What are the domain and range of the step function with the equation below?
fx)=-3[x]​

Answer:

Converges

Sum = 20.8333

Step-by-step explanation:

A geometric series has a general formula of:

[tex]\sum ar^n[/tex]

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25, and each term is being divided by -5, or multiplied by -0.2, so the general form would be:

[tex]\sum 25*(-0.2)^n[/tex]

Since 0.2 < 1.0, the series converges.

The sum of the series is given by:

[tex]S=\frac{a}{1-r}\\S=\frac{25}{1-(-0.2)}\\S=20.8333[/tex]

The sum is 20.8333.

The geometric series converges and the sum is equal to 20.83.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .

A geometric series has a general formula of:

∑arⁿ

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=25 and each term is divided by -5 or multiplied by (-0.2)

Therefore r = -0.2 and as it is <1 therefore the series converges

The sum of a convergent series is

S = a/(1-r)

S = 25/(1-(-0.2))

S= 25/1.2

S = 20.83

Therefore the sum of the series is 20.83

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Answer:

6 1/6 ft

Step-by-step explanation:

12 inches = 1 ft

So 2 inches is 2/12 of a foot

2/12 = 1/6

6 ft 2 inches = 6  1/6 ft

Answer:

Step-by-step explanation:

To find 5e. El change, find the difference between week 1 and 1.

56.92-(-16.54) = 56.92+16.54 = -73.46.

Note: this is negative, because we are calculating the difference.

Hope this helps

See attached graph: v is on the y-axis and t is on the x-axis

Answer:

Hi there!

The correct answer is: True

Step-by-step explanation:

If there is a line, there are infinite planes that pass through that line, therefore since the 4 points are in a line, they are coplanar .

Answer:

The correct option is SSS (Side-Side-Side) Theorem

Step-by-step explanation:

The question is incomplete because the diagrams of ΔLON and ΔLMN are not given. I have attached the diagram of both triangles below for better understanding of the question.

Consider the diagram attached below. We have to find the congruence theorem which can be used to prove that ΔLON ≅ ΔLMN

We can see in the diagram that both triangle have a common side that is LN. It means 1 side of both triangles is congruent because LN≅LN

Consider the sides ON and MN. Both side have a single bar on them, which means that it is given that both of these side are congruent. Hence ON≅MN

Consider the sides LO and LM. Both side have a double bars on them, which means that it is given that both of these side are also congruent. Hence LO≅LM

SSS theorem states that if all sides of the triangles are congruent, then the triangles themselves are also congruent, which is the same case in this question

Answer:

D. SSS

Step-by-step explanation:

I hope this helps.

Answer:

option D

Step-by-step explanation:

x/-3≤3

multiply by (-1) on both sides

x/3≥-3

x>=-9

Answer:

Letter D

Step-by-step explanation:

Answer:

(22/7)/6=0.523809

Step-by-step explanation:

V=4/3πr^3

V=4/3π(1/2)^3=π/6

or (22/7)/6=0.523809

Answer:

12-y------------> 9

3x-y------------>21

4y-10----------->2

1/4 xy-----------> 6

Solution,

Given,

X=8

y=3

Now,

[tex]1. \: \: 12 - y \\ \: \: \: = 12 - 3 \\ \: \: = 9 \\ 2. \: \: 3x - y \\ \: \: = 3 \times 8 - 3 \\ \: \: = 21 \\ 3. \: \: 4y - 10 \\ \: \: = 4 \times 3 - 10 \\ \: = 12 - 10 \\ \: \: = 2 \\ 4. \: \: \frac{1}{4} xy \\ \: \: = \frac{1}{4} \times 8 \times 3 \\ = 6[/tex]

hope this helps...

Good luck on your assignment...

Answer:

100

Step-by-step explanation:

Since the inscribed angle of a circle is always half of its corresponding, the measure of this angle is 200/2=100 degrees. Hope this helps!

Answer:

100

Step-by-step explanation:

Answer:

Jason likely misplaced the decimal, because 3 times 1 = 3, and if the decimal was between the 2 and the 5, the number would be near 3.

Step-by-step explanation:

Jason applied 2 and 82.242 miles

Answer:

b

Step-by-step explanation:

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared ​(units are in​ meters).

Also, v Subscript x is constant at 10.0 ​m/s.

The water from a fire hose follows a path described by the following equation below;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

The velocity of the [tex]x[/tex] component is constant at =  [tex]v_x=10.0 \text{ m/s}[/tex]

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

[tex]v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}[/tex]

Now, differentiating the above equation with respect to t, we get;

[tex]y=2.0 + 0.9x-0.10x^{2}[/tex]

[tex]\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}[/tex]

[tex]v_y = 0.9v_x -0.2v_x[/tex]

[tex]v_y = 0.7v_x[/tex]

Now, putting [tex]v_x=10.0 \text{ m/s}[/tex] in the above equation;

[tex]v_y = 0.7 \times 10.0[/tex] = 7 m/s

Now, the resultant velocity is given by = [tex]v=\sqrt{v_x^{2}+v_y^{2} }[/tex]

                            [tex]v=\sqrt{10^{2}+7^{2} }[/tex]

                               = [tex]\sqrt{149}[/tex] = 12.21 m/s

Answer:

AB=6 Units

Step-by-step explanation:

Given the following lengths of rectangle ABCD and its dilation A'B'C'D' respectively

We are to determine the length of AB. To do this, we first determine the dilation factor.

[tex]D$ilation Factor =\dfrac{B'C'}{BC} =\dfrac{9.5}{3.8} =2.5[/tex]

Therefore:

[tex]\dfrac{A'B'}{AB} =2.5\\\\\dfrac{15}{AB} =2.5\\$Cross multiply \\ 2.5 AB =15 \\AB=15 \div 2.5\\$Therefore, AB=6 Units[/tex]

Answer:

6 units

Step-by-step explanation:

edge 2022

Answer:

x = 59/7, y = -15/7

Step-by-step explanation:

4x= 2y + 38;

2 - 3y=x

We can substitute for x  in the first equation since the second equation is solved for x

4(2-3y) = 2y+38

Distribute

8 - 12y = 2y+38

Add 12y to each side

8-12y+12y = 2y+12y+38

8 = 14y+38

Subtract 38 from each side

-30 = 14y

Divide by 14

-30/14 = y

-15/7 = y

Now solve for x

2 - 3y = x

2 - 3*-15/7 = x

2 +45/7 = x

14/7 + 45/7 = x

59/7 =x

Answer:

A. 52% and B. 104/200

Step-by-step explanation:

To find the answer, we first have to find how many pet owners own cats. As percentages are x/100, when we have x/200 we divide the numerator and denominator by 2 to bring the fraction to 48/100. (96/200 divided by 2 equals 48/100). Now that we have the percentage of pet owners that own cats (48%), we need to find how many do not own cats. To do so, we just subtract 100-48 to get 52. Then, we do the same to the fraction of 96/200. (200-96 = 104). This brings our answers to A. 52% and B. 104/200

The percentage of owners that do not own cat is 52%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given here, 96 out of 200 pet owners own cats then the owners who do not own cat are 104

Therefore the number of non cat owners in percentage terms is

= (104/200) ×100

= 52.5%

Hence, the answer is 52.5%

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Answer:

-20

Step-by-step explanation:

f(x)= 2x^2 + 5x - 17,

f(-1)

Let x = -1

f(-1)= 2 *(-1)^2 + 5(-1) - 17

     = 2 *1   -5 -17

    = 2 -22

   = -20

Answer:

-20

Step-by-step explanation:

f(x)= 2x² + 5x - 17

Put x as -1.

f(-1)= 2(-1)² + 5(-1) - 17

Solve for the powers.

f(-1)= 2(1) + 5(-1) - 17

Multiply the terms.

f(-1)= 2 + -5 - 17

Add or subtract the terms.

f(-1)= -20

Answer:

Median = 3.5

Step-by-step explanation:

Median is the middlemost number.

Here, there are two middlemost numbers, 5 and 2

So, we'll take the mean of them to find out the median

Median = 5+2/2

Median = 7/2

Median = 3.5

Answer: The vertex form is h(x)=(x-3)^2-6

Step-by-step explanation:

Using the complete the square method, first complete any squares

X^2-6x+(-3)^2-(-3)^2+3

Use the binomial formula

(x-3)^2 - (-3)^2 +3

Simplify

(x-3)^2-6

Answer:

5

Step-by-step explanation:

The product of 6 and 7 is 42.

Let x be the number of times needed to add 5 to 17 to reach 42.

17 + 5x = 42

5x = 42 - 17

5x = 25

x = 5

Answer: I’m pretty sure it’s 5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

subsitute each of the x and y values for each of the equations and if they both equal each other It is correct.

Answer:

x = 2, y= -1

Step-by-step explanation:

12x - y = 25

9x + y = 17

add both equations to eliminate y

21x = 42

divide by 21

x = 42/21

x = 2

sub x in equation i to find y

12(2) - y = 25

24 - y = 25

-y = 1

therefore y = -1, x = 2

Answer:

19.49% probability that no more than 16 of them are strikes

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 30, p = 0.626[/tex]

So

[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*0.374} = 2.65[/tex]

What is the probability that no more than 16 of them are strikes?

Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So

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

[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]

[tex]Z = -0.86[/tex]

[tex]Z = -0.86[/tex] has a pvalue of 0.1949

19.49% probability that no more than 16 of them are strikes

Answer:

1. A letter, A, added to a letter, B, equals ten.

2. A letter, x, which is multiplied by 4, then has a number, y, subtracted from it to equal a letter, a.

If you try write these out, I'm sure you'd get the algebraic expression given.

Answer:

16x + 8y -3/2

Step-by-step explanation:

The expression can be represented mathematically as follows.

-2(-8x - 4y + 3/4) = - 10x - 8y - 1 1/4

-2(-8x - 4y + 3/4) = - 10x - 8y - 5/4

The first way to solve this expression is by opening the bracket by multiplying the outside values by the inner values.

-2(-8x - 4y + 3/4)

Multiply -2 by all the values in the brackets

-2 × - 8x = 16x not - 10x

-2 × - 4y = 8y not -8y

-2 × 3/4 = -6/4 = - 3/2  not -5/4

Bringing the value together the expected answer will be 16x + 8y -3/2 and not  - 10x - 8y - 5/4.

Answer

A, B, and C

Step-by-step explanation:

Hope this helps!

Answer:

The maximum height the projectile reaches is 100 feet

Step-by-step explanation:

Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.

therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:

[tex]f(x)=ax^2+bx+c[/tex]

with x-position of the vertex given by:

[tex]x_v=\frac{-b}{2a}[/tex]

Then in our case  ([tex]H(t)=-16t^2+16t+96[/tex])  we have:

Horizontal position of the vertex given by:

[tex]t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}[/tex]

and now we can find the maximum height plugging this value into the height expression:

[tex]H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft[/tex]

Answer:

Step-by-step explanation:

You didn't list any choices here, but it doesn't matter. There's only one way to get to the answer so we'll work it through and you can match it up to your choices. The only thing I don't know is how pens is identified if pencils is "p". So I'm going to use the words "pens" and "pencils" and you can take it from there at the end.

If a pen's cost IS twice as much as a pencil...

the word "is" indicates an equals sign, the words "twice as much" indicates 2 multiplied by something. To put that above sentence into an algebraic expression:

pen = 2 pencils

Now for the money part of this.

The total cost of 11 pens and 11 pencils IS (there's that word again!) 2.10

Therefore,

11 pens + 11 pencils = 2.10

But we know from the first expression that pen = 2 pencils so we make the substitution:

11(2 pencils) + 11 pencils = 2.10

I'm not sure how far you are to go with this. That's the main equation you need to solve this. If you were to go further with it you would distribute the 11 into the set of parenthesis to get:

22 pencils + 11 pencils = 2.10 and combine like terms:

33 pencils = 2.10 so

1 pencil is approximately $.06

Answer:

$6.89

Step-by-step explanation:

To find unit price divide the dollar by the amount. The dollar is 20.67. The amount of socks are 3. The equation would then be 20.67/3. Then solve and the answer would be $6.89.

[tex]42 \times 48=2016[/tex]

[tex]24 \times 84 = 2016[/tex]

The answer is 42 × 48 because even when we switch the digits, the product remains the same.

Answer:

in total she would spend 27.90 so she should bring C i got this by doing 7.80 x 3 because she is buying 3 medium pizzas then i did 0.75 x 6 and got 27.90 so at least bring 25-30 dollars with her

Step-by-step explanation: