A box contains 6 red index cards, 3 yellow index
cards, and 4 green index cards. If Gabriella pulls out
2 cards at random from this box, without replace-
ment, what is the probability that both cards are
not green?

Answer:

Gradient of A: 2

Gradient of B: -1

Step-by-step explanation:

Gradient = change in y/change in x

✔️Gradient of A using two points on line A, (2, 5) and (0, 1):

Gradient = (1 - 5)/(0 - 2) = -4/-2

Simplify

Gradient of A = 2

✔️Gradient of B using two points on line B, (0, 5) and (5, 0):

Gradient = (0 - 5)/(5 - 0) = -5/5

Simplify

Gradient of B = -1

Answer:

i believe its 162

Step-by-step explanation:

hope it helped :>

Answer:

13.97%

Step-by-step explanation:

Find her percent increase in pay by dividing 95 by 680:

95/680

= 0.1397

Multiply this by 100:

= 13.97

So, her percent increase in pay is approximately 13.97%

Answer:

5% = 1/20

15% = 3/20

6.5% = 0.065

25% = 0.25

7% = 0.07

Step-by-step explanation:

I hope this helps! Just ask me if you have any questions.

Have a nice dayy! :)

Answer:

.05  25%  .15  7% .065  100% 2000% .25

Step-by-step explanation:

Percentages to decimals :

example  

5% = .05

First remove the % sign: 5

Where is the decimal? Here : 5.00

Now move the decimal to the left two places. Fill the gaps with zeros : .05

Another way to do it is by divide the number by 100. Use a calculator if necessary.

Example 2: 6.5%

Move decimal two places to left: .065

Example 3: .56%

Move decimal to places to the left:  .0056

Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.

Example: .25 becomes 25%

                .07 becomes 07% or just 7%

Answer:

x = 6

HI = 29

Step-by-step explanation:

✔️HI = ½(AB) => Triangle Mid-segment Theorem

HI = 5x - 1

AB = 58

Plug in the values and solve for x

5x - 1 = ½(58)

5x - 1 = 29

Add 1 to both sides

5x - 1 + 1 = 29 + 1

5x = 30

Divide both sides by 5

5x/5 = 30/5

x = 6

✔️HI = 5x - 1

Plug in the value of x

HI = 5(6) - 1

HI = 30 - 1

HI = 29

Answer:

0.4 or 0.40

Step-by-step explanation:

There are 10 total numbers. 4 of them are in set B.

So, 4/10 are in set B.

The probability is 0.4 because 4 divided by 10 is 0.4.

Answer:

true

Step-by-step explanation:

complementary angles equal 90° and 34+56 is 90°

Answer:

True

Step-by-step explanation:

Complement angle means that the two angles add up to 90 degrees. We can check this by adding the two given angles together:

34+56=90

90=90

This means that this is true.

I hope this helps and have a great day!

Answer: 8

Step-by-step explanation:

Answer:

x = [tex]\frac{3}{20}[/tex]

Step-by-step explanation:

Given

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

Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10x + 15 + 10(x - 1) = 8

10x + 15 + 10x - 10 = 8

20x + 5 = 8 ( subtract 5 from both sides )

20x = 3 ( divide both sides by 20 )

x = [tex]\frac{3}{20}[/tex]

x + 3/2 + x - 1 = 4/5

Collect the same terms

x + x + 3/2 - 1 = 4/5

2x + 3/2 - 2/2 = 4/5

2x + (3 - 2)/2 = 4/5

2x + 1/2 = 4/5

2x + 0.5 = 0.8

Subtract both sides 0.5

2x + 0.5 - 0.5 = 0.8 - 0.5

2x + 0 = 0.3

2x = 3/10

Divide both sides by 2

2x ÷ 2 = ( 3/10 ) ÷ 2

x = 3/10 × 1/2

x = 3/20

_________________________________

3/20 + 3/2 + ( 3/20 - 1 ) = 4/5

3/20 + 30/20 + ( 3/20 - 20/20 ) = 4/5

(3 + 30)/20 + (3 - 20)/20 = 4/5

33/20 - 17/20 = 4/5

(33 - 17)/20 = 4/5

16/20 = 4/5

4 × 4 / 4 × 5 = 4/5

4/5 = 4/5

Thus we found the correct value of x .

And we're done...

Answer:

[tex]\displaystyle x=-\frac{2}{3}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]

We can isolate the square root. Subtract x from both sides:

[tex]\sqrt{x^2-4x+8}=2-2x[/tex]

And square both sides:

[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]

Expand:

[tex]x^2-4x+8=4-8x+4x^2[/tex]

Isolate the equation:

[tex]3x^2-4x-4=0[/tex]

Factor:

[tex]\displaystyle (3x+2)(x-2)=0[/tex]

Zero Product Property:

[tex]3x+2=0\text{ or } x-2=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]

Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.

Testing x = -2/3:

[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]

Since the resulting statement is true, x = -2/3 is indeed a solution.

Testing x = 2:

[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]

Since the resulting statement is not true, x = 2 is not a solution.

Therefore, our only solution to the equation is x = -2/3.  

Step-by-step explanation:

Hey there!

Given;

[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]

Take "X" in right side.

[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]

Squaring on both sides;

[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]

Simplify;

[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]

[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]

[tex]3 {x}^{2} - 4x - 4 = 0[/tex]

[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]

[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]

[tex]3x(x - 2) + 2(x - 2) = 0[/tex]

[tex](3x + 2)(x - 2) = 0[/tex]

Either;

3x+2 = 0

x= -2/3

Or;

x-2 = 0

x= 2

Check:

Keeping X= -2/3,

√(x²-4x+8 ) +X = 2-x

√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3

8/3 = 8/3 (True)

Now; Keeping X= 2

√{(2)²-4*2+8}+2 = 2-2

8 ≠0 (False)

Therefore, the value of X is -2/3.

Hope it helps!

Answer:

D

Step-by-step explanation:

Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect

Answer:

Step-by-step explanation:

=  [tex]\int\limits^1_0 {5x\sqrt{x} } \, dx[/tex]

=  [tex]\int\limits^1_0 {5xx^{1/2} } \, dx[/tex]

= [tex]\int\limits^1_0 {5x^{3/2} } \, dx[/tex]

= 5 [tex]\int\limits^1_0 {x^{3/2} } \, dx[/tex]

= 5*[tex]\frac{2}{5}[/tex]*[tex]x^{5/2}[/tex]  |[tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right] \left[/tex]

= 5*[tex]\frac{2}{5}[/tex]*[tex]1^{5/2}[/tex]

= 2

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

slope-inercept form: y = 3x + 3        point-slope form: y - 9 = 3(x - 2)

Step-by-step explanation:

slope-intercept form:

y2 - y1 / x2 - x1        

9 - (-6)/ 2 - (-3)      

= 3

y = 3x + b

9 = 3(2) + b

9 = 6 + b

3 = b

y = 3x + 3

point-slope form:

y - 9 = 3(x - 2)

Answer:

you divide a 8000÷ 5.5 yor answer is it

9514 1404 393

Answer:

  (a) ∠SPR = 70°

  (b) ∠SRP = 30°

Step-by-step explanation:

The applicable relationships are ...

__

QR is subtended by 35° inscribed angle QPR, so is 2×35° = 70°.

PQ is subtended by 45° inscribed angle PSQ, so is 2×45° = 90°.

RS is 2×QR, so is 2×70° = 140°.

(a) Inscribed angle SPR is half the measure of arc RS, so is 140°/2 = 70°.

__

(b) Arc SP is the remaining arc in the circle, so is ...

  arc SP = 360° -arc PQ -arc QR -arc RS = 360° -90° -70° -140° = 60°.

Inscribed angle SRP is half the measure of arc SP, so is 60°/2 = 30°

Answer:

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

Answer:

A. ^3√5 is the answer.

Step-by-step explanation:

5^( 1 / 3 ) = ^3√5

The students eligible to ride the bus are: Marinna, Kaleb and Thomas

The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

An equation of circle with center at (h, k) and radius 'r' is,

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

For given example,

Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall.

Considering positive x-axis = East

negative x-axis = West

positive y-axis = North

negative y-axis =South

Also, locate the position of each student on the graph.

Then the given situation would as shown in following diagram.

We have been given, only students who live outside a 5-mile radius from the school are eligible to ride the school bus.

Using the equation of the circle,

the equation for the area within a circle of 5-mile radius from the school would be,

[tex](x-2)^2+(y-3)^2=5^2[/tex]

From the graph we can observe that, Marinna, Kaleb and Thomas live outside a 5-mile radius from the school.

Therefore, the students eligible to ride the bus are: Marinna, Kaleb and Thomas

Learn more about the equation of circle here:

https://brainly.com/question/10618691

#SPJ2

Answer: No, it's not possible.

Explanation: An angle must only be opposite exactly one side.

Answer:

ok

What do you want me to answer ?

Answer:

ok so lets divide 90 by 15 to get 6 so she gets paid 6 per student and that means lisa gets paid 12 so lets just multiply

6*20=120 so mary gets paid 120

and lisa gets paid doable that so 420

but i don't know there base pay so the i can't answer this problem

Hope This Helps!!!

Answer:

The system has two solutions, but only one is viable because the other results in negative side lengths.

Step-by-step explanation:

correct on edmentum or plato

Step-by-step explanation:We have to graph the function g(x) which is given as:

g(x)=  x when x<2

and -3 when x ≥2.

Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.

Left hand limitat 2:

g(2-h)=lim h→0 2-h

       =2-0=2

Also right hand limit at x=2 is:

g(2+h)=lim h→0 (2+h)

         = 2+0=2

Also g(2)= -3.

As:

Left hand limit= Right hand limit but is not equal to function's value at that point.

Hence, the function is discontinuous at x=2.

so for x<2 we will get a graph of a line y=x.

and for x≥2 we will get a straight line y=-3 parallel to the domain.

Answer:

3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]

Step-by-step explanation:

(f · g )(x) = 3[tex]x^{2}[/tex] · (x + 2) = 3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]  (Multiply the two terms by distributing)

Answer:

120

Step-by-step explanation:

calculator

Hi!

[tex]3x^3-2y^3-6x^2y^2+xy=\\\\=3\cdot(\frac{2}{3})^3-2\cdot(\frac{1}{2})^3-6\cdot(\frac{2}{3})^2\cdot(\frac{1}{2})^2+\frac{2}{3}\cdot\frac{1}{2}=\\\\=3\cdot\frac{8}{27}-2\cdot\frac{1}{8}-6\cdot\frac{4}{9}\cdot\frac{1}{4}+\frac{1}{3}=\\\\=\frac{8}{9}-\frac{1}{4}-\frac{2}{3}+\frac{1}{3}=\frac{8}{9}-\frac{1}{4}-\frac{1}{3}=\frac{32}{36}-\frac{9}{36}-\frac{12}{36}=\boxed{\frac{11}{36}}[/tex]

Answer:

1/2

8

Step-by-step explanation:

When its talking about the result or output, look at the range, and then follow the line(s) back to the number(s) in the domain. Do the opposite when it's talking about the function of a certain number, e.g. f(4).