Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13

Answer:

-8x - 8

Step-by-step explanation:

You have to combine like term.

So you add 16x + -24x = -8x

And you add -12 + 4 = -8

Your answer would be -8x - 8

I hope this helps!

Answer:  [tex]y=4x-35[/tex]

y = Sidney’s weekly salary

x = Casey’s weekly salary

Answer: y=4x-35

x is Casey's salary

Y is Sidney's salary

Step-by-step explanation:

Sidney makes a quarter of Casey,

y=4x,

Then it also states that he makes 35 less than the first equation.

Therefore,

Y=4x-35

Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Given that;

Triangle ABC is similar to A"B"C".

Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)

Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

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Answer:

57°

Step-by-step explanation:

According to theorem, "any two angles in the same segment of the circle are equal"

So,

m<BED = 57°

Answer:

B

Step-by-step explanation:

Geometric series converge if |r| < 1.

A) r = 3

B) r = 1/2

C) r = -4

D) r = 2

Only B has |r| < 1.

The converging sequence of geometric progression is given by the relation A = 1 + 1/2 + 1/4 + 1/8 ... where the common ratio r = 1/2

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A = 1 + 1/2 + 1/4 + 1/8 ...

Now , the common ratio r of the GP is

r = second term / first term

On simplifying , we get

r = ( 1/2 ) / 1

r = 1/2

So , when | r | < 1 , the GP is a converging series

Hence , the GP is converging series

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First check for the critical points of f by checking where the first-order derivatives vanish.

[tex]\dfrac{\partial f}{\partial x}=4x-4=0\implies x=1[/tex]

[tex]\dfrac{\partial f}{\partial y}=2y-4=0\implies y=2[/tex]

Notice how the point (1, 2) lies on the line y = 2x ; at this point, we get a value of f(1, 2) = -5 (MIN).

Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find f(0, 0) = 1 (MAX) and f(0, 2) = -3.

Now check on the boundary lines themselves. If x = 0, then

[tex]f(0,y)=y^2-4y+1=(y-2)^2-3[/tex]

which has a maximum value of -3 when y = 2 (so we get the same critical point as before).

If y = 2, then

[tex]f(x, 2)=2x^2-4x-3=2(x-1)^2-5[/tex]

with a maximum of -5 when x = 1.

If y = 2x, then

[tex]f(x,2x)=6x^2-12x+1=6(x-1)^2-5[/tex]

with the same maximum of -5 when x = 1.

This question is based on the absolute maximum and absolute minimum.

We get this by differentiating the terms.

Given:

f(x,y) =   [tex]2x^{2} - 4x + y^2 - 4y +1[/tex], bounded by the lines x=0,y=2,y=2x in the first quadrant,bounded by the lines x=0,y=2,y=2x in the first quadrant.

We need to determined the absolute maximum and absolute minimum of the function.

Now, partial differentiating wrt x and y.

[tex]\dfrac{\partial f}{ \partial x} = 4x -4 = 0 \Rightarrow x= 1 \\\dfrac{\partial f}{ \partial y} = 2y - 4 = 0 \Rightarrow y = 2[/tex]

Now, point (1, 2) lies on the line y = 2x ; at this point, we get a value of

f(1, 2) = -5 (MIN).

Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2).

Now, find f(0, 0) = 1 (MAX) and f(0, 2) = -3.

Now check on the boundary lines themselves.

If x = 0, then we get,

[tex]f(0,y) = y^2 - 4y +1 = ( y-2)^2 -3\\[/tex]

which has a maximum value of -3 when y = 2 (so we get the same critical point as before).

If y = 2, then we get,

f(x,2) = [tex]2x^2-4x -3 = 2(x-1)^2 -5[/tex] with a maximum of -5 when x = 1.

If y = 2x, then we get,

f(x,2x) = [tex]6x^2 -12x +1 = 6(x-1)^2 -5[/tex] with the same maximum of -5 when     x = 1.

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Answer:

[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]

[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]

Step-by-step explanation:

Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(1518,325)[/tex]  

Where [tex]\mu=1518[/tex] and [tex]\sigma=325[/tex]

We want to find this probability:

[tex]P(X>1600)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]

For the other part we need to take in count that the distribution for the sampel mean if the sample size is large (n>30) is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\frac{sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]

And we can find this probability using the z score formula and the complement rule and we got:

[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]

Answer:

8

Step-by-step explanation:

y²+by+16= (y+4)²

y²+by+16= y²+2*4*y+4²

y²+by+16= y²+8y+16

by=8y

b=8

Step-by-step explanation:

Simplifying

f(x) = 2cos(3x)

Multiply f * x

fx = 2cos(3x)

Remove parenthesis around (3x)

fx = 2cos * 3x

Reorder the terms for easier multiplication:

fx = 2 * 3cos * x

Multiply 2 * 3

fx = 6cos * x

Multiply cos * x

fx = 6cosx

Solving

fx = 6cosx

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.

f = 6cos

Simplifying

f = 6cos

Answer:

  4.  the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers

Step-by-step explanation:

√9 = 3

3 is every kind of number except irrational. It belongs to the sets of ...

Answer:

0.0004% probability that the student answers at least 9 questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. All questions are answered independently. This means that we use the binomial distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this question, we have that:

[tex]n = 10, p = 0.2[/tex]

What is the probability that the student answers at least 9 questions correctly

[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0.000004[/tex]

[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0 [/tex]

[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.000004 + 0 = 0.000004[/tex]

0.0004% probability that the student answers at least 9 questions correctly

Answer:

  8 full turns

Step-by-step explanation:

80 cm is 8 times 10 cm, so is 8 times around the spool.

Alex must unwind 8 full turns of thread from the spool.

__

He must unwind it once.

Answer:

8 in total turns

Step-by-step explanation:

Answer:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we can find this probability:

[tex] P(X \geq 1)[/tex]

And we can solve this probability like this:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]

And replacing we got:

[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]

Answer:

6

Step-by-step explanation:

When the cube is folded, 6 is the opposite of 1.

2 is the opposite of 4 and 5 is the opposite of 3.

When the given net is folded into a cube, the number that we will find opposite 1 is 6.

When the net is folded, two will be folded left and up with 3 being the base. 4 will be folded right with 5 being the top of the cube.

We will then observe the following pairs opposite each other:

This means that the number that we will see opposite 1 will be the number 6.

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Answer:

105.13ft^2

Step-by-step explanation:

[tex]A=lw\\=10*8\\=80ft^2[/tex]

Rectangle

[tex]A=\frac{1}{2} \pi r^2\\=\frac{1}{2\pi } 4^2\\=25.13[/tex]

Add both together

80+25.13

=105.13

Answer :  105.13

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

2/3x - 5>3

Add 5 to each side

2/3x - 5+5>3+5

2/3x > 8

Multiply each side by 3/2

3/2 *2/3x > 8*3/2

x > 12

There is an open circle at 12 and the lines goes to the right

Answer:

[tex]y=300(1+0.16)^x[/tex]

Step-by-step explanation:

 [tex]A= P(1+r )^t[/tex]

Where

A =final amount  = y

P=initial principal balance = $300

r=interest rate  = 16%= 0.16

t=number of time periods elapsed= x

Hence the equation to model his account balance/ final amount A (y) after time (x) years is

[tex]y=300(1+0.16)^x[/tex]

Answer:

yes the above is a function.

Answer:

Step-by-step explanation:

let s note a and b

x = ap+b

we can write two equations

(1) 300=3a+b

(2) 450=1.5a+b

multiply by 2 the (2) we got

900 =3a+2b

minus (1) it gives

900 - 300 = 3a+2b-3a-b = b

so b = 600

and from (1) it gives 3a = 300-600 = -300

so a = -100

then

x=-100p+600

thanks

The correct answer is C. Mark’s method is correct because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

Explanation:

To begin Mark should determine the rate of delivery (number of houses the carrier can deliver in 1 minute). This can be found by dividing the houses by the minutes (36 / 30 = 1.2 houses per minute). This means the 1.2 rate found by Mark is correct; also, in this case, it is important to clarify, the carrier will not deliver to 1.2 houses at the same time, but this is the delivery rate or number used to understand the relationship between the number of houses, and the time.

Moreover, you can use this rate, and multiply it by 7.5 and this will show you how many houses the carrier can deliver in this time (7.5 (minutes) x 1.2 (delivery rate) = 9 houses). Thus, the method is correct, and in it, 1.2 represents the unit rate, this is why even when it is not possible to deliver to 1.2 houses all the process is correct.

Answer:

c

Step-by-step explanation:

i took the test

Answer:

[tex]\fbox{\begin{minipage}{8em}Not a solution\end{minipage}}[/tex]

Step-by-step explanation:

Step 1: Consider the assumption:

Generally, [tex](6, 7)[/tex]) is supposed to be the pair of 2 components, in which, the first component is x-component (domain), the second component is y-component (range).

Hence, [tex]x = 6, y = 7[/tex]

Step 2: Substitute [tex]x[/tex] and [tex]y[/tex] into the inequality

       [tex]y > 2x - 5[/tex]

<=>  [tex]7 > 2*6 - 5[/tex]

Step 3: Simplify

<=>  [tex]7> 12 - 5[/tex]

<=>  [tex]7 > 7[/tex]

Step 4: Evaluate

Invalid

Reason: [tex]7 = 7[/tex]

Step 5: Conclude

[tex](6, 7)[/tex] is not a solution to the inequality [tex]y > 2x - 5[/tex]

Hope this helps!

:)

Question:

It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products to find a defective product?

Answer:

P(x = 6) = 0.0655

P(x = 6) = 6.55%

Step-by-step explanation:

It is given that 20% of products on a production line are defective.

p = 0.20

Then

q = 1 - p = 1 - 0.20 = 0.80

Which means that 80% of products on the production line are not defective.

We want to find out the probability that the experimenter must inspect six products to find a defective product.

Let x is the number of inspections to get a defective product.

P(x = 6) = ?

If out of 6 inspections 1 is defective then it means 5 are not defective

so the probability is

P(x = 6) = p¹ × q⁵

P(x = 6) = 0.20¹ × 0.80⁵

P(x = 6) = 0.20 × 0.32768

P(x = 6) = 0.0655

P(x = 6) = 6.55%

Therefore, there is 6.55% chance that the experimenter finds a defetive product in 6 inspections.

Answer:

Laniece had 60 magazines

Step-by-step explanation:

Given: In the  first week, Tamia sold 30% more than Laniece. In the second  week, Tamia sold 12 magazines, but Laniece did not sell any. Tamia sold 50% more than Laniece by the end of the second  week

To find: Number of magazines sold by Laniece

Solution:

Let number of magazines sold by Laniece in the first week be x.

Number of magazines sold by Tamia in the first week = [tex]x+\frac{30}{100} x=\frac{130x}{100} =\frac{13x}{10}[/tex]

Number of magazines sold by Tamia in the second week = 12

Total number of magazines sold by Tamia at the end of the second week = [tex]\frac{13x}{10}+12[/tex]

Total number of magazines sold by Laniece at the end of the second week = x

According to question,

[tex]\frac{13x}{10}+12=x+\frac{50x}{100}=x+\frac{x}{2}\\\frac{13x}{10}+12=\frac{3x}{2}\\\frac{3x}{2}-\frac{13x}{10} =12\\\frac{15x-13x}{10}=12\\\frac{2x}{10}=12\\\frac{x}{5}=12\\x=60[/tex]

Answer:

answer for the question is 130 length

Answer:

for the 9th it is 39 for the 150th it is 607

Answer:

height = 6 mm

Step-by-step explanation:

The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.

The height of the prism can be solved as follows.

Volume of the rectangular prism = Bh

where

B = base area

h = height

Volume = 144 mm³

B = 24 mm²

volume = Bh

144 = 24 × h

144 = 24h

divide both sides by 24

h = 144/24

h = 6 mm

Answer:

c

Step-by-step explanation:

edg 2022

Answer:

1, 3, 5, 6

Step-by-step explanation:

Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16

The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.

The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.

In other words, these percentages are less than 30% and can be rightly represented by the variable s.

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Answer:

1. B

Step-by-step explanation:

1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A

2. The level of significance is 1% (99% confidence interval)

3. The null hypothesis: u = 0.8

Alternative hypothesis: u =/ 0.8

4. a. The Student's t, since we assume that x has a normal distribution with known σ

5. Using the formula t = (x - u) / σ√n

Where x = 1.22 u = 0.8 σ = 0.44 n = 9

t = (1.22-0.8) / 0.44√9

t = 0.42/(0.44x3)

t = 0.42/1.32

t = 0.318

P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.

Answer:

Step-by-step explanation:

From the question; we are given the following inclusive frequency distribution information

Class                Frequency f

1.1-1.5                           18

1.6-2.0                         27

2.1-2.5                         31

2.6-3.0                        40

3.1-3.5                         56

3.6-4.0                        55

4.1-4.5                          23

Convert the above inclusive frequency distribution to exclusive frequency distribution with respect of the upper and lower class limit ; we have:

Class                             Frequency f

1.05 - 1.55                             18

1.55 - 2.05                           27

2.05 - 2.55                          31

2.55 - 3.05                          40

3.05 - 3.55                          56

3.55 - 4.05                          55

4.05 - 4.55                          23

Class                             Frequency f                     cf

1.05 - 1.55                             18                              18            

1.55 - 2.05                           27                               45

2.05 - 2.55                          31                               76

2.55 - 3.05                          40                               116

3.05 - 3.55                          56                               172

3.55 - 4.05                          55                               227

4.05 - 4.55                          23                               250

                                       n = 250

To determine the daily sales; we can derive that from estimated Mode by using the relation :

Estimated Mode = L + fm − fm-1(fm − fm-1) + (fm − fm+1) × w

here:

L  = the lower class boundary of the modal group

fm-1 =  the frequency of the group before the modal group

fm = the frequency of the modal group

fm+1 = the frequency of the group after the modal group

w  = the group width

However;

It is easier now to determine  the modal group (i.e the group with the highest frequency), which is 3.05 -3.55

L = 3.05

fm-1 =40

fm =56

fm+1 = 55

w = 0.5

∴[tex]mode = 3.05 + \dfrac{56 - 40 }{(56 - 40) + (56 -55)} * 0.5 \\ \\ mode = 3.05 + 0.4705 \\ \\ mode = 3.5205[/tex]

To find Median Class ; we use the formula;

Median Class = value of (n / 2)th observation

Median Class  = value of (250 / 2)th observation  

Median Class = value of 125th observation

From the column of cumulative frequency cf,

we will see that the 125th observation lies in the class 3.05-3.55.

∴ The median class is 3.05-3.55.

Thus;,  

L=lower boundary point of median class =3.05

n=Total frequency =250

cf=Cumulative frequency of the class preceding the median class =116

f=Frequency of the median class =56

c=class length of median class =0.5

[tex]Median M=L+n2-cff- c \\ \\ =3.05+125-11656⋅0.5 \\ \\=3.05+0.08036 \\ \\ =3.13036[/tex]

hence median sales = $3130.36

Answer:

1/4

Step-by-step explanation:

625^x = 5

x = 1/4