Part B
Next, rewrite the exponential expression using factors of 8 so that the base of the equation is a product of two factors, with one factor being a perfect square.

Answer:

Step-by-step explanation:

Total Females = 3 + 4 + 6 + 3  = 16

Number of female seniors = 3

P ( Female | senior )

number of female seniors / total female  = [tex]\frac{3}{16}[/tex]

In percent,

[tex]\frac{3}{16}[/tex] · 100 = 0.1875 · 100 = 18.75%

18.75% rounded to nearest whole percent is 19%

The required probability is 3/4= 75%, the probability the student is a senior given that it's female.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

here, we have,

We have to compute the probability,

P(Female |Junior) because we have to find the probability of the female student and the given condition is that the student is junior.

Determine the total number of juniors. Juniors=2+6=8

Since the number of females who are junior is 6, determine the required probability.

P(Female|Junior)=6/8=3/4

Therefore, the required probability is 3/4 = 75%

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Answer:

#3

What was the area left unpainted?

Option D

#4

How big is Ben's share?

Option A

#5

The area of a circular pool whose radius is 2 m:

Option A

Answer:

sqrt(3)

Step-by-step explanation:

Each side (donated by small letter ) is opposite to its angle for example :

Side c is opposite to angle C which is 90

side b is opposite to angle B which is 60

Answer:

Nope

Step-by-step explanation:

Standard form for a linear equation in two variables is [tex]Ax+By=C[/tex] with the terms containing  x  and  y  on the left side of the equation and a number on the right side.

[tex]x+3=-5y[/tex]

Subtract 3 from both sides.

[tex]x=-5y-3[/tex]

Add 5y.

[tex]x+5y=-3[/tex]

Answer: Not possible

Step-by-step explanation: A whole number is an integer or a number without fractions. Both 15% and 40% are less than 1 since they are less than 100%; therefore, it is impossible to express them as whole numbers. They can only be expressed as the mixed numbers of 0.15 and 0.4, or 15/100 and 40/100.

As a result, we take the square root of the both sides since if two expressions are equal, then so are their square roots.

By multiplying the square root of a positive integer by oneself, the number is obtained. As an illustration, 5 is the square root of 25, since 5 × 5 equals 25. Since (5) (5) = 25, 5 is also the square root of 25 as you can see. The symbol, which is, is always used to indicate the square root of a number of a variable x.

Here,

In this case, we're using the square to solve a quadratic equation.

Never forget to use both the negative and positive roots of the equation and to square the values of both sides.

We can accomplish this because to the rule that states that if two expressions are comparable, then their square roots are also equivalent.

As a result, we take the square root of both sides since if two expressions are equal, then so are their square roots.

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Explanation:

I'm assuming your teacher meant to say "same number or letter" instead of "same number of letter" at the very end of the problem.

The best case scenario is that the person selecting the cards is very lucky to select say a king of hearts and king of clubs. This shows that 2 cards is the lowest amount of cards to select here.

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Of course, such a scenario is not that likely. That person is likely to get some other card compared to the 1st selection.

Let's assume the person selecting the cards has the worst luck possible. This means they select each card 1,2,3,...,10,J,Q,K exactly once in any order. If this happens, then the person does not have any pairs just yet. The person has selected 13 cards so far with this worst case scenario.

The 14th card is guaranteed to pair up with some other card previously chosen. There simply aren't any other options left once you've exhausted all possibilities. See the pigeonhole principle for more information.

So this is why you would need to select 14 cards to guarantee having at least two pair up together (i.e. you would have 2 or more pairs).

Answer:

See below

Step-by-step explanation:

Because it's an inequality, the upside-down parabola has dashed lines instead of a sold line. Additionally, only one side of that parabola will contain the solution set, which we can easily figure out by testing a point like (0,0):

[tex]0\stackrel{?}{ > }-3(0)^2-30(0)-48\\0\stackrel{?}{ > }-48\\\\0 > -48 \text{ is true}[/tex]

Hence, the side that contains (0,0) gets shaded. See the graph below.

Explanation:

Multiply each coordinate, of each point, by the scale factor -1/3. That means for instance x = 3 becomes x = -1, when going from P to P'. Doing this will shrink the image, and there's also a reflection going on due to the negative scale factor.

On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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Answer:

23 I thinkkkkkkkkkkkkkkkkkkkkkkkkk

Step-by-step explanation:

ehhhhh

Answer:

46

Step-by-step explanation:

Since we are finding multiples of 2, but avoiding multiples of 4, we need to skip 4 from every 2 digit multiple starting from 10 (10, 14, 18, 22, so on...). BUT. I'm not finished yet. The answer is NOT 23. Why? Well, you forgot about the negative 2-digit multiples.

Do the same (Skip NEGATIVE 4 from every 2 digit multiple, but starting from -10, -10, -14, so on...)

Doing this, I found:

46 multiples of 2, but not 4

Multiples:

10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, -98, -94, -90, -86, -82, -78, -74, -70, -66, -62, -58, -54, -50, -46, -42, -38, -34, -30, -26, -22, -18, -14, -10

The measure of the two angles, one positive and one negative, that are coterminal with -90° and closer to it than any other coterminal angle, is 270° and -450° respectively.

Given that angle is - 90°.

For the coterminal angles that are closer to -90° than any other coterminal angle, consider angles that have the same initial and terminal sides as -90°.

Since -90° is in the fourth quadrant, look for angles that also fall in the fourth quadrant.

One positive coterminal angle in the fourth quadrant would be 270°.

This angle is closer to -90° than any other coterminal angle in the fourth quadrant.

One negative coterminal angle in the fourth quadrant would be -450°.

This angle is also closer to -90° than any other coterminal angle in the fourth quadrant.

So, the measure of the two angles, one positive and one negative, that are coterminal with -90° and closer to it than any other coterminal angle, is 270° and -450° respectively, both in the fourth quadrant.

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Answer:

Measure of Hypotenuse is 7.8 cm.

Step-by-step explanation:

Since the triangle is a right angle, the formula we would use is [tex]a^2 + b^2 = c^2[/tex].

We are looking for the hypotenuse that would be c.

[tex]a^2 + b^2 = c^2[/tex]

[tex]5^2 + 6^2 = c^2[/tex]

[tex]25 + 36 = c^2[/tex]

[tex]61 = c^2[/tex]

[tex]\sqrt{61} = \sqrt{c^2}[/tex]

7.8102 = c

c = 7.8 cm

Answer:  [tex]g(x) = \frac{1}{x-6} - 4[/tex]

This can be written out as g(x) = 1/(x-6) - 4

The "x-6" is in the denominator, while the "-4" is not.

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Explanation:

We'll start with the parent function [tex]f(x) = \frac{1}{x}[/tex]

When we shift 4 units down, we're subtracting 4 from the y coordinate of each point on the curve. Which is the same as subtracting 4 from f(x) because y = f(x).

So we have [tex]h(x) = f(x) - 4 = \frac{1}{x} - 4[/tex] as an intermediate step.

Then to shift 6 units to the right, we'll replace every x with "x-6". Imagine we kept the h(x) curve completely still, and instead we moved the xy axis 6 units to the left. This would give the illusion of h(x) moving 6 units to the right if we made the xy axis stay still. So that's why we go for "x-6" instead of "x+6".

Therefore, we end up with [tex]g(x) = \frac{1}{x-6} - 4[/tex]

Side note: plugging in x = 6 leads to a division by zero error. This would mean x = 6 is not in the domain.

Answer:

it's B

[tex] - \frac{9}{4} + 2i = - \frac{9}{4} - 4i[/tex]

Answer:

C

Step-by-step explanation:

please refer to the sketch

Answer: To model the problem with a division equation, we can write 46 ÷ 7 = x, where x represents the number of swimmers that each lane will have.

To solve the equation using repeated subtraction, we can subtract 7 from 46 several times until we reach a number that is less than 7. The number of times we subtract 7 will give us the number of swimmers each lane will have. Here's one way to do it:

46 - 7 = 39

39 - 7 = 32

32 - 7 = 25

25 - 7 = 18

18 - 7 = 11

11 - 7 = 4

As you can see, we are able to subtract 7 from 46 a total of 6 times before we get a number less than 7. This means that each lane will have 6 swimmers, and the remaining 4 swimmers will practice diving. So each lane will have 6 swimmers.

So the equation 46 ÷ 7 = 6, and also by repeated subtraction method it shows the same result of 6 swimmers each lane.

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

As a straight line is equal to 180. Here, we have one angle given, which is 134. So,

w+134=180

w=46

And the sum of all the angles of a triangle is equal to 180.

By adding all the angles,

8x-10+5x-12+46=180

13x-22+46=180

13x+24=180

13x=180-24

13x=156

x=156/13

x=12

Step-by-step explanation:

➝8x-10+5x-12=134

➝8x+5x-10-12=134

➝13x-22=134

➝13x=134+22

➝13x=156

➝x=156/13

➝x=12

The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

Given, A function f(x) = x².

Now, p(x) = f(x + 3).

p(x) = (x + 3)² and it is a transformed function to the parent function f(x).

Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.

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On solving the provided question, we cans ay that - here in triangles, triangle ABC is congruent to triangle A`B`C`

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

Here,

two triangles are there

triangle ABC and triangle A`B`C`

AB =A`B`

BC = B`C`

AC =A`C`

So, by sss property

both are congruent

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Answer:4.8

Step-by-step explanation:

30/3 x 1.6

Answer:

True

Step-by-step explanation:

6 * 4/6 = 24 /6 = 24 * 1/6 = 4

This is  a true statement

Answer:

(19,1/2)

Step-by-step explanation:

you can put any number in the x coordinate as long as y is the same .

Step-by-step explanation:

a) x+20+x+90=180 [sum of 3 angel of triangle]

2x + 110 = 180

2x = 180- 110

2x = 70

x = 70÷2

x = 35

b) 2y + y + y = 180

4y = 180

y = 180÷4

y= 45

c) 4z-30 + 2z = 180

6z = 180 + 30

6z = 210

z = 35

Answer:

A) Technically he/she can, but they shouldn't really.

B) Yes

C) Yes

D) Yes he/she can but is not necessary to solve the equation

E) Yes