If CE and FH are parallel lines and m/CDG =
are parallel lines and m/CDG = 128°, what is mZHGD?

4.8 × 10^4

Answer:

Step-by-step explanation:

A is a point

AB is a line

ABC is a plane

Therefore,  ABC is a plane.

__________________

Hope this helps!

Have a great day!

Answer:

The letter a in an ellipse equation is:

Step-by-step explanation:

General equation of an ellipse

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

where:

If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.

If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.

The major axis is the longest diameter of an ellipse, so the major radius is one half of the major axis.

The minor axis is the shortest diameter of an ellipse, so the minor radius is one half of the minor axis.

Therefore the letter a in an ellipse equation is:

[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to  base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.

The most common types of logarithms are  the base 10 common logarithm, the base 2 binary logarithm, and  the base  e ≈ 2.71828 natural logarithm.

the product rule for logarithms is

[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex]  for b > 0

now ,

[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]

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1. Dianely's salary can be represented with the following table of values for 5 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

5          $50,000

2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement equating two or more mathematical expressions.

Equations use variables, numbers, mathematical operands, and the equation symbol (=).

Dianely's initial salary = $40,000

Salary raise per year = $2,500

Dianely's salary after n years in equation form, S = 40,000 + 2,500n.

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

5          $50,000 ($47,500 + 2,500)

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For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.

As given in the question,

Given system of linear equations are as follow:

6x-12y = -7           ____(1)

2x + ky = 14         _____(2)

Form equation (1)  we have,

6x -12y = -7

⇒3 ( 2x -4y) = -7

⇒ 2x - 4y = -7 /3       ____(3)

From equation (2) and (3) we have,

2x + ky = 14

2x - 4y = - 7/3

Value of k so that the given system of equations are inconsistent is given by:

k = -4

For inconsistent there is no solution.

Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is  k= -4.

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Answer:

25 percent.

Step-by-step explanation:

25 divided by 100 is equal to 0.25. You then multiply that by 100 to get percent, which is 25 percent.

Hope it helps.

The graph of the linear equation can be seen in the image at the end.

We start by defining the variables we will use:

x = number of weeks.

y = money that Anika has.

We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:

y = $5*x

To graph this linear equation we need to find two points on the line, if x = 0 we get:

y = $5*0 = $0

So we have the point (0, 0)

if x = 1

y = $5*1 = $5

So we have the point (1, 5)

Now we can graph these two points and connect them with a line, the graph can be seen below.

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The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given function,

f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x

f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)

=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)

f'(x)=0

((1/x)-4x)=0

1-4x²=0

4x²=1

x=±1/4

Given that, f(x) is decreasing function then,

f'(x)<0

((1/x)-4x)<0

(1-4x²)/x<0

1-4x²<0

1<4x²

1/4<4x²

x²>1/4

x>1/2

x∈(1/2,∞)

Hence, f(x) is decreasing on the interval x∈(1/2,∞)

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The number of trips after the cost of the plan A and plan B is 16.

According to the question,

We have the following information:

Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.

So, this will make an arithmetic progression.

The formula to find nth term of an A.P:

an = a+(n-1)d where a is the first term

Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.

145+(n-1)5 = 40+(n-1)12

145+5n-5 = 40+12n-12

5n+140 = 12n+28

140-28 = 12n-5n

7n = 112

n = 112/7

n = 16

Hence, the number of trips after the cost of the plan A and plan B is 16.

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There are 284 number of students and 152 number of adults.

Two or more expressions with an Equal sign is called as Equation.

Given,

The ratio of teachers to students on a field trip is 2:13

Let x be the number of adults

If there are 132 more students than adults on the field trip, then 132+x

To find the number of adults and number of students formulate a equation as below

2/13=(x+132)/x

Apply cross multiplication

2x=13(x+132)

Apply distributive law on RHS

2x=13x+1716

11x=1716

Divide both sides by 11

x=152

x+132=152+132=284

Hence there are 284 number of students and 152 number of adults.

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Answer:

Step-by-step explanation:

area=10×5+[(15-5)+7]/2×(10-6)

=50+(17)/2×4

=50+34

=?

Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of even numbers in a deck of cards.

= 5 x 4

= 20

The number of diamonds in a deck of cards.

= 4

Now,

The probability of drawing an even number from a deck of cards.

= 20 / 52

= 10/26

= 5/13

Now,

The remaining cards.

= 52 - 20

= 32

The probability of drawing diamonds after drawing the even numbers.

= Number of diamonds / remaining cards

= 4 / 32

= 1/8

Thus,

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

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We can learn from the graph that ANNIE is required to walk 14 blocks.

How to solve a graph.-

acc to the question-

fruit vendor=(-3,7)

pet store-=(-1,6)

supermarket=(1,5)

annie's house=(1,4)

Hence,We can learn from the graph that ANNIE is required to walk 14 blocks.

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Answer:

3:2

Step-by-step explanation:

You need to find two more equivalent ratio of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.

Another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate

Ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1

ratio of cups of sparkling water : cups of grape juice concentrate = 3 : 1

Equivalent ratio to 3 : 1 are

6 : 2,

9 : 3,

12 : 4

15 : 5

21 : 7

Non equivalent ratio of 3 : 1 are

3 : 2

4 : 2

5 : 5

6 : 4

Therefore, another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate

Answer:

10x+6xy+4

Step-by-step explanation:

2(5x+2)-(3y) 2x-4x

By removing the bracket

10x+4-6xy+12xy

10x+4+6xy

10x+6xy+4

The money available for private investment is $250 billion dollar

What is demand curve ?

The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.

Refer to the attachment for graph:

Once investments and government borrowing are added together, the total is = $400

if borrowing from the government is= $150

private investment

=( investment and and government borrowing) - (government borrowing )

= $400 - $150 = $250

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Answer: A scale factor of 1/2 was applied to the first triangle to get the resulting image.

Step-by-step explanation: The initial side length of 3.4 is twice as long as 1.7, the initial triangle was reduced to half of the initial size.

Answer:

The triangle is still an equilateral triangle as before, and the only difference is that the side length is halved from 3.4 to 1.7 (3.4/2=1.7). Therefore, the scale factor is 1.7/3.4=0.5. A scale factor <1 means that the original shape is reduced. The scale factor would be a reduction.

Step-by-step explanation:

The image would be of a triangle.
Hope this helps! :))

The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.

In all continuous probability distributions,  it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.

The area between the two boundaries is 0.67and the remaining area is 0.33  (= 1-0.56) , which is to the left of it.

Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.

Therefore, the two z values are 0.44  and -0.44.

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The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.

In all continuous probability distributions,  it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.

The area between the two boundaries is 0.67and the remaining area is 0.33  (= 1-0.56) , which is to the left of it.

Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.

Therefore, the two z values are 0.44 and -0.44.

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To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.

(12+16+10+8+14+15)/6

= 75/6

= 12.5 (answer is already rounded to nearest tenth)

The length of the railing is 105.81 inches.

Given,

The stair has 7 steps

The rise of each step = 8.5 inches

The tread of each step = 12.5 inches

Slope of each step = x

We have to find the length of the railing.

Length of railing = 7x

Then,

Slope of step, x can be determined using Pythagorean theorem.

Let rise be the height of the right angled triangle and tread be the base of the triangle

Then,

Hypotenuse= Slope, x  = [tex]\sqrt{Rise^{2} + Tread^{2} }[/tex]

x = [tex]\sqrt{8.5^{2}+ 12.5^{2} }[/tex]

x = [tex]\sqrt{72.25 + 156.25}[/tex]

x = √228.5

x = 15.12 inches

That is,

The slope, x of one step is 15.12 inches

Now,

Length of the railing = 7x = 7 × 15.12 = 105.81 inches

Therefore,

The length of the railing is 105.81 inches.

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The mean age is equal to: 44.09.

The standard deviation is equal to: 10.07.

First of all, we would determine the median of each class interval as follows:

Median 1 = (25 + 34)/2 = 29.5

Median 2 = (35 + 44)/2 = 39.5

Median 1 = (45 + 54)/2 = 49.5

Median 1 = (55 + 64)/2 = 59.5

Next, we would calculate the mean age by using this mathematical expression:

Mean age = ∑fx/∑f

Substituting the given parameters into the formula, we have;

Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)

Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118

Mean age = [5,203]/118

Mean age = 44.09.

Now, we can calculate the standard deviation as follows:

Standard deviation, S = √((∑f(xi - μ)²/∑f)

Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))

Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)

Standard deviation, S = √(11,970.48/118)

Standard deviation, S = √101.5

Standard deviation, S = 10.07.

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Answer:

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

Answer:

72.624 kg

Step-by-step explanation:

1g = 0.001 kg

104g = 0.104kg

weight of 1 bag  = 12.104kg

weight of 6 bags = 12.104 x 6

weight of 6 bags = 72.624kg

Answer: A

Step-by-step explanation:

The absolute value of a number is its relative distance from zero, so it doesn't matter if it is negative. For example, -3 and 3 are both 3 units away from zero on the number line.

The time taken for the rocket to reach its maximum height is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.

This is the z distribution given that the value of n is more than 30.

We have to make use of z when n which is the number of samples  is greater than 30.

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Answer:

its D

Step-by-step explanation:

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