sqrt{50}}\\\\=-2.42773\\\\\approx -2.43\)

Thus, the test statistic value is -2.43.

Compute the p-value of the test as follows:

 \(p-value=2\times P(t_{49}>-2.43)=0.0188\)

*Use a t-table.

Thus, the p-value of the test is 0.0188.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.0188 > α = 0.01

The null hypothesis will not be rejected at 1% level of significance.

Thus, concluding that there is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.

The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

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Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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The vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given a triangle DEF which is being dilated by a dilation factor of (2,M) we need to find the vertices of the image,

The vertices before dilation are D(2, -1), E(-1, 1) and F(-1, -1)

Since, the dilation factor is (2,M), so the new vertices are,

D'(2×2, -1×M)

D'(4, -M)

E'(-1×2, 1×M)

E'(-2, M)

F'(-1×2, -1×M)

F'(-2, -M)

Hence, the vertices of triangle DEF after dilation are D'(4, -M), E'(-2, M) and F'(-2, -M)

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Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

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Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

Define measurement?

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Answer:

30 books

Step-by-step explanation:

125%= 1.25

1.25 times 24= 30

Answer:54

Step-by-step explanation:

If we know he has 125% more books than his sister who has 24 books, then we would write 24×125%

That equations equals 30

Now you have to add 24+30 because he has 30 more books than her, so he has her amount plus his.

Based on the image attached, the solution for GE  is approximately 22.72.

To  be able to solve the equation √129 + √129 = GE, one need to simplify the  expression and then isolate GE.

Step 1: One can add the square roots:

Note that the equation:

√129 + √129 = GE.

Step 2:  Do put together the square root terms:

2√129 = GE.

Step 3:  Then Divide by 2:

√129 = GE/2.

Step 4: The Square both sides:

129 = (GE²)/4.

Step 5: So, Multiply by 4:

516 = GE².

Lastly, Take the square root:

√516 = √(GE²)

√516 = GE

GE = 22.72. approx.

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See text below



Step 26

Solve the equation for GE:

√129+√129 = GE

GE=2/129

Show steps

Correlation (GPA, Income) =1. A sample correlation coefficient is called r, while a population correlation coefficient is called rho, the Greek letter ρ. The sample correlation coefficient uses the sample covariance between variables and their sample standard deviations.

 GPA Income (GPA-average)^2 (Income-average) ^2 GPA*Income

 3 6 1 4 18

 1 2 1 4 2

 2 4 0 0 8

average 2 4 0.666666667 2.666666667 9.333333

var(GPA) = average((GPA-average)^2) = 0.666

var(Income) = average((Income-average)^2) = 2.666

Correlation (x,y)=cov (x,y) /sqrt (var(x) * var(y))

Hence

cov (GPA, Income)= average (GPA* Income) - average(GPA)* average (Income)

=9.3333-2*4

=1.333

Correlation (GPA, Income)= cov (GPA, Income)/sqrt( var(GPA)*var(Income))

=1.333/sqrt(0.666*2.666)

=1

Correlation (GPA, Income) =1

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

$25

Step-by-step explanation:

Simply by using long division, this can be solved. Change 60% into its decimal form (0.6,) and divide 15 by 0.6.

A linearly independent set that generates the subspace of diagonal matrix in M2x2(F) is {[1,0;0,0], [0,0;0,1]}.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a, b∈F.

A linearly independent set of vectors that generate this subspace is {[1,0;0,0], [0,0;0,1]}. Any diagonal matrix can be written as a linear combination of these two vectors.

A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a,b∈F. This means that all the diagonal entries in the matrix must be non-zero. To find a linearly independent set that generates this subspace, we can start by considering the simplest form of a diagonal matrix, which is [1,0;0,0]. This vector is linearly independent, as it cannot be expressed as a linear combination of any other vector in the space. Similarly, [0,0;0,1] is also linearly independent, as it can't be expressed as a linear combination of any other vector.

These two vectors form a linearly independent set that generates the subspace of diagonal matrices in M2x2(F). Any diagonal matrix can be written as a linear combination of these two vectors. For example, the matrix [2,0;0,3] can be expressed as 2[1,0;0,0]+3[0,0;0,1]. Thus, this set of vectors is sufficient to generate the entire subspace.

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