Alexa is trying to pick out an outfit for the first day of school. She can choose from 8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Alexa have to choose from?

Answer: a=8 b=-4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

d ≈ 5.4

Step-by-step explanation:

calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (4, 7 )

d = \(\sqrt{(4-2)^2+(7-2)^2}\)

   = \(\sqrt{2^2+5^2}\)

  = \(\sqrt{4+25}\)

  = \(\sqrt{29}\)

 ≈ 5.4 ( to the nearest tenth )

Answer:

1.1.1. The common difference is 12

1.1.2. The first term is 30

Step-by-step explanation:

1.1.1. The given quadratic pattern is presented as follows;

The 2nd term = 1

The 3rd term = -16

The 5th term = -14

Let 'd' represent the second difference, we have;

1 + 2d + a =  -16

2·d + a = -16 - 1 = -17

2·d + a = -17...(1)

-16 + 3d + a + 4d + a = -14

7·d + 2·a = -14 + 16 = 2

7·d + 2·a = 2...(2)

Making 'a' the subject of both equation (1) and (2) gives;

a = -17 - 2·d

a = 1 - 7/2·d

∴ -17 - 2·d = 1 - 7/2·d

(7/2)·d - 2·d = 1 + 17

(3/2)·d = 18

d = (2/3) × 18 = 12

The common difference, d = 12

a = -17 - 2·d = -17 - 2 × 12 = -41

1.1.2. Let 'x' represent the first term, we have;

x + a + d = 1

x = 1 - (a + d)

x = 1 - (-41 + 12) = 30

The first term, x = 30

Answer:

∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°

Step-by-step explanation:

l II m and p is their transversal and 1 = 120°

∠1 + ∠2 = 180 °(Straight line)

120° + ∠2 = 180° > ∠2 = 180° - 120° = 60°

∠2 = 60°

But ∠1 = ∠3 (Vertically opposite angles)

∠3 = ∠1 = 120°

Similarly ∠4 = ∠2

(Vertically opposite angles)

∠4 = 60°

∠5 = ∠1 (Corresponding angles)

∠5 = 120°

Similarly ∠6 = ∠2 (Corresponding angles)

∠6 = 60°

∠7 = ∠5 (Vertically opposite angles)

∠7 = 120°

And ∠8 = ∠6 (Vertically opposite angles)

∠8 = 60°

Hence ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°

The vector-valued function at each given value of t  is :

a) i

b)  1/√2i+9/√2j

c)−cos(θ)i+9sin(θ)j

d)  −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

The given problem is related to trigonometric Ratios of Angle, where there are six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Since it is given that a  vector valued function:

r(t)= cos(t)i + 9 sin(t)j

r(t)=cos(t)i+9sin(t)j

so ,  r(0)=  cos(0)i+9sin(0)j = i ( sine cos0 =1 and sin0 =0)

r(π/4) =  cos(0)i+4sin(0)j = cos(π/4)i+9sin(π/4)j

           = 1/√2i+9/√2j

r(θ−π)= cos(θ−π)i+9sin(θ−π)j= −cos(θ)i+9sin(θ)j

(π/6+△t)−r(π/6)= cos(π/6+△t)i+9sin(π/6+△t)j−cos(π/6)i−9sin(π/6)j

=  cos(π/6+△t)i−cos(π/6)i+9sin(π/6+△t)j−9sin(π/6)j

= −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

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Evaluate (If possible) the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.)

r(t)=cos(t)i+9sin(t)jr(t)

a)r(0)=?

b)r(π/4)=?

c)r(θ−π)=?

d)r(π/6+△t)−r(π/6)=?

Answer:

Step-by-step explanation:

\(\frac{3x^3}{12x^{-2}} = \frac{x^5}{4}\)

Tyna's mistake was that , she miswrote x^-2 as x^2

The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.

In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.

To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.

In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.

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Based on a survey of 400 non-fatal accidents, where 173 involved faulty equipment, the point estimate for the population proportion (p) of accidents that involved faulty equipment is 173/400 = 0.4325.

To calculate the point estimate for the population proportion, we divide the number of accidents involving faulty equipment (173) by the total number of accidents surveyed (400).

This gives us a ratio of 0.4325, which represents the estimated proportion of accidents involving faulty equipment in the population.

A point estimate is a single value that serves as an approximation or best guess for an unknown population parameter.

In this case, the population proportion (p) represents the proportion of all accidents that involved faulty equipment. The point estimate of 0.4325 suggests that approximately 43.25% of non-fatal accidents may involve faulty equipment based on the sample data.

It's important to note that this point estimate is subject to sampling variability and may not perfectly reflect the true population proportion. To obtain a more precise estimate with a measure of uncertainty, one would need to consider confidence intervals or conduct hypothesis testing using statistical methods.

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Answer:

\((x+1)^2+(y-2)^2=49\)

Step-by-step explanation:

The standard form for the equation of a circle is \((x-h)^2+(y-k)^2=r^2\) where  r  is the radius, and the center is (h, k).

(h, k) = (-1, 2),  r = 7

\((x-(-1))^2+(y-2)^2=7^2\\\\(x+1)^2+(y-2)^2=49\)

Answer:

See below

Step-by-step explanation:

y-0=2/3(x-6)         (expand L side)

What is the equation in slope-intercept form?

y = 2/3 x - 4

In order to determine the value of the missing length b, use the Pithagorean theorem, given by:

h² = a² + b²

where:

h = 6.5 mm

a = 2.5 mm

solve the previous equation for b, as follow:

b = √(h² - a²)

b = √(6.5² - 2.5²)mm

b = √36 mm

b = 6 mm

Hence, the value of the missing length is 6 mm

Answer:

-10y

Step-by-step explanation:

=5x-5y-5y-5x

=5x-5x-5y-5y

=-10y

\(\huge\boxed{\mathrm{\underline{\boxed{Hi\:there, \:hope\:you\:are\:having\:a\:great\:day.}}}}\)5(x-y)-5(y+x)

Let's use the Distributive Property to help us solve.

5(x-y)-5(y+x)

5x-5y-5y-5x

Now, all we have to do is combine like terms.

=>5x-5x-5y-5y

=>-10y

\(\large\boxed{\boxed{Hope\:this\:helps\:you! \:Please\:press\:the\:crown\:button.}}\)

\(\huge\mathrm{\underline{\underline{Please\:comment\:if\:you\:have\:any\:questions.}}}\)

\(\huge\mathfrak{{LoveLastsAllEternity}}\)

Answer:

i think you have to figure out if the lines are parallel

Step-by-step explanation:

Step-by-step explanation:

I'm going to explain this in standard slope intercept form (y=mx+b) because it is easiest for this situation. I will also include converting it to point slope form. I will also show how to do straight into point slope form if you find that more helpful.

First thing is to identify difference in x and y in both points. From point 1 to point to, the x changes -4 and the y changes +4. We can rapresent this in rise over run fraction

\( \frac{4}{ - 4} = - 1\)

So the slope is -1 because the slope is the simplified rise over run fraction.

Our next step is to find the y-intercept. This is easy because the first point is the y-intercept, so -3 is our y-intercept.

Now we know the equation.

\(y = - x - 3\)

All we have to do now is convert it into point-slope form. So here is point slope form: y + y1 = m(x + x1). Y1 is the y-intercept and m is the slope.

\(y - 3 = - 1(x + x1)\)

So x1 is the x intercept, so to find this you find the x value when y is 0. You can do this by using the standard form I've done because it is easiest.

\(0 = - x - 3 \\ x = - 3\)

So when y is 0, then x is -3. Here is the complete point slope form of the line.

\(y - 3 = - 1(x - 3)\)

-----------------------------------------------------

To put the line directly into point slope for you need to find the slope, y-intercept, and x-intercept and place the values in accordingly. If you aren't given the y-intercept and x-intercept straight away it can be difficult for some putting it directly in point slope form. That is why I recommend putting it into standard form then point-slope form.

Answer:

y=-1x-3

Step-by-step explanation:

First, you have to find the slope using the formula I attached. Using this formula, you will subtract the second y from the first y, which is 1-(-3) for this problem. That equals 4, so that will be the numerator of the slope. Next, you have to subtract the second x from the first x, which is -4-0 for this problem. That equals -4, so that will be the denominator for this slope. the fraction now is \(\frac{4}{-4}\), which is -1. The slope is -1. The current equation looks like this: y=-1x+b. Now we can solve for b, or the y-intercept. To do this, you have to use the x and y of one of the coordinates, it doesn't matter which one, the answer will be the same. Use the first one, for example. The x is 0 and the y is -3, so the our equation to find b is -3=-1(0)+b, which is -3=0+b, which is -3=b, or b=-3. So now we know what b is. Now we have to two components we need to write the equation, the slope (-1) and the y-intercept (-3). Now we can write the equation. y=-1x+(-3), or y=-1x-3.

Answer: 120

Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question

25 x 4.8 = 120

Answer: .10d+.25q=17.50

d+q=90

10d+10q=900

Answer:

|x - y| > 24

Step-by-step explanation:

The difference btwn 2 villages is over 24km Write this as an algebraic statement

To solve :

Let us represent the two villages with an alphabet :

Let:

Village 1 = x

Village 2 = y

The difference between the two villages : |Village 1 - Village |, that is x - y

The difference is more than 24 km, that is > 24

Hence,

Algebraically,

|x - y| > 24

Answer: Y=-5

Step-by-step explanation:

The reason is because if you look down the y axis from the origin you can see the location where the line crosses over the y axis in this case it was at (0,-5)

win / total = 6 /9

For 15 games:

x / 15

Where x is the number of wins in 15 games.

Cross multiply:

Divide both sides by 9

They will win 10 games.

Answer:

3.65

rounded to the nearest hundredth

Answer:

3.65

Step-by-step explanation:

5 rounds up. That makes the 4 in the hundredth place a 5 because of the rounding.

By using the concept of probability, it can be calculated that

a) State space S(x) = {-1, 0, 1, 2}

b) The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X  = -0.5

d) the stake of the gambler in  order to make this a fair game is $0.5

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

a) Let a number n be chosen between 1 and 6

Three fair six sided dice are thrown

The following cases can occur

1) Number n occur on none of the three dice

2) Number n occur on one dice

3) Number n occur on two dice

4) Number n occur on three dice

Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)

1) X = 0  -1 = -1

2) X = 1 - 1 = 0

3) X = 2 - 1 = 1

4) X = 3 - 1 = 2

State space S(x) = {-1, 0, 1, 2}

b) P(X = -1) = \({3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}\)

    P(X = 0) = \({3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}\)

    P(X = 1) = \({3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}\)

    P(X = 2) = \({3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}\)

    The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X = \(-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}\)

                                      = \(\frac{-125 + 0 + 15 +2}{216}\\\)

                                      = \(-\frac{108}{125}\)

                                      = -0.5

d) The gambler looses $0.5 on a average

   So this is not a fair game

   Let the stake of the gambler in  order to make this a fair game be t

   By the problem,

   -0.5 + t = 0

     t = 0 + 0.5

     t = $0.5

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Answer:

60 students don't have dogs

Step-by-step explanation:

Given data

number of students survayed= 40 students

40% of students have dogs

We can further find the number of students who have and don't have dogs

40/100*x= 40

0.4*x=40

x=40/0.4

x= 100 students

This means 60 students dont's have dogs

The demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

The demand function is the function

\(Q=a-bP\)

Here, Q is linear demand curve, a factor which influence the demand, b is slope and P is price.

A concert-promoting company has been selling an average of 175 T-shirts at performances for $23 each. Thus, the total selling price is,

\(P=175\times23\\P=4025\)

The company estimates that for each dollar that the price is lowered, an additional 25 shirts will be sold.  Thus, the total number of

\(23=175-25b\\23-175=-25b\\b=\dfrac{152}{25}\\b=6.08\)

Put the values in, the function for X number of shirt and y price,

\(y=175-6.08x\)

Hence, the demand function for the shirts of a concert-promoting company which has been selling an average of 175 T-shirts at performances for $23 each is y=175-6.08x.

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The function f(theta) is:

f(theta) = sin(theta) + cos(theta) + 3

To find the function f, we will integrate the given second derivative with respect to theta twice, and use the initial conditions to determine the constants of integration.

First, integrating f ''(theta) = sin(theta) + cos(theta) with respect to theta gives:

f '(theta) = -cos(theta) + sin(theta) + C1

where C1 is a constant of integration.

Next, integrating f '(theta) = -cos(theta) + sin(theta) + C1 with respect to theta gives:

f(theta) = sin(theta) + cos(theta) + C1*theta + C2

where C2 is another constant of integration.

To determine the values of C1 and C2, we use the initial conditions:

f(0) = 4 gives us:

4 = sin(0) + cos(0) + C1*0 + C2

4 = 1 + C2

so C2 = 3.

f '(0) = 1 gives us:

1 = -cos(0) + sin(0) + C1

1 = 1 + C1

so C1 = 0.

Therefore, the function f(theta) is:

f(theta) = sin(theta) + cos(theta) + 3

Note that there are other ways to express this function, such as using trigonometric identities to simplify the expression, but this is the most general form.

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A fingernail is a flat horn-like modification of the epidermis that serves to protect the dorsal surface of the tip of the finger or toe.

Fingernails are hard, flat structures made up of a protein called keratin. They are an essential part of our fingers and toes and serve various functions. One of their primary roles is to provide protection to the delicate tissues and nerve endings present at the tips of our fingers and toes.

The fingernail is formed by specialized cells in the nail matrix, which is located at the base of the nail underneath the cuticle. As new cells are produced, they push older cells forward, causing the nail to grow. The visible part of the nail that extends beyond the fingertip is called the nail plate.

The nail plate is composed of several layers of hardened keratinized cells that are tightly packed together. It appears translucent and has a slightly pinkish hue due to the blood vessels beneath it. The nail plate is firmly attached to the nail bed, which is the skin beneath the nail.

Fingernails play a crucial role in protecting the sensitive fingertips. They act as a shield, reducing the direct impact on the fingertips and preventing injuries from accidental bumps or knocks. They also act as a barrier, protecting the underlying tissues from external factors such as chemicals, dirt, and microorganisms.

Additionally, fingernails aid in enhancing the sensitivity of our fingertips. The presence of nails allows us to have a finer sense of touch and better manipulate objects with precision. They assist in activities like gripping, picking up small objects, and performing intricate tasks.

Nail care is important to maintain healthy and strong nails. Regular trimming, filing, and cleaning help prevent nails from becoming too long or prone to breakage. Proper hygiene, including keeping nails clean and dry, reduces the risk of infections. Additionally, maintaining a balanced diet rich in vitamins and minerals contributes to the overall health and strength of the nails.

In summary, fingernails are flat, horn-like structures that protect the tips of our fingers and toes. They serve as a shield, enhance sensitivity, and contribute to the overall functionality of our hands and feet. Taking care of our nails is essential for their health and to ensure their proper functioning.

Therefore, "A fingernail is a flat horn-like modification of the epidermis that serves to protect the dorsal surface of the tip of the finger or toe."

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