Given AD || GJ. Refer to the figure and provide an appropriate name for
LHJ
A. complementary angle
0
B. right angle
C
C. acute angle
D. obtuse angle

Answer:

P(1≤X≤3) = 0.5974

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Mean of 3

This means that [tex]\mu = 3[/tex]

P(1≤X≤3) ?

[tex]P(1 \leq X \leq 3) = P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

So

[tex]P(1 \leq X \leq 3) = P(X = 1) + P(X = 2) + P(X = 3) = 0.1494 + 0.2240 + 0.2240 = 0.5974[/tex]

Answer:

4

Step-by-step explanation:

Length of the y component is how far the vector reaches vertically, so in this case it's 4

Answer:

Step-by-step explanation:

Sum = -9

Product = 20

Factors = -5 , -4    {-4 * -5 = 20 & -5 + (-4) = -9}

x² - 9x + 20 = 0

x² - 5x  - 4x + 20 = 0     Rewrite middle term

(x² - 5x) - 4x + 20 = 0        Group terms

x(x - 5) - 4(x - 5) = 0         Factor terms

(x-5)(x -4)=0

x -5 = 0   ; x - 4 = 0

x = 5       ; x  = 4

Ans: x = 5 , 4

Answer:

D

Step-by-step explanation:

first of all, what is mode: it is the highest occuring number in a set of numbers.

now since 12 is supposed to be the mean and it occurs twice but 9 also occurs twice so for 12 to be the mode, we must add one more 12.

therefore the answer is 12

Answer:

Step-by-step explanation:

The diagonal must be an angle bisector for a rhombus.

That means that both bisected angles are equal.

2x + 16 = 5x - 8            Add 8 to both sides

2x + 16 + 8 = 5x

2x + 24 = 5x                 Subtract 2x from both sides

24 = 5x - 2x

24 = 3x                         Divide by 3

24/3 = x

x = 8

Answer:

The equation of the function: y = mx + b

Therefore, the equation is f(x) = 2x - 3

When x = 0, f(x) = 2(0) - 3 = -3

When x increases by 1, f(x) increases by 2 (slope = the rate of change)

Answer:

101 degrees

Step-by-step explanation:

the sum of all angles in a triangle is always 180 degrees.

the other not-shaded angle in the lower triangle is also 42 degrees.

the shaded angle is therefore

180 - 37 - 42 = 101 degrees

Answer:

Hello,

Step-by-step explanation:

All i can do is to show you the ellipse.

Answer:

A.) y = 3/4x + 1

Step-by-step explanation:

First let's find the slope using the slope formula, (y₂-y₁)/(x₂-x₁). The two points given are (0,1)₁ and (4,4)₂. We have to substitute those values.

y₂ = 4, y₁ = 1, x₂ = 4, x₁ = 0 --> (4 - 1)/(4 - 0) = 3/4

The slope is 3/4.

Now, we have to find the y-intercept, which is where the line meets the y-axis. It touches the y-axis at (0,1). The y-intercept is 1.

Finally, we build our equation in slope-intercept form.

y = mx + b

y = 3/4x + 1

Lets Do

[tex]\\ \sf\longmapsto p = 2(l + w) \\ \\ \sf\longmapsto l + w = \frac{p}{2} \\ \\ \sf\longmapsto w = \frac{p}{2} - l \\ \\ \sf\longmapsto \boxed{ \bf \: w = \frac{p - 2l}{2} }[/tex]

Answer:

[tex]y = - \frac{1}{5} x + 7[/tex]

Step-by-step explanation:

Slope -intercept form:

y= mx +c, where m is the slope and c is the y- intercept.

Since the given equation is already in the slope-intercept form, we can identify its slope by looking at the coefficient of x.

Slope of given line= 5

The product of the gradients of two perpendicular lines is -1.

m(5)= -1

[tex]m = - \frac{1}{5} [/tex]

Substitute the value of m into the equation:

[tex]y = - \frac{1}{5} x + c[/tex]

Substitute a pair of coordinates to find the value of c.

when x= 0, y= 7,

[tex]7 = - \frac{1}{5} (0) + c[/tex]

c= 7

Thus, the equation of the line is y= -⅕x +7.

Answer: [tex]\$100[/tex]

Step-by-step explanation:

Given

T-shirt cost 5 times as much as a singlet

Suppose the price of a singlet [tex]x[/tex]

Price of a T-shirt is [tex]5x[/tex]

According to the question, for $800, trader can buy 32 more singlet than T-shirt

[tex]\Rightarrow \dfrac{800}{x}=\dfrac{800}{5x}+32\\\\\Rightarrow \dfrac{800}{x}-\dfrac{160}{x}=32\\\\\Rightarrow 800-160=32x\\\\\Rightarrow x=20[/tex]

Thus, the price of a T-shirt is [tex]5x=\$100[/tex]

Answer:

$7 is his Hourly Wage.

Step-by-step explanation:

We can start by finding out how much money Jada started with by adding the amount of money he had after buying the cake with how much he spent on the cake, 86 + 12 = 98.

We now know how much money he had before buying anything. Now we can just divide the total amount of money by how long he worked.

98 ÷ 14 = 7

Answer:

+6

Step-by-step explanation:Look at the trend of numbers and notice. Maybe put it in a table.

Answer:

3

Step-by-step explanation:

slope = (24-18)/(23-21) = 6/2 = 3

Step-by-step explanation:

4.15 × 3.85

= (4 + 0.15) ( 4 - 0.15)

= (4)^2 - (0.15)^2

= 16 -- 0.0225

= 15.9775

HOPE IT HELPS

Answer:

drawing a blue marble is a harder then the yellow but not as hard as the red.

Answer:

The relative frequency is found by dividing the class frequencies by the total number of observations.

Step-by-step explanation:

A relative frequency distribution can be regarded as a distriburion that display the proportion of the total number of observations that is been associated with class of values or each of the value, and this relate to a probability distribution that is been used extensively in statistics. A relative frequency distribution gives the lists of the data values with percent of all observations that belongs to each group. The relative frequencies are been calculated through the division of the frequencies for each group using the total number of observations.

It should be noted that In a Relative frequency distributions, the relative frequency is found by dividing the class frequencies by the total number of observations.

Answer:

x = 17

Step-by-step explanation:

The angles are same side interior angles and they will add to 180 when the lines are parallel

6x+8  + 4x+2 = 180

10x+10 = 180

Subtract 10 from each side

10x+10-10 =180-10

10x = 170

Divide by 10

10x/10 = 170/10

x = 17

Answer:

x = 17

Step-by-step explanation:

Theorem:

If two lines are cut by a transversal such that same-side interior angles are supplementary, then the lines are parallel.

For the lines to be parallel, the sum of 6x + 8 and 4x + 2 must equal 180.

6x + 8 + 4x + 2 = 180

10x + 10 = 180

10x = 170

x = 17

Answer:

<CAB  

Step-by-step explanation:

Since CAD is equal to DAB

AD bisects CAB  

Answer:

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

[tex]=2^5\times (2^{-5} 3^{-5} )[/tex]

[tex]=2^{5-5} 3^{-5}[/tex]

[tex]=2^{0} 3^{-5}[/tex]

[tex]=3^{-5}[/tex]

[tex]OAmalOHopeO[/tex]

Answer:

B(3^-5) and D(2^5*6^-5)

Step-by-step explanation:

I put the expression in to the calculator and put the answers into the calculator and just picked the ones that matched

Answer:

7^-22

Step-by-step explanation:

Exponent laws.

Answer:

$0.25

Step-by-step explanation:

We can use System of Equations to find out how much a can of cat food costs.

Let's use variables to represent the cat food and dog food:

x = cost of 1 cat food can

y = cost of 1 dog food can

Here are our 2 equations based on the scenarios in the question:

4x + 3y = 1.99

4x + y = 1.33

Now let's set the second equation to y using basic algebra:

4x + y = 1.33

y = -4x+1.33

And we're going to plug that value of y, which is -4x+1.33 into the first equation and solve:

4x + 3y = 1.99

4x + 3(-4x+1.33) = 1.99

4x + -12x+3.99 = 1.99

-8x + 3.99 = 1.99

-8x = -2

x = 1/4

x = 0.25

1 can of cat food costs $0.25

Hope that helps (●'◡'●)

Answer:

.25

Step-by-step explanation:

set up equations

1)4c+3d=1.99

2)4c+d=1.33

Method of use:Elimination

          4c+3d=1.99

       - (4c+d)=-(1.33)

        ___________

=2d=.66

divide by two on both sides to get .33 for d.

plug in

4c+.33=1.33

subtract .33 on both sides

4c=1

divide by four on both sides to get c

c=1/4 or .25

Answer:

Relative error = 0.19

Step-by-step explanation:

From the question given above, the following data were obtained:

Measured age = 32 years

Actual age = 27 years

Relative error =?

Next, we shall determine the absolute error. This can be obtained as follow:

Measured age = 32 years

Actual age = 27 years

Absolute error =?

Absolute error = | Measured – Actual |

Absolute error = | 32 – 27 |

Absolute error = 5 years

Finally, we shall determine the relative error. This can be obtained as follow:

Absolute error = 5 years

Actual age = 27 years

Relative error =?

Relative error = Absolute error / Actual years

Relative error = 5 / 27

Relative error = 0.19

Answer:

simple 49+44=93 then you do 180 is the angle of a straight line so we do 180-93=87

Answer:

11.85

Step-by-step explanation:

Tan 28 = opposite / adjacent

Answer:

the distance from the pole is 11.85 ft.

Step-by-step explanation:

Given;

the elevation to the top of the pole, θ = 28⁰

height of the pole, h = 6.3 ft

let the distance from the pole = x

If a sketch of a right triangle is made as follows, it will be observed that the base of the triangle forms the adjacent side of the triangle, which is equal to x.

                                ↑

                                ↑ h = 6.3 ft

                                ↑

         28⁰ ---------------

                       x

[tex]tan(28) = \frac{6.3}{x} \\\\x = \frac{6.3}{tan(28)} \\\\x = 11.85 \ ft[/tex]

Therefore, the distance from the pole is 11.85 ft.

[tex]Total \: length = 1 \: yard \\ Finished \: length = \frac{3}{8} \: yard \\ \\ so \: remaining \: length \\ = total \: length - finished \: length \\ = 1 \: yard - \frac{3}{8} \: yard \\ = \frac{8}{8} \: yard - \frac{3}{8} \: yard \\ = \frac{5}{8} yard[/tex]

This is the answer.

Hope it helps!!

Given:

The endpoints of the latus rectum at (-2, 3) and (-2, 15).

The directrix at x = 4.

To find:

The equation of the parabola.

Solution:

The equation of the parabola is:

[tex](y-k)^2=4p(x-h)[/tex]                   ...(1)

Where, [tex]x=h-p[/tex] is directrix and [tex](h+p,k\pm |2p|),p<0[/tex] are the end point of the latus rectum.

The directrix at x = 4. So,

[tex]h-p=4[/tex]               ...(i)

The endpoints of the latus rectum at (-2, 3) and (-2, 15). So,

[tex](h+p,k-|2p|)=(-2,3)[/tex]

[tex](h+p,k+|2p|)=(-2,15)[/tex]

Now,

[tex]h+p=-2[/tex]              ...(ii)

[tex]k-2p=3[/tex]              ...(iii)

[tex]k+2p=15[/tex]           ...(iv)

Adding (i) and (ii), we get

[tex]2h=2[/tex]

[tex]h=1[/tex]

Putting [tex]h=1[/tex] in (i), we get

[tex]1-p=4[/tex]

[tex]-p=4-1[/tex]

[tex]-p=3[/tex]

[tex]p=-3[/tex]

Putting [tex]p=-3[/tex] in (iii), we get

[tex]k-|2(-3)|=3[/tex]

[tex]k-6=3[/tex]

[tex]k=3+6[/tex]

[tex]k=9[/tex]

Putting [tex]h=1,p=-3,k=9[/tex] in (1), we get

[tex](y-(9))^2=4(-3)(x-1)[/tex]

[tex](y-9)^2=-12(x-1)[/tex]

Therefore, the required equation of the parabola is [tex](y-9)^2=-12(x-1)[/tex].