Which of the following determines a plane?
A. 3 non-collinear points
B. line and a point on the line
C. three collinear points
D. a straight line

James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.

Let the acid solution needs to mix with 10% be x ml and the acid solution needs to mix with 50% will be 100 - x ml.

Now,

10% x + 50% ( 100 - x ) = 26% ×100

⇒[tex]\frac{10x}{100} +\frac{50(100-x)}{100}=\frac{2600}{100}[/tex]

⇒10x + 50( 100 - x ) = 2600

⇒10 x + 5000 - 50x = 2600

⇒10 x - 50 x = 2600-5000

⇒-40 x = -2400

⇒x=60

Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

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Answer:

AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle

Answer:

20

Step-by-step explanation:

Correct option is A)

let the number be x.

∴75% of x=15

∴

100

75

×x=15

∴x=15×

3

4

∴x=20

The value of x is 20.

The expression is equivalent to 2 , option C is the right answer.

An expression in maths is a statement that contains , constants , variables and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac { 4^{\frac{5}{4}} * 4^{\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm a^m * a^n = a^{m+n}[/tex]

[tex]\rm \dfrac { 4^{\frac{5}{4} +\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]

[tex]\rm { 4^{\frac{5}{4} +\frac{1}{4} -{\frac{1}{2}}}[/tex]

On solving the exponents

=(6/4) -(1/2)

=4/4

=1

=[tex]\rm 4^{\frac{1}{2}}[/tex]

= 2

Therefore the expression is equivalent to 2 , option C is the right answer.

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Answer: $36.68 or $35.97. Read below.

Step-by-step explanation: You need to multiply the 12 foot by 12 foot and you would get 144 sq feet. Then divide 47 into 144. You will be left with 3.06, and if you need to round, you can round that to 3. Then you need to multiply 3 by $11.99 and you will be left with the cost for the paint, which is $35.97 if you do round to a three, and $36.68 if you do not round the three. So your answer is either $36.68 or $35.97 depending on whether you round or not.

Answer:

Step-by-step explanation:

The best way to answer a question like this one is to use a graphing program on the internet. This graph was done with desmos

It looks to me that the equation is g(x)  = 10(x - 5)^2 - 37

I checked to see that this is correct, and thank goodness it is.

The graph is shown below.

Answer: A

tan= Opposite ÷ Alternate

tan B= 16 (which is the opposite side of B) ÷ 7 (it's the side beside B, excluding 17.46 as it's the hypotenuse)

Therefore 16÷7 = 2.285714286

= 2.29 (3sf)

Answer:

just choose one

Answer:

Step-by-step explanation:

eq of line perpendicular to 3x+5y=10 is

5x-3y=a

where a is constant.

it passes through (3,2)

5(3)-3(2)=a

a=15-6=9

reqd. eq. is 5x-3y=9

or

3y=5x-9

y=5/3 x-3

gradient=5/3

y-intercept=-3

or

5y=-3x-10

y=-3/5 x-2

slope=-3/5

slope of reqd. line=-1/(-3/5)=5/3

eq. of line through (3,2) is

y-2=5/3(x-3)

3y-6=5x-15

3y=5x-15+6

3y=5x-9

y=5/3 x-3

Answer:

C. 29

Step-by-step explanation:

[tex]f(x) = -3x^3 + 2x^2 +24[/tex]

• To calculate [tex]f(-1)[/tex] , we have to replace x with -1 in the definition of [tex]f(x)[/tex] , and calculate the value:

[tex]f(-1) = -3(-1)^3 + 2(-1)^2 + 24[/tex]

         ⇒ [tex]-3(-1) +2(1) + 24[/tex]

         ⇒ [tex]3 + 2 + 24[/tex]

         ⇒ [tex]29[/tex]

[tex]\huge\boxed{\textsf{C.}\ 29}[/tex]

We have this equation:

[tex]f(x)=-3x^3+2x^2+24[/tex]

Substitute [tex]x=-1[/tex]:

[tex]f(-1)=-3(-1)^3+2(-1)^2+24[/tex]

Simplify to find the final answer:

[tex]\begin{aligned}f(-1)&=-3(-1)+2(1)+24\\&=3+2+24\\&=5+24\\&=\boxed{29}\end{aligned}[/tex]

Hello,

    9k - 2  88

⇔ 9k - 2 + 2 ≥ 88 + 2

⇔ 9k ≥ 90

⇔ 9k/9 ≥ 90/9

⇔ k ≥ 10

S = [10 ; + ∞ [

Answer:

k ≥ 10

Step-by-step explanation:

9k - 2 ≥ 88

Step 1 : Add 2 on both sides.

9k - 2 + 2 ≥ 88 + 2

9k + 0 ≥ 90

9k ≥ 90

Step 2 : Divide 9 on both sides.

9k/9 ≥ 90/9

k ≥ 10

Answer:

any # where -2<=x<7

Step-by-step explanation:

(x-7) would be negative and (x+3) positive, resulting in f(x) being negative.

Answer:

Step-by-step explanation:

Complementary angles are angles that add up to 90°.

Let's say angle 1 is x, and angle 2 is 87.6 less than x.

We already know that angle 1 + angle 2 = 90, so we can just substitute x now.

We know that complementary angles add up to 90, so one of the angles is 90-x, and the other one is 90-x-87.6.

x = (90 - x) - 87.6

Simplifies to:

x = 2.4-x

Add x to both sides

2x = 2.4

Divide by 2

x = 1.2

To get the other angle, add 87.6 to 1.2

1.2+87.6 = 88.8

So, angle1 = 1.2, and angle2 = 88.8

Let's check our work.

88.8 + 1.2 = 90, so the angles are complementary and have a difference of 87.6

Hope this helps (:

Answer:

1.2°, 88.8°

Step-by-step explanation:

let one angle=x

other angle=y

y=x-87.6

also  

x+y=90

x+x-87.6=90

2x=90+87.6=177.6

x=88.8

other angle=88.8-87.6=1.2

Answer: B

Step-by-step explanation:

The area of entire rectangle is (9)(4)=36.

The area of the square inside is [tex]x(x)=x^2[/tex]

Subtracting the areas, we get [tex]36-x^2[/tex]

The equation for total pay is y = 10/8x.

Division is the mathematical operation that is used to determine the quotient of a number. In order to determine the total pay for hours from 0 to 8, the pay per hour has to be determined. To determine this value, divide $10 by 8.

Pay per hour = $10 / 8

y = 10/8x.

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The value of x in the given expression is; x = wz/y

We are given the expression;

w/x = y/z

Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;

Multiply both sides of the given expression by x to get;

(w/x)*x = (y/z)*x

⇒ w = xy/z

Now, multiply both sides by z/y to get;

w(z/y) = (xy/z) * (z/y)

wz/y = x

Thus, the value of x in the given expression is;

x = wz/y

The correct question is;

If w/x = y/z, then what is the value of x

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The required probability of success is given by 0.98906500

Assume the random variable X has a binomial distribution with the given probability of obtaining a success.
P(X<5), n=6, p=0.3

In binomial distribution for number trials we are investigating the probability of getting a success remain the same.

n = number of trails,
p = probability of success
x = the number of success

p(x<5) = P(x=0)+ p(x=1) + p(x=2)+p(x=3)+p(x=4)

= [tex]\binom{6}{0}(0.3)^0(1-0.3)^6+\binom{6}{1}(0.3)^1(1-0.3)^5+\binom{6}{2}(0.3)^2(1-0.3)^4+\binom{6}{3}(0.3)^3(1-0.3)^3+\binom{6}{4}(0.3)^4(1-0.3)^2[/tex]

p(x<5) = 0.98906500

Thus the required  probability of success is given by 0.98906500

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Answer:

A) 65

B) 60

Step-by-step explanation:

64.9963 rounds to 65

To the nearest 10 it would round down as the second intiger the 4 is below 5 meaning as a result it rounds down

After rounding  the given number 64.9963:

(a) Near 2 decimal places is: 64.70

(b) And the nearest 10 is: 60

When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The given number is:

64.9963

To round off the nearest 2 decimal places:

Since the third digit after the decimal is 6 which is greater than 5.

Add 1 to their previous digit.

Therefore,

After rounding near to 2 decimal places the number becomes:

64.70

To round off the nearest 10:

Since the tense digit is 4 and it is less than 5

Therefore,

The number after rounding off the nearest 10 is:

60.

Hence, after rounding the number:

Near 2 decimal places is: 64.70

And the nearest 10 is: 60

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The composite function of the paintings Jenny completes in a year is

[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

A composite function is a function made of other functions, where the output of one function is the input to the other function.

An example of the composite functions 2x+3 and [tex]x^{2}[/tex] together make the composite function [tex](2x+3)^{2}[/tex]

We have [tex]P(w)=\frac{1}{2}w+1[/tex]

Here, P(w) represents the number of paintings Jenny completes in some w weeks. and

J(y)  represents the number of weeks per year.

As J(y) is the number of weeks spent per year in painting, we can calculate the paintings completed in a year by substituting

w as J(y) in the equation we have

Then the equation becomes:[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

Hence this is the composite function that would represent the number of paintings Jenny completes in a year.

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Step-by-step explanation:

Answer

a - 8

------------+

2

The graph of the inequality can be seen in the image at the end.

Here we have the inequality:

y ≥ 4x - 3

To graph this we need to graph the line:

y = 4x - 3

With a solid line (because the points on the line are solutions) and then shade the region above that line.

The graph of the inequality can be seen below.

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Answer:   [tex]\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

Work Shown:

[tex](h,k) = (-4,-6) = \text{center}\\\\r = 7 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - (-4))^2 + (y - (-6))^2 = 7^2\\\\\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

To check the answer, you can use a graphing calculator like GeoGebra or Desmos or similar.

Answer:

If you mean:

x² = 10

√x² = √10

x = √10

if you meant:

2x = 10

2x/2 = 10/2

x = 10/2

x = 5

hope this helps

If you mean x^2 then there would be no answer after all, 3^2= 9 and 4^2= 16 so

If you mean 2x then the answer would be 5

Step-by-step explanation:

:0

Answer:

1/100

Step-by-step explanation:

The answer is 1/100 because we don't know how many people are in the group but do know that only 1 person has been taken from the group and the probability will be 1 out of how many people are in the group so we just put 100 there as we don't know how many people are in the group.

Ps: Sorry if this is wrong, this is just a guess.

If three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.

There are nine diagonals in a regular hexagon

But for one with three diagonals drawn through the center, six equilateral triangles are formed.

Thus, if three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.

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Encourage children to recognize and talk about math in everyday situations, this statement teacher not recommendation.

What is mathematics?

Quality, structure, space, and change are the subjects of study in mathematics. The study of mathematics involves utilizing symbols and numbers to quantify and analyze the characteristics of quantities and sets.

It is impossible to encourage kids to understand and discuss arithmetic in normal contexts since the subject's solutions are based on numbers and symbols, which makes it inappropriate.

As a result, option (a) is correct.

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Answer:

50%

Step-by-step explanation:

In rhe beginning, there were 24 + 20 = 44 students trying out in total. After a week, there are 44 - 6 - 2 = 36 students remaining. Of those 36 students, 18 of them are trying out for the basketball team. The percentage of students trying out for the basketball team would be 18/36 = 0.5 = 50%

Answer:

14

Step-by-step explanation:

AT/TB = AV/VC

5/7 = 10/VC

VC = 14

For the given figure length of VC = 14.

In the given figure,

We can see that,

ΔATV and ΔABC are similar triangle,

Since we know that,

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion. The '' sign here denotes the resemblance of triangles.

Therefore,

AT/TB = AV/VC

It is given that,

AT = 5

TB = 7

AV = 10

Now put these values we get,

⇒ 5/7 = 10/VC

⇒ VC = 14

Hence,

Length of VC  is 14 units.

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