PLEASE HELP!!! i am failing and im going to be held back if i dont get my grade up!!!!

Emma spent $45.20 on 5 dozen bagels and a gallon of iced tea. The price of the gallon of iced tea was $5.25. The following equation can be used to find d, the price of each dozen of bagels.

5d + 5.25 = 45.2

What was the price of each dozen of bagels?
A.
$6.99
B.
$7.99
C.
$9.04
D.
$3.79

Answers

Answer 1

Answer:

the answer to the question is B

Step-by-step explanation:

no need for explanation just trust the source


Related Questions

Can anyone help me with this question please?

Answers

‍‍‍Answer : -0.65

:)

5) A $40 shirt now selling for $28 is discounted by what percent?
A. 20%
B. 30%
C. 40%
D. 60%

Answers

B. 30%
The shirt is now 30% off
B is the answer trust me Bro

Choose which of these polynomials is a difference of squares?

x^2 -12x -36
x^2+ 12x + 36
x^2 - 36
x^2 + 36

Then factor the polynomial that is a difference of squares.

Your answer should include a polynomial from the above options and its factored form

Answers

The pοlynοmial that is a difference οf squares is: x² - 36 factοred as: (x + 6)(x - 6)

What is Pοlynοmial?

A pοlynοmial is a mathematical expressiοn that cοnsists οf οne οr mοre terms, where each term is a prοduct οf a cοefficient and οne οr mοre variables raised tο nοn-negative integer pοwers. Pοlynοmials can be used tο mοdel variοus real-wοrld phenοmena and are fundamental tο many areas οf mathematics and science.

The pοlynοmial that is a difference οf squares is: x² - 36

This pοlynοmial can be factοred as: (x + 6)(x - 6)

Tο see why this wοrks, we can write x² - 36 as (x)² - (6)², which is a difference οf squares. Then, we can use the fοrmula fοr the difference οf squares, which states that a² - b² = (a + b)(a - b), tο factοr x² - 36 as (x + 6)(x - 6).

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David, a psychologist, believes that owning a pet can make a difference in stress levels. Thus, he wants to investigate whether individuals who own a pet dog differ significantly from non-dog-owners in terms of their stress levels. Two groups of American individuals were studied and the score of each individual was recorded on the David Stress Scale (scores were out of 50). Higher scores represent higher levels of stress. Using the following data in the table below, compute the appropriate analysis. Set alpha = .01.

Answers

There is a significant difference in stress levels between dog owners and non-dog owners.

Define statistics

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves techniques for designing experiments, surveys, and observational studies to gather data, as well as methods for summarizing, visualizing, and drawing conclusions from the data.

Step 1: State the null and alternative hypotheses:

Null hypothesis: There is no significant difference in stress levels between dog owners and non-dog owners.

Alternative hypothesis: There is a significant difference in stress levels between dog owners and non-dog owners.

Step 2: Determine the level of significance (alpha) and the degrees of freedom :

Alpha = 0.01 (given in the problem)

Degrees of freedom = n₁ + n₂ - 2, where n1 and n2 are the sample sizes of the two groups.

n₁ = 20 (from the table)

n₂ = 15 (from the table)

Degrees of freedom = 20 + 15 - 2 = 33

Step 3: Calculate the sample means and standard deviations:

For dog owners:

Sample mean (x₁) = 28.25

Sample standard deviation (s₁) = 9.24

For non-dog owners:

Sample mean (x₂) = 36.20

Sample standard deviation (s₂) = 7.96

Step 4: Calculate the t-statistic:

t = (x₁ - x₂) / √[(s₁²/n₁) + (s₂²/n₂)]

t = (28.25 - 36.20) / √[(9.24²/20) + (7.96²/15)]

t = -2.75

Step 5: Determine the critical t-value:

Using a t-table with 33 degrees of freedom and a one-tailed alpha of 0.01, the critical t-value is -2.449.

Step 6: Make a decision:

Since the calculated t-value (-2.75) is less than the critical t-value (-2.449), we reject the null hypothesis.

Therefore, we can conclude that there is a significant difference in stress levels between dog owners and non-dog owners.

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Find the circumference and the area of a circle with radius 6 cm.
Use the value 3.14 for
, and do not round your answers. Be sure to include the correct units in your answers.
6 cm
Circumference:
Area:
cm
X
cm²

Answers

Answer: Circumference - 37.68

Area of the circle - 113.04

Step-by-step explanation:

We have to remember that the formula for the circumference of a circle is Pi X Diameter, and since the diameter is 2 times the radius, we would have 3.14x12, which would be 37.68. For the area, we would do Pi times R squared, meaning 6x6=36, 36x3.14=113.04. I hope you understand this.

2. Here are four equations of absolute value functions and three coordinate
pairs. Each coordinate pair represents the vertex of the graph of an
absolute value function.
Match the equation of each function with the coordinates of the vertex of its
graph. The vertex coordinates of the graph of one equation are not shown.
A p(x) = |x-9|
B q(x) = |x|+9
C r(x) = |x+9|
O t(x) = |x|-9

1 (-9, 0)
2 (9,0)
3 (0, -9)

Answers

The equation for given coordinates are A) p(x) = |x - 9| C), r(x) = |x + 9| O) ,t(x) = |x| - 9

What are coordinates ?

Coordinates are sets of numbers used to locate points on a grid or map. In mathematics, the most common type of coordinates are Cartesian coordinates, which consist of an ordered pair of numbers (x, y). The x-coordinate represents the horizontal position of the point on the x-axis, and the y-coordinate represents the vertical position of the point on the y-axis.

For example, in a two-dimensional coordinate system, the point (2, 3) has an x-coordinate of 2 and a y-coordinate of 3. This means that the point is located 2 units to the right and 3 units up from the origin, which is the point (0, 0) where the x-axis and the y-axis intersect.

According to the question :

We can determine which equation corresponds to each set of vertex coordinates by observing the general form of the equation of an absolute value function and how the vertex coordinates affect it. The general form of an absolute value function is:

f(x) = |x - h| + k

where (h, k) represents the vertex coordinates of the graph.

The vertex coordinates are (-9, 0). The value of h is -9, which means the equation involves a shift to the right by 9 units. The absolute value of x is the distance from x to 0, so when x is less than -9, the absolute value of x - (-9) will be positive, and when x is greater than -9, the absolute value of x - (-9) will be negative. Therefore, the equation with vertex coordinates (-9, 0) is:

C) r(x) = |x + 9|

The vertex coordinates are (9, 0). The value of h is 9, which means the equation involves a shift to the left by 9 units. The absolute value of x is the distance from x to 0, so when x is less than 9, the absolute value of x - 9 will be negative, and when x is greater than 9, the absolute value of x - 9 will be positive. Therefore, the equation with vertex coordinates (9, 0) is:

A) p(x) = |x - 9|

The vertex coordinates are (0, -9). The value of k is -9, which means the equation involves a vertical shift downwards by 9 units. The absolute value of x is the distance from x to 0, so the equation with vertex coordinates (0, -9) is:

O) t(x) = |x| - 9

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help pls show ur work

Answers

Using the fact that the triangles are similar, we can see that x = 5.

How to find the value of x?

We can see that the two triangles are similar, because both of them are right triangles and both have the same angle at the vertices S and P.

Then there is a constant of proportionality between all the sides, let's say that the constant of proportionality is k, then we can write two equations:

5k = 15

3k = x + 4

Solving the first equation we get:

k = 15/5 = 3

Then the second gives:

3*3 = x + 4

9 = x + 4

9 - 4 = x

5 = x

That is the value of x.

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MAX POINTS

5. Samantha measures 1.5 amps on her electric blanket. If the voltage on the circuit is 120 volts, what is the resistance in ohms, to the nearest tenth of an ohm? Use the formula R =

Answers

The resistance of the electric blanket is approximately 80 ohms.

What is Ohm's law?

Ohm's law, a fundamental tenet of physics, explains how voltage, current, and resistance interact in an electrical circuit. It claims that the voltage across two locations and the resistance between them determine the relationship between the current flowing through a conductor between those two sites.

Ohm's law is mathematically represented as:

V = IR

where the three variables are voltage (V), current (I), and resistance (R). Given the values of the other two variables, this equation may be rewritten to account for any one of the three variables.

The resistance is given as:

R = V / I

Substituting the values of voltage and current we have:

R = 120 / 1.5

R = 80 ohms

Hence, the resistance of the electric blanket is approximately 80 ohms.

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Consider the following expression.

2v+4u+7+3u

Select all of the true statements below.

7 is a constant.
2v is a factor.
4u and 3u are like terms.
2v is a term.
2v is a coefficient.
None of these are true.

Please asap need help!!

Answers

Answer:

[tex]7 \: is \: a \: constant. \\ 4u \: and \: 3u \: are \: like \: terms[/tex]

Joshua goes to a café.
Revive Café Price List
Soup & roll £3.50
Sandwich £3.90
Jacket potato £4.50
Cake £2.95
Hot drink £2.50
Cold drink £1.75
Josh wants to buy a cake and a hot drink. He has £5 to spend can he buy what he wants?






Joshua wants to buy a cake and a hot drink. He has £5 to spend
Can he buy what he wants?

Answers

The answer to your question

No

A car was purchased for $33950.00 and is expected to be worth $12950.00 in 7 years. Determine the rate at which the van depreciates in value.​

Answers

Answer:

$220,150 depreciates each year and increases in value with inflation of 7.2% per year? the useful life of the oven is considered 7 years. 10. The manager of a hotel bought...

Step-by-step explanation:

If it's wrong report the answer.........XD

A vehicle covers a distance of 43.2km in 2.4 litre petroleum. How much distance will it cover one litre petroleum?

Answers

Answer:

18 km

Step-by-step explanation:

43.2/2.4 = 18

Helping in the name of Jesus.

please help I'm tired of people who want to answer to just to steel points

Answers

Answer:

a = 7.95c = 7.4

Step-by-step explanation:

Given system of equation to us is ,

3a + 2c = 38.65

1a + 2c = 22.75

Here the given system of equation are linear equations in two variables. We can use various methods to solve them like substitution method, elimination method, etc . Here i will make use of elimination method. For that ;

Subtract both the equations , that would result to ;

3a + 2c - ( 1a + 2c ) = 38.65 - 22.75

3a + 2c - 1a - 2c = 15.9

2a = 15.9

a = 15.9/2

a = 7.95

To find out the value of c , plug in a = 7.95 in any of the two equations, as ;

a + 2c = 22.75

2c = 22.75 - 7.95

2c = 14.8

c = 14.8/2

c = 7.4

Hence the value of a is 7.95 and that of c is 7.4 .

Which is the smallest? A. -1 B. -1/2 C. -1/4 D. O​

Answers

Answer:

C. -1/4

The negative value are smaller then 0

Answer: C. -1/4

Step-by-step explanation: 0 and -1 is greater than -1/4. -1/2 is also greater than -1/4 as -1/4 goes to the left of a number line and going to the left of a number line makes the number smaller

if it's wrong, im sorry

hope this helps!!

1/2(8x+4)=6(x+2) I need help please

Answers

Answer:

x=-5

Step-by-step explanation:

(8x+4)/2=6x+12

4x+2=6x+12

-2x=10

x=-5

Answer:

x = -5

Step-by-step explanation:

Given equation:

[tex]\dfrac{1}{2}(8x+4)=6(x+2)[/tex]

Multiply both sides of the equation by 2 to eliminate the fraction on the left side:

[tex]\implies 2\cdot\dfrac{1}{2}(8x+4)=2\cdot6(x+2)[/tex]

[tex]\implies (8x+4)=12(x+2)[/tex]

[tex]\implies 8x+4=12(x+2)[/tex]

Distribute the right side of the equation:

[tex]\implies 8x+4=12\cdot x+12 \cdot 2[/tex]

[tex]\implies 8x+4=12x+24[/tex]

Switch sides:

[tex]\implies 12x+24=8x+4[/tex]

Subtract 8x from both sides of the equation:

[tex]\implies 12x+24-8x=8x+4-8x[/tex]

[tex]\implies 4x+24=4[/tex]

Subtract 24 from both sides of the equation:

[tex]\implies 4x+24-24=4-24[/tex]

[tex]\implies 4x=-20[/tex]

Divide both sides of the equation by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{-20}{4}[/tex]

[tex]\implies x=-5[/tex]

Therefore, the value of x is -5.

Given the vectors u=4i-j,and v=-3i+2j,find 2u-4v

Answers

Step-by-step explanation:

We are given the vectors:

u = 4i - j

v = -3i + 2j

To find 2u - 4v, we need to double u and subtract four times v:

2u = 2(4i - j) = 8i - 2j

4v = 4(-3i + 2j) = -12i + 8j

So, 2u - 4v = (8i - 2j) - (-12i + 8j) = 20i - 10j.

Therefore, 2u - 4v = 20i - 10j.

Which of the following comparisons are true? Select all that apply. A. 3 . 2 > 0 . 32 3 . 2 > 0 . 32 B. 4 . 7 < 4 . 70 4 . 7 < 4 . 70 C. 2 . 6 > 2 . 59 2 . 6 > 2 . 59 D. 2 . 09 = 2 . 9

Answers

Answer:

A. 3 . 2 > 0 . 32  

C. 2 . 6 > 2 . 59  

Step-by-step explanation:

YES -  A. 3 . 2 > 0 . 32  

3.2 is greater than .32

NO - B. 4 . 7 < 4 . 70  

these are the same so they are =

YES - C. 2 . 6 > 2 . 59

2.6 is greater than 2.59

NO - D. 2 . 09 = 2 . 9

these two are not equal, 2.09 < 2.9

Precalculus.

Please show all your work and answer all the questions

Answers

Using trigonometric ratio and trigonometric identities, the angle of elevation is 19.5 degrees and [tex]\cos(\arcsin(-\sqrt{2}/2)) = \frac{\sqrt{2}}{2}[/tex]

What is the angle of elevation?

To determine the angle of elevation, we will need to apply trigonometric ratio here;

Length of cable = hypothenuse = 300ft

Distance of parasailer to surface = opposite = 100 ft

Since we have the value of opposite side and hypothenuse, we can use the sine ratio;

sinθ = opposite / hypothenuse

sinθ = 100/300

sinθ = 1/3

θ = sin⁻¹(1/3)

θ = 19.5°

2. Let;

[tex]\theta = \arcsin(-\sqrt{2}/2)$. Then, $\sin\theta = -\sqrt{2}/2[/tex]

Since θ is in the fourth quadrant, cos θ is positive. To find cos θ, we can use the trigonometric identity

[tex]\sin^2\theta + \cos^2\theta = 1[/tex]

\begin{align*}

[tex]\cos^2\theta &= 1 - \sin^2\theta \\&= 1 - \left(-\frac{\sqrt{2}}{2}\right)^2 \\&= 1 - \frac{1}{2} \\&= \frac{1}{2}[/tex]

Taking the positive square root, we get:

[tex]\cos\theta = \sqrt{\frac{1}{2}} = \frac{\sqrt{2}}{2}[/tex]

Therefore,

[tex]\cos(\arcsin(-\sqrt{2}/2)) = \frac{\sqrt{2}}{2}[/tex]

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Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING...
115



A graph with a bell-shaped curve, divided into 2 regions by a vertical line. The vertical line extends from the bell curve to the x-axis, and is located on the right half, under the curve. The region on the left of this line is shaded. The x-axis below the vertical line is labeled 115.
Question content area bottom
Part 1
The area of the shaded region is enter your response here. ​(Round to four decimal places as​ needed.)

Answers

The area of the given shaded region is 0.1587 which can be calculated using the cumulative area of the normal distribution.

What is z-score?

The z-score is the number of standard deviations a data point is away from the mean. It can be calculated by subtracting the mean from the data point, and then dividing by the standard deviation.

To calculate the area of the shaded region, the z-score for the value of 115 must first be determined.

In this case, the z-score= (115 - 100)/15, or 1.

The area of the shaded region is then calculated using the cumulative area of the normal distribution.

As the area of the shaded region is the probability of a data point being greater than 115, the cumulative area of the normal distribution should be subtracted from 1 to get the area of the shaded region.

The cumulative area of the normal distribution for a z-score of 1= 0.8413,

as z-score= x - μ/σ

so the area of the shaded region

=1 - 0.8413

= 0.1587.

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Solve each quadratic equation using the method of your choice. List each root in its own box or write prime in both if you cannot factor it. Express
any non-integers as fractions.
A. 2x2-17x+8=0
B. x² - 4x-12=0

Answers

A. To solve the quadratic equation 2x² - 17x + 8 = 0, we can use the factoring method. We need to find two numbers whose product is 16 (the product of the coefficients of x² and the constant term) and whose sum is -17 (the coefficient of x). These two numbers are -1 and -16, so we can rewrite the equation as:

2x² - 17x + 8 = (2x - 1)(x - 8) = 0

Setting each factor equal to zero, we get:

2x - 1 = 0 or x - 8 = 0

Solving for x, we get:

2x = 1 or x = 8

x = 1/2 or x = 8

Therefore, the roots of the quadratic equation are x = 1/2 and x = 8.

B. To solve the quadratic equation x² - 4x - 12 = 0, we can use the factoring method. We need to find two numbers whose product is -12 (the product of the coefficients of x² and the constant term) and whose sum is -4 (the coefficient of x). These two numbers are -6 and 2, so we can rewrite the equation as:

x² - 4x - 12 = (x - 6)(x + 2) = 0

Setting each factor equal to zero, we get:

x - 6 = 0 or x + 2 = 0

Solving for x, we get:

x = 6 or x = -2

Therefore, the roots of the quadratic equation are x = 6 and x = -2.

Discriminate of 6x^2+21x=5x^2+7x

Answers

Answer:-14

Step-by-step explanation:

Answer:

Step-by-step explanation:

The roots of this discriminant x=0 or x=-14

let abcde be a pyramid, where the base abcd is a square of side length 10. the total surface area of pyramid abcde (including all five faces) is 260. let m, n, p, and q be the midpoints of $\overline{ae}$, $\overline{be}$, $\overline{ce}$, and $\overline{de}$, respectively. find the total surface area of frustum abcdmnpq.

Answers

For pyramid, ABCDE with square base ABCD, of side length 10, the total surface area of frustum ABCDMNPQ of pyramid, is equals to the 245 square units.

We have a pyramid, ABCDE, with base abcd, is a square with side length 10.

Total surface area of pyramid= 260

Let m,n,p and q are mid points of AE, BE, CE and DE, respectively. We have to determine total area of frustum ABCDMNPQ. See the above figure, we get [tex]\frac{ \bar{EM }}{\bar {EA }} = \frac{ \bar{EN }}{\bar {EB }} = \frac{ \bar{EP}}{\bar {EC }} = \frac{ \bar{EQ}}{\bar {ED }} =\frac{1}{2} [/tex] MQ

here, k = 1/2 or 1/k² = 1/4

MN = NP = PQ = MQ = k( 10 ) = 5

Now, Area of frustum, ABCDMNPQ = Area of ABMN + Area of BDMQ + Area of CDPQ + Area of BNPC + Area of square MPNQ + Area of square ABCD. There are four trapezoid and two squares.

Area of square ABCD = 10² = 100Area of square MNPQ = 5² = 25

Now, Area of ABMN + Area of BDMQ + Area of CDPQ + Area of BNPC

= ( 1 - k²) ( 260 - 100)

= 120

Total surface area of frustum ABCDMNPQ = 120 + 100 + 25 = 245. Hence, required area is 245 square units.

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Complete question:

The above figure completes the question. let ABCDE be a pyramid, where the base ABCD is a square of side length 10. the total surface area of pyramid abcde (including all five faces) is 260. let M,N,P and Q be the midpoints of $\overline{AE}$, $\overline{B}$, $\overline{CE}$, and $\overline{DE}$, respectively. find the total surface area of frustum ABCDMNPQ.

2. Apply the brute-force method to find the minimum cost Hamilton Circuit for the given graph. Start
with vertex A.
Circuit
AC,AD, AB
BA, BD, BC
I
B
8
D
Weight
26
20
20
C

Answers

The minimum cost Hamilton circuit starting with vertex A is A -> B -> D -> A, with a total cost of 48.

what is circuit?

In graph theory, a circuit is a closed path in a graph that starts and ends at the same vertex. In other words, a circuit is a sequence of vertices and edges that starts and ends at the same vertex, and every vertex in the sequence (except the first and last vertex) is visited exactly once.

In the given question,

To find the minimum cost Hamilton Circuit using the brute-force method, we need to try all possible Hamilton circuits and choose the one with the minimum cost. Since there are only 3 vertices in this graph, there are only 3! = 6 possible Hamilton circuits. We can enumerate all of them and calculate their costs to find the minimum.

Here are the 6 possible Hamilton circuits, starting with vertex A:

A -> B -> C -> A

Total cost = 26 + 20 + 20 = 66

A -> C -> B -> A

Total cost = 20 + 8 + 26 = 54

A -> B -> D -> A

Total cost = 20 + 8 + 20 = 48

A -> D -> B -> A

Total cost = 20 + 26 + 8 = 54

A -> C -> D -> A

Total cost = 8 + 20 + 26 = 54

A -> D -> C -> A

Total cost = 26 + 20 + 8 = 54

Therefore, the minimum cost Hamilton circuit starting with vertex A is A -> B -> D -> A, with a total cost of 48.

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Sudhanshu divides a circular disc of radius 7 cm into two equal parts. What is the perimeter of each semicircular piece? (show working too)

Answers

Given that radius (r) = 7 cm.

We know that the circumference of the circle = [tex]2\pi r[/tex]

So, the circumference of the semicircle = [tex]\frac{1}{2} \times2\pi r=\pi r[/tex]

[tex]=\dfrac{22}{7} \times7 \ \text{cm}[/tex]

[tex]=22 \ \text{cm}[/tex]

So, the diameter of the circle = [tex]2r=2\times7 \ \text{cm}=14 \ \text{cm}[/tex]

Thus, the perimeter of each semicircular dis = [tex]22 \ \text{cm}+14 \ \text{cm}=36 \ \text{cm}[/tex].

Mr. and Mrs. Hawell want to file their income tax return together. Which filing status should they use?

Answers

On solving the provided question we can say that Mr. and Mrs. Hawell, unitary assuming they are lawfully married and living together, have two alternatives for submitting their federal income tax return.

what is income tax return

An income tax return is a document or form filed by an individual or a business with the tax authorities, such as the Internal Revenue Service (IRS) in the United States or the HM Revenue and Customs (HMRC) in the United Kingdom.

to report their income, expenses, and other relevant financial information for the purpose of calculating and paying their income taxes.

The income tax return typically includes information such as the taxpayer's income from various sources, deductions, and credits that they may be eligible for, and the amount of taxes owed or overpaid.

Filing an income tax return is generally required by law, and failure to do so can result in penalties or legal consequences.

Mr. and Mrs. Hawell, assuming they are lawfully married and living together, have two alternatives for submitting their federal income tax return:

In general, most married couples file jointly since it results in reduced taxes and greater tax advantages. Yet, there may be times when filing separately is preferable, such as when one spouse has large medical costs or there are issues about the veracity of the other spouse's tax record.

Therefore, To identify the optimal filing status for a certain scenario, it is always preferable to speak with a tax specialist.

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100 POINTS!!!!!!
HELP ASAP

Answers

Answer: 36 cm^2

Step-by-step explanation:

The right part of this shape is a triangle so we just need to find the area of a triangle and the area of the rectangle and add them to get the total area.

Area of a triangle:

We know the height is 4. The base will be 10 - 8 = 2 since the 10 includes the 8cm which need to be subtracted.

A = b*h/2

= 4*2/2

= 4 cm^2

Area of rectangle:

The height is 4 and the base is 8.

A = b*h

= 4*8

= 32 cm^2

Now we add them to get the total area

A = 4 + 32

A = 36 cm^2

Least common factor multiple of 15 and 6 ? Pls need ASAP

Answers

Answer: 30

Step-by-step explanation: 15x2=30 6x5=30 so: the least common multiple is:30

know the meaning of least multiple

HELP ASAP Aaron is the manager for the Mathland Middle School math team. They are trying to put the events in order of likeliness of the event occurring.

Which event is UNLIKELY?

P(honor roll) = 100%
P(left-handed) = 33%
P(failing math) = 0%
P(taking Spanish) = 60%

P(honor roll)

P(failing math)

P(taking Spanish)

P(left-handed)

Answers

Therefore , the solution of the given problem of probability comes out to be , the occurrence that is UNLIKELY is P (failing math).

What precisely is probability?

Each of the procedure's criteria-based methods have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from zero to one, where 0 typically represents percentage and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

From most likely to least likely, the following occurrences are most likely to occur:

=> P(Honor score) = 100% Spanish class = 60%

=> P(left-handedness) = 33% P(math failure) = 0%

Because there is no chance of it happening, the occurrence that is UNLIKELY is P (failing math).

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find sin^2a-cos^2a, where cosa+Sina=1/2, 0<a<2π​

Answers

Answer:

We know that:

sin^2a + cos^2a = 1 (1)

Also, we have:

cos a + sin a = 1/2

Squaring both sides of the above equation, we get:

cos^2a + 2cos a sin a + sin^2a = 1/4

Using equation (1), we can simplify this to:

1 + 2cos a sin a = 1/4

Subtracting 1 from both sides, we get:

2cos a sin a = -3/4

Squaring both sides, we get:

4cos^2a sin^2a = 9/16

Using the identity:

sin^2a = 1 - cos^2a

We can rewrite the above equation as:

4cos^2a (1 - cos^2a) = 9/16

Expanding and rearranging, we get:

4cos^4a - 4cos^2a + 9/16 = 0

Multiplying both sides by 16, we get:

64cos^4a - 64cos^2a + 9 = 0

Letting x = cos^2a, we can rewrite this as a quadratic equation:

64x^2 - 64x + 9 = 0

Solving for x using the quadratic formula, we get:

x = (64 ± √16384)/128

x = 1/2 or x = 9/64

Since 0 < a < 2π, we know that cos a is positive, so we can take the positive square root:

cos a = √(1/2) = 1/√2

Substituting this into the equation sin a + cos a = 1/2, we get:

sin a = 1/2 - cos a = 1/2 - 1/√2 = (√2 - 1)/2

Therefore:

sin^2a - cos^2a = ((√2 - 1)/2)^2 - (1/√2)^2

= (3 - 2√2)/4

Therefore, sin^2a - cos^2a = (3 - 2√2)/4.

Find the maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x+y+z=1.

Answers

The maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x+y+z=1, is equals to the 1/27.

Volume of something is defined as the amount of space it takes up inside. When we measure inside of something then we measure volume. We have, a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x + y + z = 1 --(1)

First from the above equation, z = 1 -x- y.

The volume of the box is, V = xyz --(2)

Plug the value of z from equation (2),

=> V = xy(1 − x − y)

=> V = xy - x²y - xy²

Now, we determine the partial derivatives to determine the critical points, Vₓ = y − 2xy − y² , Vᵧ = x - x² - 2xy

For maxima and minima we equate the partial derivatives equal to zero, Vₓ = 0 and Vᵧ = 0

=> y − 2xy − y² = 0

=> y² + y( 2x - 1) = 0

=> 2x + y = 1 --(3)

Also, x - x² - 2xy = 0

=> x( 1 - x - 2y ) = 0

=> x + 2y = 1 --(4)

Solving equations (3) and (4), x = 1/3 and y = 1/3.

So, from equation (1), z = 1 - 1/3 - 1/3 = 1/3. Therefore, volume of box is V

= (1/3)(1/3)(1/3)

= 1/27

Hence, required volume is 1/27 cubic units.

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