In the word "COURSE” what is the probability of choosing a vowel?

Answer:

Simply Put:

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 200 and 350 is 50

Divide both terms by the GCF, 50:

200 ÷ 50 = 4

350 ÷ 50 = 7

The ratio 200 : 350 can be reduced to lowest terms by dividing both terms by the GCF = 50 :

200 : 350 = 4 : 7

Therefore:

200 : 350 = 4 : 7

Step-by-step explanation:

Answer:

sqrt(2-sqrt(3))/2

Step-by-step explanation:

sin(15)=sin(30/2)=sqrt(1-cos(x))/sqrt(2)=(1-sqrt(3)/2)/sqrt(2)

Again we don't like compound fractions so multiply top and bottom inside sqrt( ) by 2.

sin(15)=sqrt(2-sqrt(3))/sqrt(4)

simplify

sin(15)=sqrt(2-sqrt(3))/2

Answer:

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

Step-by-step explanation:

[tex]sin(\frac{u}{2} =\sqrt[+]{\frac{1-cosu}{2} }                              =\sqrt{\frac{1-cos30^0}{2} } \\=\sqrt{(\frac{1-\frac{\sqrt{3} }{2)} }{2}  } \\=\sqrt{\frac{2-\sqrt{3} }{4} } \\=\sqrt{\frac{2-\sqrt{3} }{\sqrt{4} } } \\=\sqrt{\frac{2-\sqrt{3} }{2} } \\[/tex]

Answer:

B. Similar

D. Same Shape

Step-by-step explanation:

In the given triangles:

∠A ≅ ∠D = 22°

∠B ≅ ∠E = 120°

∠C ≅ ∠F = 38°

Hence using the AAA axiom of geometry

Triangle ABC and DEF are similar.

More over due to the similarity of angles the triangles also have same shape.

One more thing, that can be observed is that

DE = 2* AB

EF = 2*BC

DF = 2*AC

The sides of triangle ABC are scaled with a factor of 2 which makes it similar to DEF ..

Hence,

Option B and Option D are correct ..

Answer with explanation:

Given two triangles ΔABC and ΔDEF

 ⇒Ratio of Sides

[tex]\rightarrow \frac{AB}{DE}(\frac{5}{10})=\frac{BC}{EF}(\frac{3}{6})=\frac{AC}{DF}(\frac{7}{14})=\frac{1}{2}[/tex]

⇒Comparison of Angles

→∠A=∠D=22°

→∠B=∠E=120°

→∠C=∠F=36°

⇒As length of corresponding sides are Proportional ,as well as corresponding Angles of two triangles are same.So Two Triangles are similar either by SSS Similarity or AA Similarity or S AS Similarity.

→If Triangles are similar then they are congruent also.

→The description which accurately describe the relationship between ΔABC and ΔDEF is:

→ Option B: Similar

Answer:

[tex]\large\boxed{f(x)-g(x)=x^2-4x+13}[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2-4x-3\\\\g(x)=(x-4)(x+4)=x^2-4^2=x^2-16\qquad\text{used}\ a^2-b^2=(a-b)(a+b)\\\\f(x)-g(x)=(2x^2-4x-3)-(x^2-16)\\\\=2x^2-4x-3-x^2-(-16)\\\\=2x^2-4x-3-x^2+16\qquad\text{combine like terms}\\\\=(2x^2-x^2)-4x+(-3+16)\\\\=x^2-4x+13[/tex]

Answer:

8, 36, 81, 11, 7, 1000

Step-by-step explanation:

A

Lets start with number one.

x^2 = 64.

That means that x times x equals 64.

To find x's value, simply find the square root of 64, which is 8.

So x = 8.

For the second one, the square root of x is 6.

That means that 6 x 6 = x

6 x 6 = 36.

So, x = 36.

B

For the third one, the square root of x is 9.

That means that 9 x 9 = x

9 x 9 = 81

So, x = 81.

For the fourth one, x^2 = 121

That means x times x = 121

To find x's value, simply find the square root of 121, which is 11

So, x = 11.

C

For the fifth one, x^3 = 343.

That means that x times x times x = 343

To find x's value, simply find the square root of 343, which is 7.

So, x = 7.

For the sixth and last one, the cube root of x is 10.

That means 10 x 10 x 10 = x.

10 x 10 x 10 = 1,000

So, x = 1,000

I hope this helps! :)

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies -4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=-4[x-(-2)]\implies y-3=-4(x+2)[/tex]

Answer:  [tex](y-3)=(-4)(x+2)[/tex]

Step-by-step explanation:

We know that the equation of a line in point-slope form that is passing through a point (a,b) and has slope m is given by :-

[tex](y-b)=m(x-a)[/tex]

Then, the point-slope form of a line with slope -4 that contains the point (-2,3) :-

[tex](y-3)=(-4)(x-(-2))\\\\\Rightarrow\ (y-3)=(-4)(x+2)[/tex]

Hence, the point-slope form of a line with slope -4 that contains the point (-2,3) is [tex](y-3)=(-4)(x+2)[/tex]

Answer:

9.5 inches

Step-by-step explanation:

We are given that in a right angled triangle, one leg is 3 inches long while the hypotenuse is 10 inches long. We are to find the length of the other leg.

For this, we will use the Pythagoras Theorem.

Assuming x to be the length of the other leg.

[tex] 1 0 ^ 2 = 3 ^ 2 + x ^ 2 [/tex]

[tex]100=9+x^2[/tex]

[tex]x^2=91[/tex]

[tex]\sqrt{x^2} =\sqrt{91}[/tex]

x = 9.5

Answer:

9.53 inches

Step-by-step explanation:

In a right  angles triangle, the sum of the squares of the two legs (a and b) equals the square of the the hypotenuse.

a²+b²=c²

Substituting for the values provided in the question we get the following:

3²+b²=10²

b²=10²-3²

b²=91

b=9.53 inches.

Answer:

(5,0) and (5,-2)

Step-by-step explanation:

we know that

If two points are on the line x=5, then the x-coordinates of the points must be equal to 5

therefore

The coordinates of two points that are on the line x=5 are

(5,0) and (5,-2)

Answer:

x^3 +8x^2 +13

Step-by-step explanation:

(6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16​)

Distribute the minus sign

6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16​

Combine like terms

x^3 +8x^2 +13

Answer:

Simplify (6x2 − 3 + 5x3) − (4x3 − 2x2 − 16).

its (C) -------> x^3 + 8x2 + 13

Step-by-step explanation:

Answer:

y = - 5x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

here m = - 5 and b = - 7, hence

y = - 5x - 7 ← equation of line

Since b equals the y-intercept, we automatically know that the answer will be in slope-intercept form which is y = mx + b where m equals slope and b equals the y-intercept.

Given.

m = –5, b = –7

Slope intercept formula.

y = mx + b

Plug in m = -5 and b = -7.

y = -5x - 7 ← Choice C

Answer: Infinitely Many Solutions

Step-by-step explanation:

Substitute y into the second equation:

2(-2x-6)=-4x-12

Then you get -4x-12=-4x=-12. Since this is 0=0 it would make it infinitely many solutions.

There are infinitely many solutions to the given system. The equations in the system are y = -2x - 6 and 2y = -4x - 12.

For a system of linear equations, there are three types of solutions. They are,

Infinitely many solutions are there for a system if they both are equal on both sides while solving. (their graphs intersect at all the points)

Given the system of equations as

y = -2x - 6

2y = -4x - 12

Using substitution method, substituting first equation into the second equation,

2( -2x -6) = -4x - 12

⇒ -4x -12 = -4x - 12

Thus, both sides are equal, and the given system has infinitely many solutions.

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Answer:

x = 5/6 , y = 8/5

Step-by-step explanation:

Solve the following system:

{12 x + 15 y = 34 | (equation 1)

{5 y - 6 x = 3 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{12 x + 15 y = 34 | (equation 1)

{0 x+(25 y)/2 = 20 | (equation 2)

Multiply equation 2 by 2/5:

{12 x + 15 y = 34 | (equation 1)

{0 x+5 y = 8 | (equation 2)

Divide equation 2 by 5:

{12 x + 15 y = 34 | (equation 1)

{0 x+y = 8/5 | (equation 2)

Subtract 15 × (equation 2) from equation 1:

{12 x+0 y = 10 | (equation 1)

{0 x+y = 8/5 | (equation 2)

Divide equation 1 by 12:

{x+0 y = 5/6 | (equation 1)

{0 x+y = 8/5 | (equation 2)

Collect results:

Answer:  {x = 5/6 , y = 8/5

Apollo Spas would require approximately 17.325 liters of muriatic acid to service all 105 hot tubs.

The student is looking to find out the total amount of muriatic acid, noted in liters, required to service all hot tubs. The problem states Apollo Spas needs to service 105 hot tubs, with each one requiring 165 mL of acid.

Firstly, we need to multiply the number of hot tubs by the amount of acid each one needs: 105 hot tubs * 165 mL/hot tub = 17325 mL.

However, the student needs the amount in liters, not milliliters. To convert mL to L, we need to divide the total mL by 1000 because there are 1000 mL in a liter.  Therefore, 17325 mL / 1000 =  17.325 L.

So, Apollo Spas will need 17.325 liters of muriatic acid to service all 105 hot tubs.

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Answer:

(x-6)^2

Step-by-step explanation:

x^2-12x+36

What two numbers multiply to 36 and add to -12

-6 * -6 = 36

-6 + -6 = -12

(x-6) (x-6)

(x-6)^2

Answer:

Step-by-step explanation:

The easiest to solve for is y in the second equation.   Just subtract 3x from both sides, obtaining y = -3x + 9.

The value of x = 1 and y = 6. The easiest to solve for is y in the second equation.

Let the equations be

2x + 4y = 26 ......(1)

3x + y = 9 ........(2)

From (2), we get

3x + y = 9

y = -3x + 9 .......(3)

then substitute the value of y in (1), then we get

2x + 4y = 26

2x + 4(-3x + 9) = 26

Simplifying the above equation, we get

2x - 12x + 36 = 26

-10x + 36 = 26

-10x = 26 - 36

-10x = -10

Then the value of x = 1

Substitute the value of x in (3), then we get

y = -3x + 9

Simplifying the equation, we get

y = -3(1) + 9

y = -3 + 9

y = 6

The value of x = 1 and y = 6.

Therefore, the correct answer is option (d) The easiest to solve for is y in the second equation.

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Answer:

x>-18

Step-by-step explanation:

Answer:

the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]

Step-by-step explanation:

We need to find the simplifies form of

[tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex]

We need to find product of above terms

We can write as

[tex](7*7)(\sqrt{x^5}*\sqrt{x^5})\\(7^2)((\sqrt{x^5})^2)\\49\,x^5[/tex]

So, the product of [tex]7\sqrt{x^5} * 7\sqrt{x^5}[/tex] is [tex]49\,x^5[/tex]

Answer:

Clara's body eliminated the antibiotic at the same rate as Heidi's body.

Answer:

Option. B is the answer.

Step-by-step explanation:

Clara is taking a medicine for a common cold. Table that shows the amount f(t) that was present in Clara's body after time t is

t (hours)      1             2           3            4             5

f(t) (mg)   236.5   223.73   211.65    200.22   189.41

Now we will find the explicit formula of geometric sequence.

f(1) = 236.5

and f(2) = 223.73

Therefore, common ratio of the sequence = [tex]\frac{f(2)}{f(1)}=\frac{223.73}{236.5}[/tex]=0.946

So the equation will be f(t) = [tex]236.5(0.946)^{t}[/tex]------(1)

At the same time Heidi was administered 300 mg of same medicine of the same sample.

Amount of medicine in her body f(t) after time t is shown by the equation

f(t) = [tex]300(0.946)^{t}[/tex]----(2)

By comparing these equations 1 and 2, we find common ratio is same as (0.946), which reflects the rate of elimination of the antibiotic was same for both Clara and Heidi.

Option B is correct.

Answer:

Option B R(2,4) is correct

Step-by-step explanation:

The equation of the circle is:

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]

Where r = radius

a and b are coordinates of the center of circle.

To check which point lies on a circle, we need to verify the equation

[tex](x-6)^2 + (y-1)^2 = (5)^2[/tex]

We will check for each option.

Option A Q(1,11)

x=1 and y =11

[tex](1-6)^2 + (11-1)^2 = 25\\(-5)^2 + (10)^2 = 25\\25 + 100 = 25\\125 \neq 25[/tex]

So, Option A is incorrect

Option B R(2,4)

x =2 and y = 4

[tex](2-6)^2 + (4-1)^2 = 25\\(-4)^2 + (3)^2 = 25\\16 + 9 = 25\\25 = 25[/tex]

Option B is correct.

Option C S(4,-4)

x =4 and y =-4

[tex](4-6)^2 + (-4-1)^2 = 25\\(-2)^2 + (-5)^2 = 25\\4 + 25 = 25\\29 \neq 25[/tex]

Option C is incorrect

Option D T(9,-2)

x =9 and y =-2

[tex](9-6)^2 + (-2-1)^2 = 25\\(3)^2 + (-3)^2 = 25\\9 + 9 = 25\\18 \neq 25[/tex]

Option D is incorrect.

Answer:

B.

Step-by-step explanation:

The general equation of a circle is [tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] where (h,k) is the center and r the radius. In this case, the general equation of the circle with radius 5 and center at (6,1) is [tex](x-6)^{2}+(y-1)^{2} = 5^{2}[/tex], so the point that satisfies the equation will be in the circle.

A.  [tex](1-6)^{2}+(11-1)^{2} = 25+100 = 125[/tex] this option is not correct.

B.   [tex](2-6)^{2}+(4-1)^{2} = 16+9= 25[/tex] this option is correct so is the answer.

The conversion from 2000 Swiss francs to Dutch guilders requires a historical exchange rate which is not provided. The Dutch guilder is obsolete since 2002, and precise conversions cannot be made without the rate from the time period when both currencies were in use.

To convert 2000 Swiss francs to Dutch guilders, you would need to know the specific exchange rate between the Swiss franc and the Dutch guilder at the time of the conversion. Unfortunately, as of today, the Dutch guilder is no longer in use, as the Netherlands adopted the euro as its currency in 2002. However, if you were to convert currencies similar to how holders of dollars are willing to exchange $2,500 for euros or vice versa, you would need the specific exchange rate from Swiss francs (CHF) to Dutch guilders (NLG) during the time when both currencies were in use.

Without historical exchange rate data, it is impossible to provide an exact number of Dutch guilders you would receive for 2000 Swiss francs. If you have a specific date in mind, you could find the historical exchange rate for that date and then calculate the conversion using this formula:

Amount in Swiss francs * Exchange rate (CHF to NLG) = Amount in Dutch guilders

Remember, when performing historical currency conversions, it's essential to use the correct exchange rate from the time period in question.

Answer:

c = 6.1 in

Option B.

Step-by-step explanation:

Your full question can be found in the image below

Since we are dealing with a right triangle, we can use a great number of properties,

We know that

cos(35°)  = Adj cathetus / Hypotenuse

cos(35°)  = 5 in / c

c = 5 in / cos(35°)

Option B.

c = 5 in / 0.82

c = 6.1 in

Answer:

D. c=5/sin(35°)

Step-by-step explanation:

got it right on edge

Answer:

x = {4, 4}

Step-by-step explanation:

(x - 4)(x - 4) = 0 has two real, equal roots:  x = 4 and x = 4.  Notice that subbing 4 for x in this equation results in a TRUE equation.

The value of x in  (x - 4)(x - 4) = 0 is x = (4, 4) repeated roots.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given (x - 4)(x - 4) = 0.

∴ Either (x - 4) = 0 or (x - 4) = 0.

x - 4 = 0 ⇒ x = 4 or x - 4 = 0 ⇒ x = 4.

So, x = (4, 4).

This is a case when a quadratic equation has real repeated roots.

The vertex of this graph of this quadratic equation just touches the x-axis.

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Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x)

= - 4x² - 6x - 1 + (- x² - 5x + 3) ← remove parenthesis

= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms

= - 5x² - 11x + 2 → C

Answer:

A: Day 6

B: 8196 grams (He will become obese for sure)

Step-by-step explanation:

Part A:

As you can infer from the problem, Ali halves his bar everyday, regardless of how the bar is.

Day 1= 32 grams left

Day 2= 16 grams left

Day 3= 8 grams left

Dat 4= 4 grams left

Day 5= 2 grams left

Day 6=1 gram left

He will have one gram left on Day 6

Part B:

This part is basically vice versa. Instead on halving, we need to be doubling. I will do Part a in reverse until Day 14 comes

Day 1= 1

Day 2= 2

Day 3= 4

Day 4= 8

Day 5= 16

Day 6= 32

Day 7 = 64

Day 8= 128

Day 9= 256

Day 10= 512

Day 11= 1024

Day 12= 2048

Day 13= 4096

Day 14= 8192

He will need 8192 grams of chocolate!!!

The number of days when he has only 1 gram left will be 6. And the chocolate needs to weigh to last All 14 days will be 1/256 grams.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

Ali has a 64 grams bar of chocolate.

On day 1 he eats half of his chocolate.

And on day 2 he eats half of what is left.

He does the same each day.

Then the value of a is 64 grams and b is 1/2.

y = 64 · (1/2)ⁿ

Where n is the number of days.

The number of days when he has only 1 gram left will be

1 = 64 · (1/2)ⁿ

1/64 = (1/2)ⁿ

(1/2)⁶ = (1/2)ⁿ

n = 6

The number of days when he has only 1 gram left will be 6.

The chocolate needs to weigh to last All 14 days will be

y = 64 · (1/2)¹⁴

y = 64 · (1/16384)

y = 1/256 grams

The chocolate needs to weigh to last All 14 days will be 1/256 grams.

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Answer:

20 pts

Step-by-step explanation:

50 points corresponds to a 100% grade.  How many points (x) correspond to a 40% grade?

     x            40%

------------ = ---------

50 pts       100%

Then 100x = 2000, and so x = 20.

A score of 20 points would correspond with a test score of 40%.  

Answer:

A score of 20 points would correspond with a test score of 40%.  

Step-by-step explanation:

    x            40%           How many points (x) correspond to a 40% grade?

------------ = ---------

50 pts       100%          50 points corresponds to a 100% grade.  

100x = 2000                divide both sides by 100

x = 20

Answer:

$44,800

Step-by-step explanation:

Original salary : $40,000

12% of original salary = 12% x 40,000 = 0.12 x 40,000 = $4,800

New salary = $40,000 + $4,800 = $44,800

Follow below steps;

The probability of drawing a blue marble from the bag:

Calculate the total number of marbles in the bag: 3 red + 4 white + 5 blue = 12 marbles.

Calculate the probability of drawing a blue marble: Number of blue marbles / Total number of marbles = 5 / 12 = 5/12.

Answer:

A. -5/4, 9

Step-by-step explanation:

The solution is in the picture

Answer:

A

Step-by-step explanation:

Given

4m² - 31m - 45 = 0

Consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 4 × - 45 = - 180 and sum = - 31

The factors are - 36 and + 5

Use these factors to split the m- term

4m² - 36m + 5m - 45 = 0 ( factor the first/second and third/fourth terms )

4m(m - 9) + 5(m - 9) = 0 ← factor out (m - 9) from each term

(m - 9)(4m + 5) = 0

Equate each factor to zero and solve for m

m - 9 = 0 ⇒ m = 9

4m + 5 = 0 ⇒ 4m = - 5 ⇒ m = - [tex]\frac{5}{4}[/tex]

Answer:

Many possible answers, including

Major Arc: JKM

Minor Arc: JM

Step-by-step explanation:

The answers you selected in this photo are correct. But let's see why.

A major arc is an arc that is bigger than a minor arc.

They are defined using a starting point and an ending point.  In this case, you have many reference points (J, K, L and M), and none is identified in the question.  However, the answers shown indicate they're using point J as starting point and M as ending point.

If you look at the positions of J and M on the diagram, you see you can take two routes to join them... the shortest route is the minor arc (going counter-clockwise direction from J to M).  While the other route, going clockwise passes through the points K and L is much longer.... and forms the major arc.

That major arc could be identified as JKM, JLM or JKLM, since it starts at J, ends in M, but passes through points K and L, in that order.

Answer:

B.4

Step-by-step explanation:

1.5(x+4) - 3 = 4.5( x-2)-----------------------open brackets on both sides

1.5 x +6 -3= 4.5x- 9.................................collect like terms

3+9 = 4.5 x- 1.5x

12=3x..................................divide by 3 both sides to get x

12/3=x

x=4

ANSWER

x=4

EXPLANATION

The given equation is

[tex]1.5(x + 4) - 3= 4.5(x - 2)[/tex]

Multiply through by 10

[tex]15(x + 4) - 30= 45(x - 2)[/tex]

We expand to get:

[tex]15x + 60 - 30= 45x - 90[/tex]

Group similar terms to get;

[tex]15x - 45x = - 90 - 60+ 30[/tex]

[tex] - 30x = - 120[/tex]

[tex] x= 4[/tex]