A rectangle has a perimeter equal to 24 if we consider its width x how could we talk about its length y in terms of x what are the possible values of x what aree the possible values of y

Answer:

p = [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Probability that you make the hockey team only: 2/3 * (1-3/4) = 1/6

Probability that you make the swimming team only: 3/4 * (1-2/3) = 1/4

Probability that you make the both team: 1/2

the probability that you at least make one of the teams: 1/6 + 1/4 + 1/2 = 11/12

9514 1404 393

Answer:

Step-by-step explanation:

From the law of cosines, you can find the length of side b to be ...

  b = √(a² +c² -2ac·cos(B))

  b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36

  b ≈ 757.7

__

From the law of sines, you can find the measure of angle C to be ...

  C = arcsin(c/b·sin(B))

  C ≈ arcsin(358/757.7·sin(148.5°)) ≈ arcsin(0.246872)

  C ≈ 14.3°

  A = 180° -148.5° -14.3°

  A = 17.2°

_____

Some graphing calculators have built-in triangle-solving functions. Apps are available for the purpose for phone or tablet. The screenshot shows a web site that does a nice job of solving the triangle.

Answer:

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

Step-by-step explanation:

An automobile manufacturer has given its jeep a 51.3 miles/gallon (MPG) rating.

At the null hypothesis, we test if the mean is of 51.3, that is:

[tex]H_0: \mu = 51.3[/tex]

An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating.

This means that at the alternative hypothesis, we test if the mean is different of 51.3, that is:

[tex]H_0: \mu \neq 51.3[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

51.3 is tested at the null hypothesis:

This means that [tex]\mu = 51.3[/tex]

After testing 230 jeeps, they found a mean MPG of 51.1. Assume the population variance is known to be 6.25.

This means that [tex]n = 230, X = 51.1, \sigma = \sqrt{6.25} = 2.5[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{51.1 - 51.3}{\frac{2.5}{\sqrt{230}}}[/tex]

[tex]z = -1.21[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 51.1 by at least 0.2, which is P(|z| > 1.21), which is 2 multiplied by the p-value of z = -1.21.

Looking at the z-table, z = -1.21 has a p-value of 0.1131.

2*0.1131 = 0.2262

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

The pillars and the pyramids in the stadium gate means that we have to calculate the area of the items that make up the gate one after the other. At the end of the calculation, the calculated areas are then added up.

The total cost of painting is Rs.21344

First, we calculate the area of 1 side of 1 pillar using:

[tex]A = Height * Base[/tex]

Where

[tex]Height = 10ft[/tex] --- Height of the pillar

[tex]Base = 3ft[/tex] --- Base of the pillar

So:

[tex]A = 10ft * 3ft[/tex]

[tex]A = 30ft^2[/tex]

The area of the 4 sides of the pillar is:

[tex]A_2 = 4 * A[/tex] --- i.e. 4 multiplied by the area of 1 side

[tex]A_2 = 4 * 30ft^2[/tex]

[tex]A_2 = 120ft^2[/tex]

The area of the 2 pillars is:

[tex]Area_1 = 2 * A_2[/tex] --- i.e. 2 multiplied by the area of 1

[tex]Area_1 = 2 * 120ft^2[/tex]

[tex]Area_1 = 240ft^2[/tex]

Because one part of the pyramid won't be visible, we calculate the area of the pyramid using:

[tex]Area = lw + l\sqrt{(w/2)^2 + h^2} + w\sqrt{(l/2)^2 + h^2}[/tex]

Where:

[tex]h = 2[/tex] -- the height

[tex]l = w = 3[/tex] --- the base of the pillar is the length & width of the pyramid.

So, we have:

[tex]Area = 3\sqrt{(2/2)^2 + 2^2} + 3\sqrt{(2/2)^2 + 2^2}[/tex]

[tex]Area = 3\sqrt{1 + 4} + 3\sqrt{1 + 4}[/tex]

[tex]Area = 3\sqrt{5} + 3\sqrt{5}[/tex]

[tex]Area = 6\sqrt{5}[/tex]

For the two pyramids, the area is:

[tex]Area_2 = 2 * 6\sqrt 5[/tex] -- 2 multiplied by area of 1

[tex]Area_2 = 12\sqrt 5[/tex]

[tex]Area_2 = 26.8[/tex]

So, the total area to be painted is:

[tex]Total = Area_1 + Area_2[/tex] --- the sum of the area of the pillars and the pyramids

[tex]Total = 240+26.8[/tex]

[tex]Total = 266.8ft^2[/tex]

The unit cost of paint is:

Rate = Rs80 per sq.ft

The total cost of painting is:

[tex]Cost = 80 * 266.8[/tex]

[tex]Cost = Rs.21344[/tex]

Hence, the total cost of painting is Rs.21344.

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Answer:

The answer is a.

Step-by-step explanation:

Answer is in attached image...

hope it helps

Answer:

its a

Step-by-step explanation:

just did it

Answer:

24.8 units

Step-by-step explanation:

Given

[tex]n = 10[/tex] --- sides

The attached decagon

Required

The perimeter

The decagon is made up of 10 isosceles triangles.

The angle at the vertex of each is:

[tex]Angle = \frac{360}{10}[/tex]

[tex]Angle = 36[/tex]

Next, we create a right-angled triangle from the shape (see attachment)

[tex]\theta[/tex] is calculated as:

[tex]\theta = \frac{Angle}{2}[/tex]

[tex]\theta = \frac{36}{2}[/tex]

[tex]\theta = 18[/tex]

Next, calculate x using:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

So, we have:

[tex]\sin(18) = \frac{x}{4}[/tex]

Make x the subject

[tex]x = 4 * \sin(18)[/tex]

[tex]x = 1.24[/tex]

So, the length (L) of one side of the decagon is:

[tex]L = 2x[/tex]

[tex]L = 2 * 1.24[/tex]

[tex]L = 2.48[/tex]

The perimeter (P) of the shape is:

[tex]P = 10 *L[/tex]

[tex]P = 10 * 2.48[/tex]

[tex]P = 24.8[/tex]

The perimeter of the given polygon rounded to the nearest tenth is; 24.7

The given polygon as we can see has 10 sides.

Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.

Thus, the other two angles will be; (180 - 36)/2 = 72° each

Using sine rule, we can find the length of a side of the polygon as;

x/sin 36 = 4/sin 72

x = (4 * sin 36)/sin 72

x = 2.472

Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7

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X <0 means x would be negative.

For x/y, a negative divided by a positive would give a negative answer.

A negative multiplied by a positive would result in a negative.

The answer would be B. Negative

Answer:

c 112⁰

Step-by-step explanation:

cuz the triangle is the same and x is on a straight line so get 180 - 68 = 112

Answer:

the angle opposite to x is 61 degree (being alternate angle)

so

x+ 61 = 180(being linear pair)

or, x = 180 - 61

so, x = 119

the answer is 119(d).

Answer:

21

Step-by-step explanation:

Answer:

x = 12.15 oz

Step-by-step explanation:

z = 1.8808

 1.8808 = (x - 12)/.08

Answer:

Correct answer is 4 because the last 2 terms can be combined:

Step-by-step explanation:

4x3 + 9y2 – 3x + 2 – 1 = 4x3 – 3x + 9y2 + 1.

Answer:

Each chocolate truffle is $2.125

Step-by-step explanation:

Honestly, I'm not 100% sure if this is correct, and I am truly sorry if this is wrong, but its worth a try :)

Answer:

x=12,y=3

Step-by-step explanation:

x/6-y/3=1

x can equal 12 because 12/6 is equal to 2.

y can equal 3 because 3/3 equals 1

2-1=1

9514 1404 393

Answer:

Step-by-step explanation:

Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...

  preimage point ⇒ reflection over x ⇒ reflection over y

A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)

B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)

C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)

D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)

Answer:

1/8=12.50%

Step-by-step explanation:

Take the pizza as a whole = 100

Then consider 1/8 of 100

or   1/8 * 100  

= 1/4 * 50

=   1/2 * 25

= 12.50

Therefore it is 12.50%

Answer:

Because it's a negative.

Step-by-step explanation:

The value of a positive number is still a positive number.

let the number be x

ATQ

[tex]\\ \sf\longmapsto 5x+2x+2=16[/tex]

[tex]\\ \sf\longmapsto (5+2)x+2=16[/tex]

[tex]\\ \sf\longmapsto 7x+2=16[/tex]

[tex]\\ \sf\longmapsto 7x=16-2[/tex]

[tex]\\ \sf\longmapsto 7x=14[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{14}{7}[/tex]

[tex]\\ \sf\longmapsto x=2[/tex]

Answer:

The number is

2

Explanation:

Let

n

represent the number.

Translating the given statement into algebraic notation, we have

XXX

5

n

+

2

n

+

2

=

16

Therefore

XXX

7

n

+

2

=

16

XXX

7

n

=

14

XXX

n

=

2

answered by: Alan P.

Answer:

cos C = 12/13

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

Cos theta = adj/ hyp

cos C = 36/39

Dividing the top and bottom by 3

cos C = 12/13

CosØ=Base/Hypotenuse

It's divergent because 1/√(5 - x) is defined only for x < 5, which means the integral from 5 to infinity doesn't exist.

9514 1404 393

Answer:

  B

Step-by-step explanation:

To find the inverse of y = f(x), solve the equation x = f(y) for y. For these functions, that's about the easiest way to do it.

  A. x = ∛(3y)   ⇒   x³ = 3y   ⇒   x³/3 = y . . . . . does not match g(x)

  B. x = 11y -4   ⇒   x +4 = 11y   ⇒   (x +4)/11 = y . . . . matches g(x)

  C. x = 3/y -10   ⇒   x +10 = 3/y   ⇒   3/(x+10) = y . . . . does not match g(x)

  D. x = y/12 +15   ⇒   x -15 = y/12   ⇒   12(x -15) = y . . . . does not match g(x)

_____

Additional comment

This is repeated application of the "solve for ..." process. In general, that process "undoes" what is "done" to the variable. The order of operations can tell you the order of the things that are done. The undoing is in the reverse order.

You need to be completely comfortable with the properties of equality (addition, subtraction, multiplication, division), and you need to understand the inverse functions of the functions we usually use: (powers, roots), (exponentials, logarithms), (trig functions, inverse trig functions). Of course, the inverse of addition is subtraction; the inverse of multiplication is division.

__

Above, we used a "shortcut" a couple of times:

  a = b/c   ⇒   c = b/a . . . . . equivalent to multiplying both sides by c/a.

Answer:

10538.07

Step-by-step explanation:

find the effective semiannual rate: .06/2= .03

conver this into an effective monthly rate

[tex](1.03)^2=(1+i)^{12}\\(1.03)^{1/6}-1=i\\i=.0049386220312[/tex]

this is our montlhy effective rate. use this to calculate teh present value of 9 1200 dollars payments

[tex]1200(\frac{1-(1+.0049386220312)^{-9}}{.0049386220312})=10538.0729871[/tex]

which rounds to 10538.07

The invested amount would be $10538.52 in order to cover your expenses if you need to withdraw $1200 each month for 9 months of university.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt} \\\\\\rm A = P(1+\dfrac{r}{n})^{nt}+\dfrac{PMD((1+\dfrac{r}{n})^{nt}-1)}{\dfrac{r}{n}}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is or borrowed (in years)

It is given that:

You need to withdraw $1200 each month for 9 months of university,

The effective semiannual rate = 0.06/2 = 0.03

[tex]\rm i = (1.03)^{1/6} - 1[/tex]

i = 0.00493

The invested amount:

[tex]= 1200\dfrac{[1- (1 + 0.00493)^{-9}]}{0.00493}[/tex]

After simplification:

= $10538.52

Thus, the invested amount would be $10538.52 in order to cover your expenses if you need to withdraw $1200 each month for 9 months of university.

Learn more about the compound interest here:

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#SPJ2

Answer:

3.  3x^2 + 15x

4.  x=36

Step-by-step explanation:

The area of a rectangle is

A = l*w

A = (3x)*(x+5)

Distribute

3x^2 + 15x

2/3x - 4 = 20

Add 4 to each side

2/3x -4+4 = 20+4

2/3x = 24

Multiply each side by 3/2

2/3*3/2 =24*3/2

x = 12*3

x=36

Answer:

Less than 3.6 years.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.8 years, and  standard deviation of 1.7 years.

This means that [tex]\mu = 5.8, \sigma = 1.7[/tex]

The 10% of items with the shortest lifespan will last less than how many years?

Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 5.8}{1.7}[/tex]

[tex]X - 5.8 = -1.28*1.7[/tex]

[tex]X = 3.6[/tex]

Less than 3.6 years.

Answer:

Test Statistic = 10

Critical Value = 9.488

Step-by-step explanation:

Given :

Grade A _ B _ C _ D _ F

_____14 _ 18 _32_ 20_16

H0 : distribution of grade is uniform

H1 : Distribution of grade is not uniform

Using the Chisquare statistic :

χ² = (observed - Expected)² / Expected

The expected value :

(14+18+32+20+16) / 5 = 20

χ² = (14-20)^2 / 20 + (18-20)^2 / 20 + (32-20)^2 / 20 + (20-20)^2 / 20 + (16-20)^2 / 20

χ² statistic = 10

The χ² critical at df = (n - 1) = 5 - 1 = 4

χ² Critical(10, 4) = 9.488

Answer:

The hottest month for the northern hemisphere is August.

The hottest month for the southern hemisphere is January and February (these top two might be the opposite)

It's globally warmer during the months of June July and August

During april and november, the southern hemisphere and northern hemisphere are the same, or very close.

During July and August the southern and northern hemispheres have the largest difference in temperature

Answer:

-13 degrees celcius.

Step-by-step explanation:

6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.

35-48 is -13. The room temperature will be -13 eight hours after the process begins.

Step-by-step explanation:

Let,

[tex] \sf \vec{a} = 5 \hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{a}| = \sqrt{ {5}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{25 + 1 + 1} \\ = \sqrt{27} \\ \\ \sf \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{b}| = \sqrt{ {2}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{4 + 1 + 1} \\ = \sqrt{6} \\ \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} - \hat{j} + \hat{k}).(2\hat{i} - \hat{j} + \hat{k}) \\ = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\ = 10 + 1 + 1 \\ = 12 \\ \\ \sf \: angle \: between \: \vec{a} \: and \: \vec{b} \: = \theta \\ \\ \: so \\ \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos\theta \\ = > \sf \: cos \theta \: = \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| } \\ = > cos \theta = \frac{12}{ \sqrt{27} \times \sqrt{6} } = 0.94 \\ = > \theta = {cos}^{ - 1} (0.94) \\ = > \green{\theta = 19.47 ^{ \circ} }[/tex]

Answer:

sadia is 32

Step-by-step explanation:

sadia : father : total

3          6          9

Divide 96 by 9

96/9 = 32/3

Multiply each by 32/3

sadia :     father : total

3*32/3    6*32/3  9*32/3

32                 64          96