what is the sum of x and 16 is less than 32?

Answer:

16 pencils and 17 glue sticks

Step-by-step explanation:

X=pencils

Y=glue sticks

X+Y=33

1.50X+2Y=58

times ten to get whole numbers

=15X+20Y=580

same for e1

=10X+10Y=330

15X+20Y=580

10X+10Y=330

elimination mthd

150X+200Y=5800

150X+150Y=4950

50Y= 850

Y=17

X+17=33

X=33-17

X=16

Answer:

a. $14.99k + $24+ $25 = x

b. $14.99(3) + $24+ $25 = x

   $44.97 + $24 + $25 = $93.97

Step-by-step explanation:

Answer:

i) C= $14.99 k + $24

ii) $93.97

Step-by-step explanation:

Let the number of models be represented by -----------k

Let the amount spent on books to be--------$24

The equation that represent amount spent in the mall is given as;

C= $14.99 k + $24   ---------------where ;

C= the equation for the total amount spent in the mall

k = the number of plane models

ii)

Using the equation : C= $14.99 k + $24    and if k = 3 and the amount spent on the store is $25  then ;

C= $14.99 * 3 + $24 = $44.97 + $24 = $68.97

C+ 25 = $68.97 + 25 =$93.97

Answer:

33.60

Step-by-step explanation:

Multiply 28 by 20%

28*20%=5.6

Add 5.6 and 28 together

28+5.6=33.60

Sorry if it is wrong Im still really tired

Answer: 4/3 or 1 & 1/3 cups of vinegar

Step-by-step explanation:

1. Set a proportion: 3/4 : 1/2

2. Divide 2 by 3/4 to get 2 & 2/3

3. Multiply 2 & 2/3 and 1/2 together to get 4/3 or 1 & 1/3

Answer:

20 x 9 = $180 just multiply hours worked times rate per hour

Step-by-step explanation:

a)

well, it is kind of written already :

228 miles and 6 gallons.

so, miles/gallon = 228/6 = 38 miles/gallon.

b)

it is not mentioned, but I guess we have to assume that he got the same miles/gallon ratio on this trip as well.

so, again

38 miles/gallon

and he used 9 gallons.

so, he drove 38×9 = 342 miles

a) Rocky Mountain should order 200 tires each time it places an order.

b) The total cost of this policy is $17,160.

a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:

If fewer than 200 tires are ordered: The purchase price is $25 per tire.

If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.

If 8,000 or more tires are ordered: The purchase price is $13 per tire.

Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.

b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:

Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200

Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950

Therefore, the total cost of this policy is $40,950.

Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.

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Answer:

It's 5 which is A.

Step-by-step explanation:

Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

At the null hypothesis, it is tested if the mean is of 7 ounces, that is:

\(H_0: \mu = 7\)

At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:

\(H_1: \mu \neq 7\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

The values of the parameters are given by:

\(\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18\)

Hence the value of the test statistic is found as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}\)

t = 1

Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of \(t^{\ast} = 1.7341\)

Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.

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Answer:

D

Step-by-step explanation:

The company's WACC is 9.95%. This implies that the company must generate a return of at least 9.95% on its investments to cover its cost of capital.

WACC (Weighted Average Cost of Capital) is a measurement used to determine a company's cost of capital. It is calculated as a weighted average of the costs of equity and debt, considering the company's capital structure. The formula for WACC is:

WACC = (E / V x Re) + [(D / V x Rd) x (1 - T)]

Where:

E = Market value of the company's equity

D = Market value of the company's debt

V = Total value of the company (equity + debt)

Re = Cost of equity

Rd = Pretax cost of debt

T = Tax rate

Given the following values:

Debt-equity ratio = 0.55

Cost of equity (Re) = 15.4%

Pretax cost of debt (Rd) = 7.8%

Tax rate = 32%

We can calculate the after-tax cost of debt, Rd, by multiplying the pretax cost of debt with (1 - tax rate). Thus,

Rd = 7.8% x (1 - 32%) = 5.292%

Now, we can substitute the values into the WACC formula:

WACC = [(E / V x Re) + (D / V x Rd) x (1 - T)]

WACC = [(1 / 1.55 x 15.4%) + (0.55 / 1.55 x 5.292%) x (1 - 32%)]

WACC = 9.95%

Therefore, the company's WACC is 9.95%. This implies that the company must generate a return of at least 9.95% on its investments to cover its cost of capital.

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Answer:

i) 0.1056

ii) 0.105

iii) 0.1

iv) 0.1056

Step-by-step explanation:

0.36, to the power of 2 (0.36×0.36) is 0.1296

0.1296-0.03×0.8=0.1056

Answer:

A

Step-by-step explanation:

y = 12x + 8

The correct equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased is,

⇒ y = 12x + 8

Now,

Let p be the price of one bucket of popcorn and t be the price of one ticket.

Since, The total cost for a bucket of popcorn and 4 movie tickets is, $56

⇒ p + 4t = 56  .. (1)

And, the total cost for the same size bucket of popcorn and 6 movie tickets is $80.

⇒ p + 6t = 80   ..(2)

Now, Equation (1) - Equation (2),

-2 t = - 24

⇒ t = 12

By substituting this value in equation (1),

We get,

p + 48 = 56

⇒ p = 8

Thus, the price of one bucket of popcorn = $8

And, the price of one ticket = $12

Thus, The total price (y) of one bucket of popcorn and x tickets is,

y = 8 + 12 x

y = 12x + 8

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Answer: y= 4x - 16

Step-by-step explanation:

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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The statement that describes parallelism is option C: a surface of revolution having all points equidistant from a common axis. Parallelism refers to the condition in which lines or surfaces are equidistant and never meet.

In the case of surfaces of revolution, all points on the surface are equidistant from a common axis, which makes them parallel to each other. This means that any two points on the surface of the revolution will have the same distance from the axis. Parallelism is an important concept in geometry, engineering, and architecture as it allows for the construction of structures and machines that require precise and uniform spacing. Equidistance is also a key aspect of parallelism as it ensures that all points on the surface maintain the same distance from the axis, thereby preserving the parallel condition.

In summary, option C, "a surface of revolution having all points equidistant from a common axis," is the statement that describes parallelism.

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Answer:

corresponding angles postulate

Step-by-step explanation:

just took the test ;)

Answer: Corresponding angles postulate

Answer:

$1,471.5625

Step-by-step explanation:

Monthly salary = $1850

Weekly salary = $1850/4 weeks

= $462.5

Hourly rate = $462.5/40 hours

= $11.5625

Overwork time = 62 hours - 40 hours

= 22 hours

Time and a half = 1.5 times the normal salary

Overwork time payment per hour = 1.5 × $11.5625

= $17.34375

Overwork time payment for 22 hours = 22 × $17.34375

= $381.5625

Last week salary = weekly salary + overtime payment

= $462.5 + $381.5625

= $84.0625

Gross salary for the month = 3 weeks regular salary + last week salary

= (3 × $462.5) + $84.0625

= $1387.5 + $84.0625

= $1,471.5625

Answer:

The 95% confidence interval based on this sample is =

[6.41, 7.79]

Step-by-step explanation:

The formula for Confidence Interval =

Mean ± z × standard deviation/√n

Sample mean = 7.1 hours

Standard deviation = 5 hours

n = 200 students

z = 95% confidence interval z score

= 1.96

C.I = 7.1 ± 1.96 × 5/√200

C.I = 7.1 ± 0.693

Hence, Confidence Interval

= 7.1 - 0.693

= 6.407

Approximately = 6.41

= 7.1 + 0.693

= 7.793

Approximately = 7.79

Therefore, the 95% confidence interval based on this sample is

[6.41, 7.79]

Using the given information, the coordinates of BB are (5, 1)

From the question, we are to determine the coordinates of point BB

From the given information,

The midpoint of AB is M(4, 0)

and

The coordinates of AA are (3, -1)

If the coordinates of BB are (x, y)

Then,

4 = (x +3)/2

8 = x + 3

x = 8 - 3

x = 5

Also,

0 = (-1+y)/2

0 = -1 + y

y = 1

Hence, the coordinates of BB are (5, 1)

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The critical points are neither maxima nor minima, but rather saddle points. The function is unbounded above and below on the ellipse x² + 2y² = 1.

To find the extremes of the function 4x - 4y subject to the constraint x² + 2y² = 1, we can use the method of Lagrange multipliers.

Let f(x,y) = 4x - 4y, and g(x,y) = x² + 2y² - 1 be the constraint function. Then, we want to find the values of x and y that maximize or minimize f(x,y) subject to g(x,y) = 0.

Using the method of Lagrange multipliers, we set up the following system of equations:

∇f(x,y) = λ∇g(x,y)

g(x,y) = 0

Taking partial derivatives of f and g with respect to x and y, we have:

∂f/∂x = 4

∂f/∂y = -4

∂g/∂x = 2x

∂g/∂y = 4y

Setting these equal to λ times their corresponding partial derivatives, we get:

4 = λ(2x)

-4 = λ(4y)

Dividing these equations gives:

x/y = -1/2

Substituting this into the constraint equation, we get:

(-1/2)² + 2y² = 1

Solving for y, we get:

y = ±√(3/8)

Then, using x/y = -1/2, we can find x:

x = (-1/2)y

So the critical points are:

(√(3)/4, -√(3)/2) and (-√(3)/4, √(3)/2)

To determine whether these are maxima or minima, we need to use the second derivative test or the bordered Hessian method. Since the bordered Hessian is somewhat complicated in this case, we will use the second derivative test.

The second partial derivatives of f are:

∂²f/∂x² = 0

∂²f/∂y² = 0

∂²f/∂x∂y = 0

At the point (√(3)/4, -√(3)/2):

D = ∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = (0)(0) - (0)² = 0

Since D = 0, the second derivative test is inconclusive.

At the point (-√(3)/4, √(3)/2):

D = ∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = (0)(0) - (0)² = 0

Again, the second derivative test is inconclusive.

Therefore, the critical points are neither maxima nor minima, but rather saddle points. The function f(x,y) = 4x - 4y is unbounded above and below on the ellipse x² + 2y² = 1.

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Answer:

I think the answer is B

Step-by-step explanation:

Answer:

we know that,

y-y1=m(x-x1)

or, y-1=-3(x-5)

or, y-1=15-3x

or 3x+y-16=0 is the required equation

The graph of the line with slope -3 passing through the point (5,1) is attached.

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.

The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.

The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.

The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).

We are asked to graph a line with a slope = -3, passing through the point (5, 1).

We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).

Substituting these values in the equation y - y₁ = m(x - x₁), we get

y - 1 = -3(x - 5)

or, y = -3x + 15 + 1

or, y = -3x + 16.

or, 3x + y = 16

The equation of the line in the slope-intercept form is y = -3x + 16.

The equation of the line in the standard form is 3x + y = 16.

To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.

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Answer:

11235.35

Step-by-step explanation:

Given data

P=8225

R=4.2%=0.042

T=8years

The simple interest formula is

A=P(1+rt)

Substitute

A=8225(1+0.042*8)

A=8225(1+0.336)

A=8225*1.366

A=11235.35

Hence the balance will be 11235.35

We assume the opposite of what we want to prove and show that it leads to a contradictionContradiction implies that our initial assumption is false, thereby establishing the validity of the statement.

Proof by Contradiction:Suppose there exists an integer x such that x^2 - 12x + 23 is even, but x is not odd. That is, assume x is even.Since x is even, we can write x = 2k for some integer k. Substituting this into the expression x^2 - 12x + 23, we have (2k)^2 - 12(2k) + 23 = 4k^2 - 24k + 23.

Now, let's consider the parity of 4k^2 - 24k + 23. We know that the product of two even numbers is always even (4k^2 and -24k are both even). Also, the sum of an even number and an odd number is always odd. Since 23 is odd, the overall expression is odd.

However, we assumed that x^2 - 12x + 23 is even, which leads to a contradiction. Therefore, our initial assumption that x is even must be false.Hence, we conclude that if x^2 - 12x + 23 is even, then x must be odd. QED.In this proof, we assume the opposite of what we want to prove and show that it leads to a contradiction. This contradiction implies that our initial assumption is false, thereby establishing the validity of the statement.

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The rectangular coordinate form of the equation ρ = 1 is x² + y² + z² = 1. It represents a sphere of radius 1 with its center at the origin of 3-dimensional rectangular coordinates.

To convert rho = 1 to rectangular coordinates and write it in standard form, use the following equation;`

x² + y² + z² = ρ²`.

The given equation is `ρ = 1` ,We know that `ρ = √(x² + y² + z²)` ,Substitute ρ in the given equation and solve for rectangular coordinatesx² + y² + z² = 1

The above equation is a sphere of radius 1 with its center at the origin of 3-dimensional rectangular coordinates, where x, y, and z are the standard rectangular coordinates of any point in 3-dimensional space.

Therefore, the rectangular coordinate form of the given equation ρ = 1 is `x² + y² + z² = 1` which is in standard form.

The rectangular coordinate form of the equation ρ = 1 is x² + y² + z² = 1. It represents a sphere of radius 1 with its center at the origin of 3-dimensional rectangular coordinates.

In standard form, this equation is a mathematical expression of a sphere in rectangular coordinates.

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A.(x,y)--->(x-2,y-4)

The measure of the angles are: K, L, C, N, O G = -3/4, 65, 8 40.4, 89 and 44 respectively

To determine K

9x + 2 = 23 + 5x -1

9x -5x = -1 +2

4x = -3Making x the subject we have

x= -3/4

To find the value of L

Let angle L be x

x + 65 = 130

x=130-65

That is x = 65

To find the m<C

4x + 7 = 3x + 15

Collecting like terms

4x - 3x = 15-7

Making x the subject of the relation we have

x=8

To find the m<N

7x + 6x - 1 = 90

13x = 89

x=89/13

x= 6.9

Substitute x = 6.9 in 6x -1

6(6.9) -1

m<L = 40.4

To find the m<O

5x - 11 = 4x +9

5x-4x = 9 +11

x=20

By substitution in 4x +9 we have

4(20) +9

80+9

m<S = 89

To find the value of the angle G

6x - 4 = 5x +4

6x - 5x = 4+4

x = 8

Therefore the m<G is

5x +4

5(8) +4

40+4 = 44 digress

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Answer:

0≤x<3, 4≤x≤7

Step-by-step explanation:

-1≤|x-3|-2≤1, 1≤|x-3|≤3,

1. if x-3>0, x>3

4≤x≤7

2. if x-3<0, x<3

-3≤x-3≤1, 0≤x≤4 -> 0≤x<3