evaluate 21.5 multiplied by 2.51 to 2 decimal place

Answer:

(a) [tex]x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}[/tex]

(b) [tex]x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex]

Step-by-step explanation:

It is given that [tex]0\leq x\leq 2\pi[/tex].

(a)

[tex]\sqrt{2}\sin 2x=1[/tex]

[tex]\sin 2x=\dfrac{1}{\sqrt{2}}[/tex]

[tex]\sin 2x=\dfrac{\pi}{4}[/tex]

[tex]2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}[/tex]     [tex][\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny][/tex]

[tex]x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}[/tex]

(b)

[tex]\csc^2 x-\csc x-2=0[/tex]

[tex]\csc^2 x-2\csc x+\csc x-2=0[/tex]

[tex]\csc x(\csc x-2)+1(\csc x-2)=0[/tex]

[tex](\csc x+1)(\csc x-2)=0[/tex]

[tex]\csc x=-1\text{ or }\csc x=2[/tex]

[tex]\sin x=-1\text{ or }\sin x=\dfrac{1}{2}[/tex]         [tex][\because \sin x=\dfrac{1}{\csc x}][/tex]

[tex]x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex]

Therefore, [tex]x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}[/tex].

Answer:

Jamie must sprint 107 meter to pass Shelly at point A.

Step-by-step explanation:

Circumference of a sector of the circle is represented by,

Circumference = [tex]\frac{\theta}{360}(2\pi r)[/tex]

where θ = central angle subtended at the center by an arc

r = radius of the circle

[tex]m(\widehat{AB})[/tex] = [tex]\frac{123}{360}(2\pi )(50)[/tex]

           = 34.1667π

           = 107.34 meter

           ≈ 107 meter

Therefore, Jamie must sprint 107 meter to pass Shelly at point A.

Answer:

[tex]\boxed{\sf \ \ \ x=\dfrac{3}{4} \ \ \ }[/tex]

Step-by-step explanation:

hello,

f(x)=x-1

[tex]g(x)=2x^2+3[/tex]

so

[tex]fog(x)=f(g(x))=f(2x^2+3)=2x^2+3-1=2x^2+2 \ and \\gof(x)=g(f(x))=g(x-1)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5 \ \ So\\\fog(x)=gof(x) <=>2x^2+2=2x^2-4x+5\\<=>4x=5-2=3\\<=>x=\dfrac{3}{4}[/tex]

hope this helps

[tex]\frac{3}{4}[/tex]

The composition of a function is a process in which two functions [tex]f,g[/tex], are combined to produce a new function, [tex]h[/tex], with the formula [tex]h(x)=g(f(x))[/tex]. It means that the [tex]g[/tex] function is being applied to the [tex]x[/tex] function.

[tex]f(x)=x-1\\g(x)=2x^2+3[/tex]

[tex]f(g(x))=f(2x^2+3)[/tex]

            [tex]=2x^2+3-1\\=2x^2+2[/tex]

[tex]g(f(x))=g(x-1)[/tex]

           [tex]=2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5[/tex]

[tex]f(g(x))=g(f(x))[/tex]

[tex]2x^2+2=2x^2-4x+5[/tex]

       [tex]4x=3[/tex]

        [tex]x=\frac{3}{4}[/tex]

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Answer:

x = 12

Step-by-step explanation:

We can use the Cross Products Property.

9 / 12 = x / 16

12x = 9 * 16

x = 9 * 16 / 12 = 12

Answer:

x = 12

Step-by-step explanation:

→ First we work out the multiplier between 16 and 12 so,

16 ÷ 12 = 1.3 recurring

→ Multiply this multiplier by 9

9 × 1.3 recurring = 12

→ x = 12

Hey there! I'm happy to help!

We want to find how much paper we need to make the cup. So, we need to find the surface area of the cylinder, which is basically the "walls and floors" of the cup. So, this is the circle on the bottom and the surrounding stuff that goes up. There is no circular top to this cup, which will be important when finding the total area of paper.

So, first we need to find how much paper we need to make the bottom circle. The formula for the area of a circle is A=πr². This r represents the radius, or the distance from the center of the circle to the edge. We are given that the cup is 3 cm completely across, and the radius is be half of that, so the radius is 1.5 cm. Let's find the area. We will use 3.14 for π.

π×1.5²=7.065

Now, we need  to find the area of the walls of the cup. The wall is a rectangle that is basically wrapped around the circle. The height of the rectangle is the height of the cup and the length of the rectangle is the circumference (perimeter) of the bottom circle because the length of the rectangle wraps completely around the circle.

First, let's find the circumference of the circle. The circumference is the diameter (distance across the circle, so 3 cm) multiplied by π. We will use 3.14 for π.

3π=9.42

So, this means that the long side of the rectangle is 9.42 cm, and now we multiply this by the height.

9.42×6.4=60.288

Now, we add the rectangle area and the bottom circle area.

60.288+7.065=67.353

But, they want us to round to the nearest centimetre, so we will just say 67 square centimetres.

An important thing to note is that this is not  the area of a normal cylinder (one with a top and a bottom circle) because it is a cup so it does not have a top. If you have a cylinder with a top and a bottom, you would just multiply the area of the circle by two, so then you have the top and bottom. If that were the case, the area of our cylinder would be 74 cm with the numbers we have been given here.

Have a wonderful day!

Answer:

A) 1/6

Step-by-step explanation:

There are six sides on a dice and one number 3.

That means that you have a chance in one of six roles to get a 3 one time.

This may not be very clear so you can ask more questions in the comments!

Answer: C) $33

Step-by-step explanation:

1973 tax rate :

2% on the first $1000 income

3% on next $2000 or any part thereof ;

Brown's total income of $1800

2% of $1000

0.02 × $1000 = $20

3% of $800

0.03 × 800 = $24

Total tax = $(20 + 24) = $44

1/4 tax deduction:

(1/4) of total tax

(1/4) × $44

0.25 × $44

= $11

Total tax - tax deduction

$44 - $11 = $33

Tax amount = $33

Answer:

Step-by-step explanation:

We that the area of a circle is Pi times r^2 where r is the radius

Let A be the area of the first circle and S the area of the second one and T the total one

A=4^2× Pi

S=6^2× Pi

T = Pi( 4^2 +6^2)

= Pi ( 16+36) = Pi× 52

52 is the radius square

So r = root square 52 = 2 root square 13

Answer: PQT and TUV

Step-by-step explanation:

Answer: 0.0009

Step-by-step explanation:

Given : Babies born in a large hospital have a mean weight of 3366 grams, and a variance of 244,036.

i.e. [tex]\mu=3366[/tex]  and [tex]\sigma^2 = 244036\Rightarrow\ \sigma= \sqrt{244036}=494[/tex]

Sample size = 1118

Let [tex]\overline{X}[/tex] be the sample mean weight of babies.

Then, the probability that the mean weight of the sample babies would be greater than 3412 gram:

[tex]P(\overline{X}>3412)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3412-3366}{\dfrac{494}{\sqrt{1118}}})\\\\=P(Z>\dfrac{46}{14.7743})\ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\\approxP(Z>3.11)\\\\= 1-P(Z<3.11)\\\\=1-0.9991=0.0009[/tex]

Hence, the required probability = 0.0009

Answer:

Step-by-step explanation:

f(-5) = -5 + 8 = 3

g(3) = 3^3 = 27

Answer:

x= 15 and y=4

Step-by-step explanation:

Let's start by finding y first using the basic proportionality

now time to find x using the same way:

Answer:

C and E

Step-by-step explanation:

Midpoint, as the word suggests, means the point which lies in the middle of something. The statements that are correct are 1, 3, and 5.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statements which are correct about the given figure are:

Hence, the statements that are correct are 1, 3, and 5.

Learn more about Midpoint:

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Answer:

The Area of the required figure is  [tex]315\:cm^2[/tex]

Step-by-step explanation:

[tex]Area = (21\times 7)+(14\times 7) + (7\times 10)\\\\=147+98+70\\\\=315[/tex]

Best Regards!

Answer:

Step-by-step explanation:

Exponential Growth:

1). The value of a home in a growing community every year.

2). The amount of money in a saving account that earns interest annually.

Exponential decay:

1). The monthly sale of albums of a band whose popularity is declining.

2). The amount of radioactive element remaining in a sample every decade.

3). The temperature of a hot cup of coffee left on the counter every minute.

Answer: 9/15, 16/25, 3/4 and 5/6.

Step-by-step explanation:

From the question, we have been given four fractions which are 3/4, 5/6, 16/25 and 9/15. We are told to write them in order starting from the smallest. For this to be done, we will have to change the fractions to percentages. This will be:

3/4 = 3/4 × 100 = 75%

5/6 = 5/6 × 100 = 83.3%

16/25 = 16/25 × 100 = 64%

9/15 = 9/15 × 100 = 60%

From the above percentages, arranging the fractions from the smallest will be:

9/15, 16/25, 3/4 and 5/6.

Answer:

This is approximately [tex]37.7 ft^{2}[/tex] to the nearest hundredth

Step-by-step explanation:

First of all, we will need to understand that to find the lateral surface area of the cylinder, we simply need to multiply the circumference of the circular base by the height of the cylinder.

In this case, the circumference of the circular base can be obtained by the formula

[tex]2 \pi r[/tex]

Hence we will have the circumference as [tex]2 \times \pi \times \frac{2.5}{2}=7.85 feet[/tex]

Tp get the Lateral area, we will simply have to multiply this value (7.85 feet )

by the height (4.8 feet)

7.85 X 4.8 =[tex]37.68 feet ^{2}[/tex]

This is approximately [tex]37.7 ft^{2}[/tex] to the nearest hundredth

Answer:

2½ h  

Step-by-step explanation:

Assume the graph is like the one below.

The graph shows how Erin's distance varies with time.

To find out how long it takes Erin to cover 25 mi, find 25 mi on the vertical axis.

From there, draw a horizontal line until it hits the graph.

Then drop a vertical line to the horizontal axis.

It hits half-way between 2 and 3.

It takes Erin 2½ h to run 25 mi.

Answer:

2½ h

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

First you must find the circumference of the entire circle and to do this you use 2πr. The radius in this case is PX=15. This means that the circumference is 30π. Now to find the arc length, we know that the measure of arc XY is 23 degrees, and since there are 360 total degrees in a circle, we must subtract 23 from 360 to get 337° as the measure of arc XQY. Now we have to find what portion of the circumference of the circle is in this arc, and to do this you divide the arc length (337°) by 360° and multiply by the circumference of the circle. Doing this would get you [tex]\frac{337}{360} *30\pi[/tex] which equals ~28. Finally, you have to multiply this by the value of pi and get approximately 88, which is your answer.

Answer:

he proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

Step-by-step explanation:

In this case we need to determine if the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The hypothesis can be defined as follows:  

H₀: The proportion of people over 55 who dream in black and white is not greater than the proportion of those under, i.e. p₁ - p₂ ≤ 0.  

Hₐ: The proportion of people over 55 who dream in black and white is greater than the proportion of those under, i.e. p₁ - p₂ > 0.  

The information provided is:

n₁ = 290

n₂ = 288

X₁ = 68

X₂ = 19

Compute the sample proportions and total proportions as follows:

 [tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{68}{290}=0.235\\\\\hat p_{2}=\frac{X_{2}}{n_{1}}=\frac{19}{288}=0.066\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{68+19}{290+288}=0.151[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

    [tex]=\frac{0.235-0.066}{\sqrt{0.151(1-0.151)[\frac{1}{290}+\frac{1}{288}]}}\\\\=5.67[/tex]

The test statistic value is 5.67.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 [tex]p-value=P(Z>5.67)\\=1-P(Z<5.67)\\=1-\approx1\\=0[/tex]

The p-value of the test is quite small.

The null hypothesis will be rejected at 5% significance level.

Thus, the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The significance level of the test is 5%.

Then the confidence level will be:

Confidence level = 100% - Significance level

                             = 100% - 5%

                             = 95%

Compute the 95% confidence interval for the difference between proportions as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]

The critical value of z for 95% confidence level is z = 1.96.

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]

      [tex]=(0.235-0.066)\pm1.96\cdot\sqrt{\frac{0.235(1-0.235)}{290}+\frac{0.066(1-0.066)}{288}}\\\\=0.169\pm 0.057\\\\=(0.112, 0.226)[/tex]

The null hypothesis would be rejected if the null value, i.e. (p₁ - p₂) ≤ 0 is not contained in the interval.

The 95% confidence interval consist of values greater than 0.

Thus, the null hypothesis will be rejected.

Concluding that the proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

Answer:

58.43%

Step-by-step explanation:

In this case we have that the probability that they are different is the opposite of the probability that they are the same, therefore, in each case it would be:

P (plain, plain) = (12/20) (11/19)

P (p, p) = 132/380

P (chocolate, chocolate) = (5/20) (4/19) = 20/380

P (ch, ch) = 20/380

P (currant, currant)= (3/20) (2/19) = 6/380

P (c, c) = 6/380

The probability that they are equal is the sum of each:

P (equal) = 132/380 + 20/380 + 6/380

P (equal) = 0.4157

Therefore, the probability that they are different is:

P (different) = 1 - 0.4157

P (different) = 0.5843 = 58.43%

It means that the probability is 58.43%

Answer:111/190

Step-by-step explanation:

Answer:

D. No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

Step-by-step explanation:

Two figures are congruent if their vertices can be mapped into one another by appropriate rigid transformation or combination of rigid transformations. Examples of the transformation are; reflection, dilation, rotation and translation.

Comparing the two figures, it would be observed that they are not congruent. Since there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

Answer:

it is D just took the test

Step-by-step explanation:

Answer:

this is a right angled triangle

Step-by-step explanation:

It has a 90 degree angle

the hypotenuse is the longest

The other two sides adjacent to the right angle are perpendicular

It could also be called an isosceles right angled triangle

Answer:

Right angled and Isosceles

Step-by-step explanation:

Right angled because one corner of the triangle is marked with a square, which shows it is 90degrees.

Isosceles because 2 angles and 2 sides have been marked with similar lines and curves, which shows that they are equal in length. When 2 angles and 2 sides are equal, the triangle is isosceles.

Hope this helps.

Good Luck

Answer:

3) [tex]\frac{(25)^{3/2} * (243)^{3/5}}{(16)^{5/4}*(8)^{4/3}}[/tex]

=> [tex]\frac{(5^2)^{3/2}*(3^5)^{3/5}}{(2^4)^{5/4}*(2^3)^{4/3}}[/tex]

=> [tex]\frac{5^3*5^3}{2^5*2^4}[/tex]

=> [tex]\frac{5^6}{2^9}[/tex]

4) [tex]\frac{3-2\sqrt{2} }{3+2\sqrt{2} }[/tex]

Multiplying and dividing by conjugate [tex]3-2\sqrt{2}[/tex]

=> [tex]\frac{(3-2\sqrt{2})(3-2\sqrt{2}) }{(3+2\sqrt{2})(3-2\sqrt{2})}[/tex]

=> [tex]\frac{9-6\sqrt{2}-6\sqrt{2} +8 }{9-8}[/tex]

=> [tex]\frac{17-12\sqrt{2} }{1}[/tex]

=> [tex]17-12\sqrt{2}[/tex]

Comparing it with [tex]a+b\sqrt{2}[/tex], we get

a = 17, b = -12

Answer:

5/2 or 2.5

Step-by-step explanation:

6/5=3/d

6*d=3*5

d=3*5/6

d= 5/2 or 2.5

Answer:

Solution,

[tex] \frac{6}{5} = \frac{3}{d} \\ or \: 6 \times d = 5 \times 3(cross \: multiplication) \\ or \: 6d = 15 \\ or \: d = \frac{15}{6} \\ d = 2.5[/tex]

hope this helps...

Good luck..

Answer:

(12, 190). This represents that after selling 12 ice creams, I gain $190.

Step-by-step explanation:

I just found a scatter plot online. Ignore the current label on the x-axis that says TemperatureC, I just changed that to ice creams. You can change the title of the graph to whatever you want.

Answer:

b. 8

Step-by-step explanation:

To solve, we need to plug in the x and y values since we already have the values given to us

1/2(4)(2^2)

We should do the exponents first, 2^2 is 4

Now we are left with 1/2(4)(4)

4 times 4 is 16

16 times 1/2 is the same as 16/2

16/2=8

b. 8

Answer:

y = 2x + 7

Step-by-step explanation:

Step 1: Find slope

m = (9 - 3)/(1 + 2)

m = 2

y = 2x + b

Step 2: Find b

9 = 2(1) + b

9 = 2 + b

7 = b

Step 3: Rewrite equation

y = 2x + 7

Answer:

B) y - 9 = 2(x - 1)

Step-by-step explanation:

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

[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{9-3}{1-[-2]}\\\\=\frac{6}{1+2}\\\\=\frac{6}{3}\\\\=2[/tex]

(1, 9 ) ;  m = 2

Equation: [tex]y - y_{1}=m(x - x_{1})\\\\[/tex]

y - 9 = 2(x - 1)

y - 9 = 2x -2

      y = 2x - 2 + 9

      y = 2x + 7

Answer:

1, 4, 5, 7, 8

Step-by-step explanation:

once you plot the points you will see that these coordinates are inside the star

Answer:

sorry please....what is the end of the question ....no task to do