In parallelogram JKLM if LJ=28 find LN.

Answer: 21 people voted

Step-by-step explanation:

an easy way to do this is simply multiply 84 * 0.25.

This gives you [tex]\frac{1}{4}[/tex] of the original amount

in this case 84×0.25 = 21

This means that 21 people voted

The product of the expressions 2 × 10⁵⁸ and 2 × 10⁻²³ in the scientific notation will be 2 × 10³⁵.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

The expressions are given below.

2 × 10⁵⁸ and 2 × 10⁻²³

Then the product of the expressions will be

(2 × 10⁵⁸) × (2 × 10⁻²³) = 2 × 10⁵⁸⁻²³

(2 × 10⁵⁸) × (2 × 10⁻²³) = 2 × 10³⁵

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Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Let [tex]z=r(\cos\theta+i\sin\theta)[/tex] be a complex number, where [tex]n[/tex] is an integer and [tex]n\geq 1[/tex]. By DeMoivre's Theorem, if [tex]z^n=r^n(\cos\theta+i\sin\theta)^n[/tex], then [tex]z^n=r^n(\cos n\theta+i\sin n\theta)[/tex].

Hence, we must first convert from rectangular to polar form:

[tex]z=-1-i\\\\r=\sqrt{a^2+b^2}\\\\r=\sqrt{(-1)^2+(-1)^2}\\\\r=\sqrt{1+1}\\\\r=\sqrt{2}[/tex]

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)\\\\\theta=\tan^{-1}\biggr(\frac{-1}{-1}\biggr)\\ \\\theta=\tan^{-1}(1)\\\\\theta=45^\circ[/tex]

Therefore, the rectangular form for the complex number is [tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)[/tex], and now we can apply DeMoivre's Theorem to raise the complex number to the 10th power:

[tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)\\\\z^{10}=\sqrt{2}^{10}(\cos45^\circ+i\sin45^\circ)^{10}\\\\z^{10}=2^5(\cos10\cdot45^\circ+i\sin10\cdot45^\circ)\\\\z^{10}=32(\cos450^\circ+i\sin450^\circ)\\\\z^{10}=32(0+i)\\\\z^{10}=32i[/tex]

Therefore, [tex]z^{10}=32i[/tex] in rectangular form.

Problem 2

[tex]3\:\text{cis}\:90^\circ=3(\cos90^\circ+i\sin90^\circ)=3(0+i)=3i[/tex]

Therefore, [tex]3\:\text{cis}\:90^\circ=3i[/tex] in rectangular form.

Answer:

€ 1800

Step-by-step explanation:

x - 20% of x = 1440

x - 20x/100 = 1440

x - x/5 = 1440

(5x - x)/5 = 1440

4x/5 = 1440

therefore x = 1440 × 5/4 [ transpose 4/5 to right hand side ]

x = 360 × 5

= € 1800

Triangles are similar

Option E

Answer:

Both of the triangles are similar but they look like they have been rotated a bit.  Sides x is similar to 12 and side 5 (the hypotenuse) is similar to 13.  Therefore we can just set up an equation and cross-multiply.

[tex]\frac{x}{5} = \frac{12}{13}[/tex]

[tex](x * 13) = (5 * 12)[/tex]

[tex]13x = 60[/tex]

Divide 12 from both sides

[tex]13x/13 = 60/13[/tex]

[tex]x=4.615[/tex]

Best option would be Option E, 4.62

D. This is an experiment because it is applying a treatment

Experiments and observational studies are both ways to find new information about a hypothesis but in different ways.

Vocabulary

First, to understand the question, let's define the key terms.

These definitions eliminate the answer choices A and C because both of them match the incorrect definition of the term.

Experiment vs. Observational Study

Now, we need to figure out if this specific example is an experiment or an observational study. In this case, the nutritionist is giving a treatment of vitamins. This means that this cannot be an observational study because the scientist is interfering with people. It has to be an experiment because there is a specific treatment being applied.

Answer:

suddenly

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex]x=-9,\:x=1[/tex]

Step-by-step explanation:

[tex]x^2+8x=9\\x^2+8x-9=0\\(x+9)(x-1)=0\\x=-9,\:x=1[/tex]

Answer:

5.9 C

Step-by-step explanation:

Plug in 16°C for the initial amount, 0.06 for the rate of decrease, and 16 minutes for the time elapsed.

y= a(1–r)t

y= 16(1–0.06)16 Plug in values

y= 16(0.94)16 Subtract

y= 16(0.37157…) Simplify

y= 5.94518… Multiply

Round to the nearest tenth.

5.94518… → 5.9

To the nearest tenth, the difference in temperature will be 5.9°C.

Answer:

Substitution

Step-by-step explanation:

In your premises, the state AB = BC is given to be true. In math, substitution is taking one value in an equation and "subbing it out for" one that we know has the same value. This means anywhere we see AB, we can substitute BC and the equation will still be true, because AB = BC.

In the example given, that changes AB + BC = AC to AB + AB = AC.

We substituted the AB with BC, because we know that they are of the same value.

The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}

where,

n is the number of choices available,

r is the choices to be made.

The number of ways a pizza with three different toppings out of 7 can be made is ⁷C₃(35).

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Answer:To find the mean of a data set, add all the values together and divide by the number of values in the set.

Step-by-step explanation:

Answer:

5. 5.8

6. 6

7. 6

Step-by-step explanation:

5. mean - add all values and divide by the number of values

2 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 9 + 10 = 75

mean = 75/13 = 5.8

6. median - middle value of values written in ascending order.

2 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 9 + 10

median = 6

7. mode - value that occurs most times

mode = 6

Answer:

A, 3

Step-by-step explanation:

Just look at x axis, find 6, and then start going up until you hit the line. Then record the point you hit.

Answer:

232

Step-by-step explanation:

→ Find the percentage multipier

( 100 + 45 )÷ 100 = 1.45

→ Multiply this by the original amount

1.45 × 160 = 232

Based on the triangle inequality theorem, the inequality that gives the range of possible values for x is: 4 < x < 20.

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side.

Therefore, the range of values that is possible for x would be:

12 - 8 < x < 12 + 8

4 < x < 20

The inequality is: 4 < x < 20

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Answer:

144

Explanation:

In a regular polygon all angles and sides are equal. to find out to what all the angles add up to you take the number of sides subtract 1 and multiply by 180.

(10-2)*180=1440

1440/10=144

The volume of the solid will be equal to V=64 Cubic inches.

The space occupied by any solid object in the three-dimension is called as the volume.

Here we have 8 cubes in the solid object each cube has the side equal to 2 inches.

So the volume of one cube will be:

V=a³=2³=8 cubic inches

Since total number of the cubes are 8 so total volume will be:

V=8x8=64 cubic inches

hence the total volume will be equal to 64 cubic inches`

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Answer:

A I think this is it

Step-by-step explanation:

Hope this helps :) :)

Answer:

75.96°

Step-by-step explanation:

Answer:

(-7,-14)

Step-by-step explanation:
Going left is adding a negative value, so it would be -6-1 which is -7 for the x value and going down 5 units is also a negative value so it would be -9-5 which is -14 giving you (-7,-14)

Answer:

hello!!!!

the answer is 280

im not really sure... read the description.... since i dont see a picture attached i dont know the figure shape which makes it difficult to guarantee the correct answer for you....

please read the explanation.. it always helps...

Step-by-step explanation:

okay im going to guess that the figure is a rectangular prism... if not please correct me

if so.... then...

2(10*5 + 10*6 + 5*6)= 280

Answer: 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Prime factorization

60 = 2 x 2 x 5 x 3  

9  15  and 6   are NOT prime numbers !

A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

It should be noted that a function simply means an expression that shows the relationship between the variables.

In this case, a real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

The function will be:

= 20 + 5w

where w represents the number of weeks.

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Answer:

£3263.98 (nearest penny)

Step-by-step explanation:

Compound interest formula

[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

Substituting given values into the formula and solving for A:

[tex]\implies \sf A=2900(1+\frac{0.03}{1})^{1 \times 4}[/tex]

[tex]\implies \sf A=2900(1.03)^{4}[/tex]

[tex]\implies \sf A=3263.975549[/tex]

Therefore, Colin will have £3263.98 after 4 years (to the nearest penny).

Answer:

$3264

Explanation:

[tex]\sf compound \ interest : P(1+\frac{r}{100} )^n[/tex]  
"P" is principal, "r" is rate of interest, "n" is time (years)

Here given:

After 4 years amount:

[tex]\rightarrow \sf 2900(1+\frac{3}{100})^4[/tex]

[tex]\rightarrow \sf 2900(1.03)^4[/tex]

[tex]\rightarrow \sf 3263.9755[/tex]

[tex]\rightarrow \sf 3264[/tex]  (rounded to nearest whole number)

(a) Collision claims tend to be skewed right because there are a few very large collision claims relative to the majority of claims.

These large collision claims skew the data to the right because they are outliers that draw the mean higher than it should be.

The answer cannot be "no large collision claims" or "many large collision claims" because then the data would not be skewed.

(b) Since there are two random samples comparing two means, we will be using a 2-Samp-T-Test. We will use Welch's approximate t-test, where we test the hypothesis that these two populations have the same mean.

We want to determine if 20-24 year old drivers have the same mean collision cost as 30-59 year old drivers.

(c) The null hypothesis is that the mean claim of collision costs for 20-24 year old drivers is the same as the mean claim of collision costs for 30-59 year old drivers.

We can also rewrite this as:

The alternative hypothesis is that the mean claim of collision costs for 20-24 year old drivers is higher than the mean claim of collision costs for 30-59 year old drivers.

We can rewrite this as:

(d) In order to calculate the p-value, we must find the test statistic first.

We can do so by using this formula:

We are given these variables in the problem:

Substitute these variables into the formula for the test statistic.

You can use the calculator to solve this expression, or plug the numbers into your calculator using: STAT - TESTS - 4:2-SAMPTTEST.

Your test statistic should be: t = 1.8962.

The calculator should also tell you the p-value; p = .0308.

(e) Since p = .0308 < α = .1, reject the null. We have convincing statistical evidence that the mean claim of collision costs for 20-24 year old drivers is higher than the mean claim of collision costs for 30-59 year old drivers.