what is the equation of the line that passes through (-3,-1) and has a slope of 3/5 ​

62 plus 48 is 110

Then add everyone together to find the total 62+48+36 which is 152

110 over 152 is the probability that a person selected at random will be a doctor or woman

Hope this helps;)

The probability that a person at random from the conference is either a doctor or a woman (or both) is 74%, computed from the principle of inclusion and exclusion.

The probability of a person at the conference being a Doctor or a Woman (or both) can be found by adding the individual probabilities - that of being a woman and that of being a doctor - and subtracting the probability of being both a doctor and a woman because this is counted twice in the addition. This is called the principle of inclusion and exclusion in probability theory. So by substituting the given percentages, P(Doctor or Woman) = P(Doctor) + P(Woman) - P(Doctor and Woman) = 62% + 48% - 36% = 74%. So, the probability that a person chosen at random from the conference is either a doctor or a woman (or both) is 74%.

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Answer:

2(3x + 7)(2x - 1)

Step-by-step explanation:

You can see it a little easier if you take out a common factor of 2

2(6x^2 + 11x - 7)

The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.

Let 6 factor into 2 and 3 and the 7 into 7 and 1

2(3x - 1 )(2x + 7)

Now remove the brackets.

2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.

2(6x^2 + 19x - 7)

So we'll try it again

2(3x + 7)(2x - 1)

2(6x^2 + 14x - 3x - 7)    Looks like we have it.

2(6x^2 + 11x - 7)

So the right factors are

2(3x + 7)(2x - 1)

Answer:

P = 76%

Step-by-step explanation:

We look for the percentage of employees who are at least 25 years old.

We know that:

μ = 32 years

[tex]\sigma = 10[/tex] years

And we want to find

[tex]P(X\geq25) [/tex]

Then we find the z-score

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

So

[tex]Z = -0.7[/tex]

Then

[tex]P (X\geq25) = P(\frac{X- \mu}{\sigma}\geq\frac{25-32}{10})\\\\\P (X\geq25) = P (Z\geq -0.7)[/tex]

By symmetry of the distribution

[tex]P(Z\geq -0.7)= 1-P(Z<-0.7)[/tex]

[tex]P(Z\geq -0.7)= 1-0.242[/tex]

Looking in the normal standard tables

[tex]P(Z\geq -0.7)= 0.758[/tex]

Finally P = 76%

45% :) Step-by-step explanation:

In this diagram, there are a total of 20 squares, and 9 of them are shaded. This means that 9/20 of them are shaded, and to find what percent this is, divide 9 by 20 and multiply what you get by 100.

9 divided by 20 =0.45

0.45 x 100 = 45%.

45% is your final answer!

I hope this helps and have a great rest of your day!

Answer:

Step-by-step explanation:

To find the equation of directrix of the parabola, we need to identify the axis of the parabola i.e, parabola lies in x-axis or y-axis.

We have 4 parts in this question i.e.

For each part the value of directrix will be different.

For x²  = 12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = -a

So, we need to find the value of a.

The general form of equation for y-axis parabola having positive co-efficient is:

x² = 4ay  eq(i)

and our equation in question is: x² = 12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

4ay = 12y

a= 12y/4y

a= 3

Putting value of a in equation of directrix: y = -a => y= -3

The equation of the directrix of the parabola x²= 12y is y = -3

For x²  = -12 y

The above equation involves x² , the axis will be y-axis

The formula used to find directrix will be: y = a

So, we need to find the value of a.

The general form of equation for y-axis parabola having negative co-efficient is:

x² = -4ay  eq(i)

and our equation in question is: x² = -12y eq(ii)

By putting value of x² of eq(i) into eq(ii) and solving:

-4ay = -12y

a= -12y/-4y

a= 3

Putting value of a in equation of directrix: y = a => y= 3

The equation of the directrix of the parabola x²= -12y is y = 3

For y²  = 12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = -a

So, we need to find the value of a.

The general form of equation for x-axis parabola having positive co-efficient is:

y² = 4ax  eq(i)

and our equation in question is: y² = 12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

4ax = 12x

a= 12x/4x

a= 3

Putting value of a in equation of directrix: x = -a => x= -3

The equation of the directrix of the parabola y²= 12x is x = -3

For y²  = -12 x

The above equation involves y² , the axis will be x-axis

The formula used to find directrix will be: x = a

So, we need to find the value of a.

The general form of equation for x-axis parabola having negative co-efficient is:

y² = -4ax  eq(i)

and our equation in question is: y² = -12x eq(ii)

By putting value of y² of eq(i) into eq(ii) and solving:

-4ax = -12x

a= -12x/-4x

a= 3

Putting value of a in equation of directrix: x = a => x= 3

The equation of the directrix of the parabola y²= -12x is x = 3

Answer:

The father is 40 and the son is 4.

Step-by-step explanation:

40 + 5 = 45.

4 +5=9.

45 divided by 5 = 9

Answer:

The father is 40 and the son is 4.

Step-by-step explanation:

Answer:

1/64x^12

Step-by-step explanation:

Answer: x^12/64

Step-by-step explanation:

Apply exponent rule: a^-b = 1/a^b

(4x^-4)^-3 = 1/(4x^-4)^3 : 64/x^12

= 1/64/x^12

Apply the fraction rule: 1/b/c = c/b

=x^12/64

Answer:

y ≥ 3x +4

Step-by-step explanation:

The line is solid, so the inequality will include the "or equal to" case. The shading is above the line, so values of y greater than or equal to those on the line are in the solution set. The only choice with the correct (≥) inequality symbol is ...

y ≥ 3x +4

Answer:

2x2,2+2=4

Step-by-step explanation:

2*2=4

2+2=4

Answer:

[tex]a_n=a_{n-1}+16[/tex]

Step-by-step explanation:

The given arithmetic sequence is

14,30,46,62

The first term of this sequence is

[tex]a_1=14[/tex]

The common distance is obtained by subtracting a subsequent term from a previous term;

d=30-14

The common difference is

d=16

The recursive formula is given by:

[tex]a_n=a_{n-1}+d[/tex]

We now plug in the known value for the common difference to get;

[tex]a_n=a_{n-1}+16[/tex]

The recursive formula for the arithmetic sequence 14, 30, 46, 62 is an = aₙ₋₁ + 16 with the initial term a₁ = 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In this case, we have the sequence: 14, 30, 46, 62.

Step-by-Step Process

1. Determine the common difference (d) by subtracting the first term from the second term:

2. Using the first term (a1) and the common difference (d), we can now write the recursive formula.

Therefore, each subsequent term is obtained by adding 16 to the previous term.

the answer is A multiply 3x2 and multiply 4x3 then add hope that helps

Answer:

A

Step-by-step explanation:

It is asking for the total amount of miles the boys walked therefore addition for step 3.

Answer: The answer to the first question is C(20%)

Step-by-step explanation: 1. you need to find the absolute decrease which is subtracting 350-280= 70.

2. now you need to find the percent decrease which is dividing the absolute decrease by the whole price.. so.. 70/350= .20

3. now just multiply .20 *100 = 20%

Since we're trying to find out how much the price was reduced by, first you will do this

[tex]350 - 280 = 70[/tex]

The price was dropped by $70.

Then we find out how much $70 is of the original price which is 350

[tex]70 \div 350 = 0.2[/tex]

Then you convert 0.2 into a percentage which is 20%.

The price of the digital camera was reduced by 20%.

Answer:

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the equation:

[tex]x^2+y^2=2[/tex]

Convert to the standard form:

[tex](x-0)^2+(y-0)^2=(\sqrt2)^2[/tex]

State the center and radius of x^2+y^2=2

solution

-4t < 12 3t-15<-3

-4 -4 3t<-3+15

t>-3 3t<12

3 3

t<4

therefore the numbers that makes both equations right is -3<t<4

Answer:

t<4

dont worry its right

ANSWER

[tex]2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]

EXPLANATION

The complex number given to us is in the polar form,

32(cos 280° + i sin 280°)

The fifth root is

[tex] {32}^{ \frac{1}{5} } ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]

This is equal to:

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } [/tex]

According to the DeMoivre's Theorem,

[tex]( { \cos \theta \: \degree + i \sin\theta \degree) }^{ \frac{p}{q} } = ( { \cos \frac{p}{q} \theta \degree + i \sin \frac{p}{q} \theta \degree) }[/tex]

We now use the DeMoivre's Theorem to obtain:

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: \frac{1}{5} \times 280 \degree + i \sin \:\frac{1}{5} \times 280 \degree) }[/tex]

[tex]2 ( { \cos280 \degree + i \sin280 \degree) }^{ \frac{1}{5} } = 2 ( { \cos \: 56 \degree + i \sin \:56 \degree) }[/tex]

Answer:

YOur answer would be -1/5.

Step-by-step explanation

rise/run

-4--5/-2-3

=-1/5

For this case we have by definition, that the slope of a line is given by:

 the following formula:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

Having two points through which the line passes:

[tex](x_ {1}, y_ {1}): (- 2, -4)\\(x_ {2}, y_ {2}) :( 3, -5)[/tex]

Substituting:

[tex]m = \frac {-5 - (- 4)} {3 - (- 2)}\\m = \frac {-5 4} {3 2}\\m = \frac {-1} {5}[/tex]

Finally, the slope of the line is:

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

Answer:

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

Answer:

The arc PS would be a minor arc

Step-by-step explanation:

As a minor arc is one that is less that 180 degrees, it would be the only viable solution.

Line SO is not an arc, so it cannot be chosen

the measures of arcs SQ and PSR are each 180 degress, so they would not be minor.

The arc which is a minor arc  is:

                      Arc PS.

Minor arc--

A minor arc is a arc which subtend an angle of measure less than 180 degree in the center.

i.e. such a arc should be smaller than a semicircle.

1)

Arc SQ

This arc subtend an angle of 180 degree in the center,

This means it is a semicircle and not a minor arc.

2)

arc PSR

This is again a semicircle and not a minor arc.

Since  PR is the diameter of the circle and hence the arc so formed will be a semicircle.

3)

arc PS

The angle subtended at the center of the circle by this arc is less than 180 degree and hence it is a minor arc.

4)

Line SO

O is the center of the circle and S is a point on the circumference of the circle and hence it denotes the radius of the circle.

Answer:

The answer is C! I just took the quiz and got 100% shout out to all the cheaters out there, let's get this E2020 bread!

The percentage profit on a wheelbarrow is 512%

The percentage profit of an item is the amount of profit when the item is sold, expressed in terms of percentage

The selling price is given as:

SP = $42.50

The cost price is given as:

CP = $6.94

The percentage profit is then calculated as:

[tex]Profit = \frac{SP - CP}{CP} * 100\%[/tex]

This gives

P = (42.50 - 6.94)/6.94 * 100%

Evaluate the difference

P = 35.56/6.94 * 100%

Evaluate the quotient

P = 5.12 * 100%

Evaluate the product

P = 512%

Hence, the percentage profit on a wheelbarrow is 512%

Read more about percentage profit at:

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Answer:

x = 5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

15x-30=45

    +30 +30

 15x=75

15/15=1

75/15=5

x=5

Quick answer, it's B.

For this case we must rationalize the following expression:

[tex]\frac {2 \sqrt {5}} {- 3 \sqrt {50}}[/tex]

Multiply the numerator [tex]\sqrt {50}:[/tex]

[tex]\frac {2 \sqrt {5} * \sqrt {50}} {- 3 \sqrt {50} * \sqrt {50}} =\\\frac {2 \sqrt {5 * 50}} {- 3 (\sqrt {50}) ^ 2} =\\\frac {2 \sqrt {250}} {- 3 * 50} =\\\frac {2 \sqrt {250}} {- 150}[/tex]

Answer:

Option B

Answer:

320in^3

Step-by-step explanation:

V=lwh/3

V=(10)(8)(12)/3

V=960/3

V=320

For this case we have by definition, that the volume of a rectangular pyramid is given by:

[tex]V = \frac {a * b * h} {3}[/tex]

Where:

a, b: Are the sides of the rectangular base

h: It's the height of the pyramid

Substituting the values:

[tex]V = \frac {10 * 8 * 12} {3}\\V = \frac {960} {3}\\V = 320[/tex]

Thus, the volume of the pyramid is 320 cubic inches

Answer:

[tex]320 \ in ^ 3[/tex]

Answer:

P = 73%

Step-by-step explanation:

We look for the percentage of employees who are not more than 40 years old.

This is:

[tex]P = \frac{x}{n} *100\%[/tex]

Where x is the number of new employees who are not over 40 years old and n is the total number of new employees.

We do not know the value of x or n. However, the probability of randomly selecting an employee that is not more than 40 years old is equal to [tex]P = \frac{x}{n}[/tex]

Then we can solve this problem by looking for the probability that a new employee selected at random is not more than 40 years old.

This is:

[tex]P(X< 40)[/tex]

Then we find the z-score

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

We know that:

μ = 34 years

[tex]\sigma = 10[/tex] years

So

[tex]Z = 0.6[/tex]

Then

[tex]P (X<40) = P (\frac{X- \mu}{\sigma} < \frac{40-34}{10})\\\\P(X<40) = P(Z<0.6)[/tex]

So we have

[tex]P(Z<0.6)[/tex]

Looking in the normal standard tables:

[tex]P(Z<0.6)=0.726[/tex]

Finally P = 73%

Answer:

D. [tex]x>0[/tex]

Step-by-step explanation:

We have been given a quotient [tex]\sqrt{6x^2}\div\sqrt{4x}[/tex]. We are asked to find an inequality that represents all values of x for which the quotient below is defined.

We can rewrite our given expression as:

[tex]\sqrt{6x^2}\div\sqrt{4x}[/tex]

We know that a square root expression is defined for all values of x greater than or equal to 0. We also know that a fraction is defined when its denominator is greater than 0.

So our fraction will be defined for all values of x greater than 0.

[tex]4x>0[/tex]

Upon dividing both sides of our inequality by 4, we will get:

[tex]\frac{4x}{4}>\frac{0}{4}[/tex]

[tex]x>0[/tex]

Therefore, the inequality [tex]x>0[/tex] represents all values of x for which the given quotient is defined and option D is the correct choice.

Answer: 1/16=1/4*1/4

              125=5*5*5

               24= (2*6)*2

               125= 5*5*5

Step-by-step explanation:

They can be described as a horizontal movement, a vertical movement, or a combination of the two (horizontal and vertical.)

Answer: three type of life cycles are Haploid life cycle,Diploid life cycle, and alternation of generations.

The three main life cycles in multicellular organisms are the haploid life cycle, found in some fungi and algae, the diploid life cycle, common in animals like humans, and the alternation of generations, seen in plants and some algae. Insects may undergo complete metamorphosis, with distinct life stages.

Types of Life Cycles in Multicellular Organisms

There are three main types of life cycles in multicellular organisms, which are characterized by the prominence of either the haploid or diploid stages and the process of alternation between these stages. In the haploid life cycle, organisms spend most of their life in the haploid state, such as many single-celled eukaryotes. Fertilization briefly produces a diploid zygote, which immediately undergoes meiosis to form new haploid gametes. An example of this life cycle can be found in certain fungi and algae.

The diploid life cycle is where organisms spend the majority of their lives as diploid individuals. Here, only the gametes are haploid. Most animals, including humans, follow this type of life cycle.

The alternation of generations life cycle is characterized by alternating haploid and diploid stages. This is common in plants and some types of algae. The diploid stage, called the sporophyte, produces haploid spores by meiosis that develop into the haploid stage, known as the gametophyte, which in turn creates haploid gametes. Fertilization of these gametes will result in a new sporophyte, continuing the cycle.

In summary, sexual reproduction leads to varying life cycle types based on the dominancy and alternation of haploid and diploid stages, each vital for the propagation and genetic diversity of species.

Additionally, in the context of insects, which undergo distinct transformations, there are three types of metamorphosis: no metamorphosis, gradual metamorphosis (or incomplete), and complete metamorphosis. Most insects, such as butterflies, undergo complete metamorphosis, exhibiting different forms at each stage of their life cycle: egg, larva, pupa, and adult.

Answer:

x = 5/3

Step-by-step explanation:

We have the fifth root of 8^3 and we want it equal to 8

(8^3) ^ (1/5) ^x = 8

We know that a^b^c = a^ (b*c)

8 ^ (3*1/5x) = 8

8 ^ (3/5x) = 8

We can rewrite 8 as 8^1

8 ^ (3/5x) = 8^1

The exponents must be the same

3/5 x = 1

Multiply each side by 5/3 to isolate x

5/3 * 3/5x = 1 * 5/3

x = 5/3

Answer:

(6, -11)

Step-by-step explanation:

The translation (x-2,y+3) means "subtract 2 from x coordinate" and "add 3 to the y coordinate".

After the transformation, we have the point B'(4,-8). Which point, let it be (x,y), after being transformed is B'(4,-8)??

According to the transformation rule, we have to "subtract 2 from x coordinate" and "add 3 to the y coordinate", thus

x-2=4

x=4+2

x=6

and

y+3=-8

y=-8-3

y=-11

THe coordinate of B are (6,-11)

Answer:

60x + 18

Step-by-step explanation:

8x - 4 [2x - 5 ( 3x + 1 )] - 2 [x - (x - 1)]

distribute

8x - 4 [2x - 15x - 5] - 2 [x - x + 1]

combine like-terms

8x - 4 [- 13x - 5] - 2 [1]

distribute again

8x + 52x + 20 - 2

combine like-terms again

60x +18

Answer:

[tex]y-12=13(x-15)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=13[/tex]

[tex](x1,y1)=(15,12)[/tex]

substitute

[tex]y-12=13(x-15)[/tex] -----> equation of the line into point slope form

Answer:

Y-12=13(x-15)

Step-by-step explanation: