Jorimiah scored 85 points in a basketball game. That was 1/8 of the points that he scored for the season. How many points did jorimiah score in the season.

Small market orders copies of a certain magazine for its magazine rack each week. The number of copies to order to generate more revenue is 4.

Let the profit y, the demand for the magazine be x , the number owner ordered k , then we get :

y = 4x - 2m ( m > x)

y = 2m        ( m ≤ x)

If m = 3 we get

E (y) = 1/14 (4 - 2x3) + 2/14 (4x2 - 2x3) + 3/14 (2x3) + 3/14 (2x3) + 2/14 (2x3) + 3/14 (2x3)

E(y) = 68/14

If m = 4 get,

E (y) = 1/14 (4 - 2x4) + 2/14 (4x2 - 2x4) + 3/14 (4x3 -2x4) + 3/14 (2x4) + 2/14 (2x4) + 3/14 (2x4)

E(y) = 72/14

E (y)m=4 > E(y)m=3

So order number is 4.

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The formula for the area of the parallelogram-like figure is A = πr

parallelogram can be defined as  a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

bh, where h is the height of the parallelogram-like figure.

Therefore, The formula for the area of the parallelogram-like figure is A = πr.

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When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin, this statement is false.

The span of two nonzero vectors u and v, Span{u, v}, is the set of all linear combinations of u and v. This set can include not only the lines through u and the origin, and the line through v and the origin, but also all other points on the plane defined by these two lines.

For example, if u = (1, 0) and v = (0, 1), then Span{u, v} would be the set of all points in the x-y plane, since every point in the plane can be represented as a linear combination of u and v.

Therefore, Span{u, v} contains not only the lines through u and the origin, and the line through v and the origin, but all other points on the plane defined by these two lines.

Correct Question :

When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin. True or fasle.

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Answer:

A = $2,800 B = $12,600

Step-by-step explanation:

a. How much will the insurance company pay?

The liability insurance will cover the damages to the other car ($1,400) and the personal injury claims ($12,800 + $9,200) up to the limit of $10,000. So the insurance company will pay $10,000.

The collision insurance covers the damage to Rusty's own car, minus the $300 deductible, so the insurance company will pay $3,100 - $300 = $2,800.

Therefore, the insurance company will pay a total of $10,000 + $2,800 = $12,800.

b. What is Rusty’s share of the responsibility?

Rusty is responsible for paying the remaining amount not covered by insurance, which is $1,400 + $3,100 + $12,800 + $9,200 - $12,800 = $12,600.

Therefore, Rusty's share of the responsibility is $12,600.

The newspaper's assertion is unjustified. It can be shown that the interval does not contain 0.5 based on the 99% confidence interval of (0.322, 0.511). (which is half).

This indicates that the population parameter (mean, percentage, and standard deviation) is between a and b with x% confidence.

This indicates that at least half of students prefer using a computer to take their notes. Since the interval's lower limit (0.322) is higher than 0.5, there is a 99% likelihood that the actual percentage of students who prefer taking notes on computers is higher than 0.5.

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An interest rate of 2.5 % is required to obtained a current capital of $ 143,000 after a period of 16 years.

In this problem we find that Jayden deposits an amount of money for a period of 16 years and such account is under composite interest, that is, that the account increases its capital continously in time. Compound interest model is shown:

C' = C · (1 + r / 100)ˣ

Where:

If we know that C = 97,000, C' = 143,000 and x = 16, then the interest rate is:

143,000 = 97,000 · (1 + r / 100)¹⁶

143 / 97 = (1 + r / 100)¹⁶

1.025 = 1 + r / 100

0.025 = r / 100

r = 2.5

The needed interest rate needed for a capital of $ 143,000 after a period of 16 years is equal to 2.5 %.

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Rotating a triangle 270 degrees counterclockwise is the same as rotating a figure 90 degrees clockwise. The solution has been obtained using the concept of rotation.

What is rotation?

A rotation in mathematics is a transformation that revolves a shape around a fixed point.

We have a specific rule that we can use to do this that is based on the fact that a 270° anticlockwise rotation is the same as a 90° clockwise rotation. One such rotation is to rotate a triangle 270° anticlockwise.

On a graph, we can rotate a triangle 270° anticlockwise by passing each of its vertices through the transformation shown below:

Change the x and y coordinates after multiplying the x coordinate by a negative number.

Consequently, (x,y) becomes (y,-x).

Hence, this way we can rotate a triangle 270 degrees counterclockwise.

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The actual weight of a pound is 0.45359237 kilos.

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The general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t.

A differential equation is an equation that contains at least one derivative of an unknown function, either an ordinary derivative or a partial derivative. Suppose the rate of change of a function y with respect to x is inversely proportional to y, we express it as dy/dx = k/y.

In calculus, a differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). The derivative represents nothing but a rate of change, and the differential equation helps us present a relationship between the changing quantity with respect to the change in another quantity. y=f(x) be a function where y is a dependent variable, f is an unknown function, x is an independent variable.

We have to find the general solution for d²y/dt² - 2 dy/dt - 15y = e^4t

Solving the above ordinary differential equation, we get:

y = c₁e^5t + c₂e^-3t - (1/7)e^4t

Thus, the general solution for given equation is y = c₁e^5t + c₂e^-3t - (1/7)e^4t

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Answer: 3.99

Step-by-step explanation:

The speed distance of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.

The speed of the faster runner is 8 mph.

The speed of the slower runner is 6 mph.

The distance from the starting point is 5.5 miles.We can use the formula d = rt, where d is the total distance, r is the rate (speed) and t is the time taken to cover the distance.

Let us assume that the speed of the faster runner is x mph. Then, the speed of the slower runner is (x-2) mph.

Since the two runners meet 1 hour 6 minutes after starting, the total time taken is 1 hour 6 minutes = 66 minutes.

Thus, the total distance covered = (x * 66) + (x - 2) * 66 = 132x - 132

But, the total distance covered is 11 miles, so

132x - 132 = 11

Solving for x, we get

x = 8 mph

Therefore, the speed of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.

Since they meet 1 hour 6 minutes after starting, they have travelled a total distance of (8 * 66) + (6 * 66) = 5.5 miles. Therefore, the distance from the starting point at which they meet is 5.5 miles.

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By solving a system of equations we will see that a large plant costs $4.50 and a medium one $2.75

Let's define the variables:

x = cost of a large plant.

y = cost of a medium plant.

We know that " The cost of 4 large plants and 8 medium plants is $40"

4*x + 8*y = 40

And "The cost of 5 large plants and 2 medium plants is $28."

5*x + 2*y = 28

So we have a system of equations:

4*x + 8*y = 40

5*x + 2*y = 28

We can isolate x on the first equation to get:

4x + 8y = 40

4x = 40 - 8y

x = (40 - 8y)/4

x = 10 - 2y

Replacing that in the other equation we will get:

5*(10 - 2y) + 2*y = 28

50 - 10y + 2y = 28

50 - 28 = 8y

22 = 8y

22/8 = y

2.75 = y

And the value of x is:

x = 10 - 2*2.75 = 4.5

Then the cost of a lare plant is $4.5 and the cost of a medium plant is $2.75.

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To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.

For example:

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On the right side, we can just simplify the expression to 1+tanθ+cotθ

Yes, this is true.

The left side of the equation can be simplified to 1, which is equal to the right side.

Left side:

(cotθ/1-tanθ)+(tanθ/1-cotθ)

= (cotθ + tanθ)/(1 - tanθ - cotθ)

= (tanθ + cotθ)/(1 - tanθ - cotθ)

= 1/(1 - tanθ - cotθ)

= 1

Right side:

1 + tanθ + cotθ = 1

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Answer:

See proof below

Step-by-step explanation:

(Please excuse any typos and point them out to me. It is a pain typing in LateX)

We are asked to prove:

[tex]\dfrac{\cot\theta}{1-\text{\ensuremath{\tan\theta}}}+\dfrac{\tan\theta}{1-\cot\theta}=1+\tan\theta+\cot\theta[/tex]

Since
[tex]\tan\theta =\dfrac {\sin\theta}{\cos\theta}\\\\\cot\theta = \dfrac {\cos\theta}{\sin\theta}\\\\[/tex]

the left side becomes

[tex]\dfrac{\cos\theta/\sin\theta}{1-\sin\theta/\cos\theta}+ \dfrac{{\sin\theta/\cos\theta}}{1-\cos\theta/\sin\theta} \cdots \cdots \cdots(1)[/tex]

For ease of expressing this let

[tex]a = \sin\theta\\b = \cos\theta\\[/tex]

Substituting the above in expression (1) gets us
[tex]\dfrac{b/a}{1- a/b} + \dfrac{a/b}{1-b/a}[/tex]

Let's take the individual terms and simplify each
[tex]\dfrac{b/a}{1- a/b} = \dfrac{b}{a}\cdot \dfrac{1}{1-\dfrac{a}{b}}[/tex]

[tex]\dfrac{1}{1-\dfrac{a}{b}}= \dfrac{1}{\dfrac{b-a}{b}}=\dfrac{b}{b-a}[/tex]

Therefore

[tex]\dfrac{b}{a}\cdot\dfrac{b}{b-a} = \dfrac{b^2}{a(b-a)}[/tex]

For the second term we get

[tex]\dfrac{a/b}{1-b/a} = \dfrac{a^2}{b(a-b)}[/tex]

Noting that (a - b) = - (b - a)

the entire expression becomes

[tex]\dfrac{b^2}{a(b-a)} = - \dfrac{a^2}{b(b-a)}[/tex]

Multiply this expression throughout by the LCM which is
[tex]ab(b-a)[/tex]

[tex]\dfrac{b^2 \cdot b - {a^2}\cdot a}{ab(b-a)}\\\\= \dfrac{b^3 - a^3}{ab(b-a)}\cdots\cdots(2)\\[/tex]

(b -a) cancels in numerator and denominator on both sides giving

For the numerator we have the identity
[tex]b^3 - a^3 = (b-a)(b^2 + ab + b^2)[/tex]

So the expression in (2) becomes
[tex]\dfrac{(b-a)(b^2 + ab + a^2)}{ab(b-a)}\\\\\textrm{(b-a) cancels from the numerator and denominator}\\\\[/tex]

This leaves us with:

[tex]\dfrac{(b^2 + ab + a^2)}{ab}[/tex]

Substituting for a = sinθ and b = cosθ we get

[tex]\dfrac{\cos^2\theta + \sin^2\theta+ \cos\theta\sin\theta}{\sin\theta\cos\theta}[/tex]

Divide each term in the numerator by [tex]\sin\theta \cos\theta[/tex]

==> [tex]\dfrac{cos^2\theta}{\sin\theta\cos\theta} + \dfrac{\sin^2\theta}{\sin\theta\cos\theta}+ \dfrac{\sin\theta\cos\theta}{\sin\theta\cos\theta}}[/tex]

==> [tex]\dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta} + 1[/tex]

[tex]\cot\theta + \tan\theta + 1\\== > 1 + \tan\theta + \cot\theta[/tex]

Hence PROVED

The line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10) is 12√5.

Using the two-point form of the line, we can compute the equation of the line connecting the points and obtain:

y = 2x

Consider x = t. Now the result is:

y = 2t

We can write C as:

[tex]\vec{r}(t)=t\hat{i}+2t\hat{j}[/tex]

Now, t ranges from t = 1 to t = 5 since x = t and x range from x = 1 to x = 5. When we differentiate the C equation, we obtain:

[tex]\vec{r}'(t)=\hat{i}+2\hat{j}[/tex]

Now finding the magnitude

[tex]|\vec{r}'(t)|=\sqrt{(1)^2+(2)^2}[/tex]

[tex]|\vec{r}'(t)|=\sqrt{1+4}[/tex]

[tex]|\vec{r}'(t)|=\sqrt{5}[/tex]

Now, the integral will be:

I = [tex]\int_{t=1}^5t\:(\sqrt 5)dt[/tex]

I = [tex]\sqrt {5}\int_{t=1}^5tdt[/tex]

Now integrating

I = [tex]\sqrt {5}\left(\frac{t^2}{2}\right)_{t=1}^{5}[/tex]

I = [tex]\sqrt {5}\left(\frac{5^2}{2}-\frac{1^2}{2}\right)[/tex]

I = √5(25/2 - 1/2)

I = √5(12.5 - 0.5)

I = 12√5

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The complete question is:

Evaluate the line integral [tex]\int_{c}xds[/tex]where c is the straight line segment from point (1, 2) to point (5, 10).

Answer:66

Step-by-step explanation:

336666

Answer:

8.40

Step-by-step explanation:

Since, the simple interest is,

I= p x r x t

     100

Where,

P=Principal

r= rate per periods

t= number of periods

Here, P=140, r=3%, t = 2,

the simple interest will be

I= 140 x 3 x 2

         100

= 840

  100

=8.40

Answer:

y = 64

x = 99

Step-by-step explanation:

180 - 116 = y

y = 64

A parallelogram is 360 degrees.

360 - 72 -125 - 64 = x

x = 99

I hope this helps!

Mary's monthly pension benefit is $3,649.80.

First, we have to find the average salary.

The average is the sum of the salaries divided by the number of salaries.

($78,000 + $80,000)/2 = $79,000

Next, we can find the annual retirement rate.

The annual retirement pension is the product of the average, the rate and the number of years employed.

$79,000 x 1.98% x 28 = $43,797.60

Finally, we can find the monthly retirement pension.

The monthly retirement pension is then the annual retirement pension divided by the number of months in a year.

There are 12 months in a year.

$43,797.60 / 12 = $3,649.80

Therefore, Mary's monthly pension benefit is $3,649.80.

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Among the given, the function that has a percent rate of decrease equal to 5% is: F(x) = 3(0.95)

Hence, option (D) is the correct choice.

For (A):

We have,

F(x) = 3(0.5), Here percentage rate decrease = 50%

For (B):

We have,

F(x) = 3(1.5), Here there is percentage rate increase which will be = 50%

For (C):

We have,

F(x) = 3(0.05), Here percentage rate decrease = 95%

For (D)

F(x) = 3(0.95)

Here, percent rate of decrease equal to 5%

This function represents the relationship between input x and the output y where y = 3(0.95^x).

The number 0.95 can be interpreted as 95% of the original value, which means a 5% decrease.

For (A):

We have,

F(x) = 3(1.05), Here there is percentage rate increase which is = 5%

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The range of the function lies between  -∞<y<∞ and the domain of the function is given by -1<x<3

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph of a function

We know  The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

It is clear from the graph that y ∈ (-∞,∞) and x∈ (-1,3)

we know a function is given by y=f(x)

where y is the range values and x is the domain.

Hence, The range of the function lies between  -∞<y<∞ and the domain of the function is given by -1<x<3

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Answer: 10.30

Step-by-step explanation:

Distance formula = [tex]\sqrt{(x_{2} +x_{1})^2+(y_{2} +y_{1})^2}[/tex]

A ([tex]x_{1} ,y_{1}[/tex]) = A(-3,-6) so [tex]x_{1} = -2[/tex] and [tex]y_{1} =-6[/tex]

B ([tex]x_{2} ,y_{2}[/tex]) = B(-6, 1) so [tex]x_{2} = -6[/tex] and [tex]y_{2} = 1[/tex]

Plug in the values. You should get [tex]\sqrt{(-6 +-3)^2+(1 +-6)^2}=\sqrt{(-9)^2+(-5)^2}=\sqrt{81+25}=\sqrt{106}[/tex]

≈10.30

1.5 cm is the data range. The number sequence "4, 6, 9, 3, 7" is an example where the lowest value is 3 and the highest is 9. The range is therefore 9 3 = 6. Just like that!

Q3 - Q1 is the interquartile range (IQR).

The third quartile (Q3) of the box plot is the data value that exactly matches the end of the box's edge (7 cm).

The data value exactly at the box's outside edge (5.5 cm) is the first quartile (Q1).

Range between quartiles (IQR): 7 - 5.5 = 1.5 cm

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The function written in vertex form is:

f(x) = 4(x + 6)² - 26

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one 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,

f(x) = 4(x² + 12x) + 10

Now,

f(x) = 4(x² + 12x) + 10

f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10

f(x) = 4(x + 6)² - 26

Thus,

f(x) = 4(x + 6)² - 26 is the function in vertex form.

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Answer:

B is correct

Step-by-step explanation:

The value of the equations if they are zero each are: 3, 5, -13/4 and 5

By definition, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =

The given equations are

-5x+15=0

-5x = -15

Making x the subject of the relation we have

x=3

2) 5x-25 = 0

Collecting like terms

5x=25

Making x the subject

x=5

3) 4a+13=0

4a = -13

Making a the subject of the relation

a=-13/4

4)  5x-25=0

Collecting like terms

5x=25

Making x the subject of the relation

x=5

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The company needs to produce 8 units in order for the net income to equal $0

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

the equation given can be simplified as:

f(x) = 9x² - 54x - 144.

f(x) = 9(x² - 6x - 16)

Then factoring we have:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, so the variables are:

x + 2 = 0 -> x = -2

x - 8 = 0 -> x = 8

As the amount of products sold have to be positive the amount of product is 8

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xplanation:

a b c your way out the picture

The CEO should allocate $144,000 to labor and $216,000 to capital equipment.

Step-by-step explanation given below

The CEO should allocate $144,000 to labor and $216,000 to capital equipment. This allocation maximizes the output of the factory, which can be found by taking the partial derivatives of the function Q with respect to K and L and setting them equal to 0.

Partial derivative of Q with respect to K = -20K^-4/3L^2/3 = 0

20K^-4/3L^2/3 = 0

K^4/3L^2/3 = 20

K = (20L^2/3)^1/4

Partial derivative of Q with respect to L = -40K^-1/3L^-1/3 = 0

40K^-1/3L^-1/3 = 0

K/L = 40

K = 40L

Solving for K and L, we get:

K = (20*L^2/3)^1/4

L = 40K

Substituting K into the equation for L, we get:

L = (40*(20L^2/3)^1/4)

L = 80(20L^2/3)^1/4

L^3/4 = 160L^2/3

L^3 = 1280L^2

L^2 = 1280L

L = 1280

Substituting L into the equation for K, we get:

K = (20*1280^2/3)^1/4

K = (307200/3)^1/4

K = 144

Therefore, the CEO should allocate $144,000 to labor and $216,000 to capital equipment.

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Note that the angle that is vertical to ∠AEB is ∠BEC.

Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the normal connotation of up-down.

Vertical angles of equal measure are always congruent. Both vertical angle pairings (four angles total) always add up to 360 degrees. Angles formed by each pair of vertical angles are referred to as neighboring angles, and they are supplementary (the angles sum up to 180 degrees).

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The isolation of variable in the equation will result in the formula - Breadth = (Perimeter - 2length)/2.

As per the known information, the formula of the perimeter of rectangle is -

Perimeter = 2 (length + breadth)

Expanding the formula we get -

Perimeter = 2length + 2breadth

Rewriting in terms of breadth -

2Breadth = Perimeter - 2length

Breadth = (Perimeter - 2length)/2

The process to isolate the variable will require expanding and rewriting the equation with breadth on Left Hand Side of the equation. Now, move the constant on Right Hand Side and you will get the formula.

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Answer: br uh is this even a high school question? anyway, look at the image that i sent you can see the answer there.
better give me brainliest

Step-by-step explanation: