solve for x
103.5
4.7
55.0

We know that ratios can be shown with both fractions and colons.

20:705

or

[tex]\frac{20}{705}[/tex]

It also looks like we can simplify this by dividing by 5.

20/5 = 4

705/5 = 141.

This means that for every 4 teachers, there are 141 students.

The ratio for teachers to students is:

4 : 141

Answer:

A. 14, because it says that only 14 liked English language ONLY

B. It’s 7.

14 liked only English, 7 liked both languages, 12 liked only French.

Add those them together.

14 + 7 + 12

21 + 12

33

33 - 40 = 7

( 33 is the number of students that liked a language and 40 is ALL the students in total )

So it would be 7.

C. 26 liked one language.

7 liked both languages and 7 didn’t like neither. You could add them together.

7 + 7 = 14

40 - 14 = 26

OR

14 + 12 = 26
( just English + just French )

D. The probability of a student chosen at random that ONLY likes French would be 12/40.

Since only 12 of the 40 students liked ONLY French, it would be 12/40 or 12 : 40

Step-by-step explanation:

I hope it helps! Have a great day!

Pan~

Answer:

a) 14
b) 7
c) 33
d) P = 12/40 = 3/10 (In decimal P=0.3)

Step-by-step explanation:

Hope this helps

Answer:

$96

Step-by-step explanation:

a) As the constants are equal, the situation represents a proportional relationship.

b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constants for each situation are:

k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.

Since the constants are equal, the situation represents a proportional relationship.

The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

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Answer:

0.03 seconds

Step-by-step explanation:

10,000km = 300secs

1km = x seconds

Cross multiply the equation

10,000x = 300

Divide both sides by 10,000

10,000x = 300

10,000 10,000

x = 0.03 seconds

When the completing the square is applied, the rewritten function is (x + 2)^2 = 4

The equation is given as:

x^2 + 4x = 0

The above equation is a quadratic equation and the coefficient of x in the above equation is 4.

So, we have:

k = 4

Divide the variable k by 2

k/2 = 4/2

k/2 = 2

Square the above result

(k/2)^2 = 4

Next, we add 4 to both sides of x^2 + 4x = 0

x^2 + 4x + 4 = 4

Expand the equation by expressing 4x as 2x + 2x

This gives

x^2 + 2x + 2x + 4 = 4

Factorize the above equation

x(x + 2) + 2(x + 2) = 4

Factor out x + 2 from the above equation

(x + 2)(x + 2) = 4

Rewrite the equation as a perfect square of (x + 2)

(x + 2)^2 = 4

Hence, the rewritten function after completing the square is (x + 2)^2 = 4

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The total amount of money received from sales of shoes that month = $4968

Salary = $11000

Number of shoes sold = 360

Cost of 1 shoe = $460

Total cost of shoes sold = 360 x 460

Total cost of shoes sold = $165600

Since $165600 is greater than $100000, she will earn a commission of 3%

Commission = (3/100) x $165600

Commission = $4968

The commission is the amount of money received from sales of shoes. Other earnings are salary or increment

Therefore, the total amount of money received from sales of shoes that month = $4968

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The solution of the given equation can be all real numbers, except c = 0 and c = 3.

Lets simplify the given problem,

1/c-3 - 1/c = 3/ (c-3)

As the denominators cannot be equal to zero (0) because a division by zero (0) is undefined.

Next, we would multiply both sides of the given by the lowest common multiple (LCM).

The lowest common multiple (LCM) is c(c - 3).

c-[c-3] = 3

c-c+3 = 3

0 = 3-3

0=0

Therefore, the solution of the given equation can be all real numbers, except c = 0 and c = 3.

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Answer:

(f-g)(x)= (3x + 10) - (5x -3)

f-g = 3x + 10 - 5x + 3

f-g = -2x + 13

Hi! ❄

  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The eccentricity of the conic section below is 1, since the conic section given is a parabola.

The eccentricity of a parabola is 1.

Hope that made sense !!

  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\star\tiny\pmb{_{calligraphy}}\star[/tex]

Hi!

[tex]{}[/tex] - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The eccentricity of the conic section below is 1, since the conic section given is a parabola.

What is parabola?

a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

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Question 6

1) [tex]\overline{AB} \cong \overline{BD}[/tex], [tex]\overline{CD} \perp \overline{BD}[/tex], O is the midpoint of [tex]\overline{BD}[/tex], [tex]\overline{AB} \cong \overline{CD}[/tex] (given)

2) [tex]\angle ABO, \angle ODC[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle ABO, \triangle CDO[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\overline{BO} \cong \overline{OD}[/tex] (a midpoint splits a segment into two congruent parts)

5) [tex]\triangle ABO \cong \triangle CDO[/tex] (LL)

Question 7

1) [tex]\angle ADC, \angle BDC[/tex] are right angles), [tex]\overline{AD} \cong \overline{BD}[/tex]

2) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)

3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)

5) [tex]\overline{AC} \cong \overline{BC}[/tex] (CPCTC)

Question 8

1) [tex]\overline{CD} \perp \overline{AB}[/tex], point D bisects [tex]\overline{AB}[/tex] (given)

2) [tex]\angle CDA, \angle CDB[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\overline{AD} \cong \overline{DB}[/tex] (definition of a bisector)

5) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)

6)  [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)

7) [tex]\angle ACD \cong \angle BCD[/tex] (CPCTC)

Postulate: SAS

Similarity statement: [tex]\triangle CAB \sim \triangle EDF[/tex]

The confidence interval for the meannumber of dresses purchased each year is (7.2,7.4).

Given sample mean of 7.3 and sample standard deviation of 1.4 and confidence interval of 95%.

We have to find confidence interval for the mean number of dresses purchased each year.

Because the sample size is more than 30 so z test test will be used.

Margin of error is the difference in real values and calculated values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where zis the criticalvalue of confidence level.

σ is sample standard deviation,

n is sample size.

z value for 95% confidence level=1.96

Margin of error=1.96*1.4/[tex]\sqrt{523}[/tex]

=2.744/22.869

=0.12

Upper level= Mean + margin of error

=7.3+0.12

=7.42

Rounding off

=7.4

Lower level=Mean - margin of error

=7.3-0.12

=7.18

Rounding

=7.1

Hence the confidence interval is (7.1,7.4).

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In a two-tailed hypothesis test the null hypothesis is rejected.

According to the statement

The test statistic is 3.06 and the critical values are /-2.086.

If we find the value of t by using the formula the then it comes with Negative sign and it lies under the critical region.

That's why In a two-tailed hypothesis test the null hypothesis is rejected.

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Answer:

Step-by-step explanation:

A + B= 180°

(5x+20)+(9x-92)=180°

14x-72=180°

14x=252

x=18

A=5(18)+20

A=110

Answer:

x = 18 , ∠ A = 110°

Step-by-step explanation:

∠ A and ∠ B are same- side interior angles and sum to 180° , that is

5x + 20 + 9x - 92 = 180

14x - 72 = 180 ( add 72 to both sides )

14x = 252 ( divide both sides by 14 )

x = 18

Then

∠ A = 5x + 20 = 5(18) + 20 = 90 + 20 = 110°

Considering the piece-wise function described, the catering cost for a dinner with 40 guests is of $600.

A piece-wise function is a function that has different definitions, depending on the input.

In this problem, considering between 0 and 40 guests, the definition is the open circle at (0, 100) and goes up to a closed circle at (40, 600), hence the catering cost for a dinner with 40 guests is of $600.

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Answer:

600

Step-by-step explanation:

edge

Answer:

Just 1 positive, odd factor

Step-by-step explanation:

48 has many factors. But not many odd factors. Only 3 is odd and bigger than 2 and less than 10.

So, just one odd, positive factor.

The probability P(E) is 13/15.

According to the statement

we have given that the S = {1, 3, 5, 7, 9}, E = {1, 5, 7}

And we have to find the probability P(E).

So, For this purpose

Recall the formula for the probability of an event E in case when all outcomes are equally likely:

P(E)= n(E) /n(S)

in which S is the sample space.

But we have the S = {1, 3, 5, 7, 9},

so, n(S) = Sum of all outcomes / number of outcomes

n(S) = 1+3+5+7+9 /5

n(S) = 25 /5

n(S) = 5 and

For n(E) = Sum of all outcomes / number of outcomes

n(E) = 1+5+7 /3

n(E) = 13 /3

n(E) = 13 /3

Substitute these values in the above written formula then

P(E)= n(E) /n(S)

P(E)=  (13/3)/ 5

P(E)= 13 /15

So, The probability P(E) is 13/15.

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Answer:

No. The slopes of parallel lines are equal.

Step-by-step explanation:

If you have two lines and their slopes are the same, then the lines are parallel.

If the two lines have slopes that are negative reciprocals (opposite signs and flipped over) then when you multiply the slopes together, you get -1... THOSE lines are perpendicular (they make right angles or make 90° angles or square angles).

Lines in the same plane that have different slopes will intersect at one point.

The events are independent events and probability of tossing a head and drawing a red marble is 1/7

a) The answer is present in the image attached below

b) Tossing of a coin and drawing of a marble are independent events as these two events do not interfere in the probability of each others events.

c) The probability of tossing a head and drawing a red marble is = [tex]\frac{1}{2}.\frac{2}{7}[/tex]=1/7 as we can see from the tree diagram that probability of tossing a coin and getting head is 1/2 and probability of drawing a red marble is 1/7. As they are independent events, their probability can be multiplied. Hence the probability of tossing a head and drawing a red marble is 1/7.

d) The probability of drawing two blue marbles if the first marble is not replaced and one at a time is 1/7. Probability of drawing first blue marble from the lot is 3/7 as favorable outcomes are 3 and total outcomes are 7. As the ball is not replaced the outcomes are changed. Now the number of blue balls are 2 and total number of balls are 6. So now the probability becomes 2/6. Hence the total probability becomes = 1/7

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Answer:

B

Step-by-step explanation:

44/77

=0.55

Answer:

Step-by-step explanation:

y=2*|x-3|+2

y=|2*x-2*3|+2

y=|2x-6|+2

1)

y=2x-6

x | 2 | 3 |

y | -2| 0 |

2)

y=|2x-6|

3)

y=|2x-6|+2

y=2*|x-3|+2.

The area of the semicircle = 8π

A semicircle is formed when the panel passing through the center touches both ends of the circle. Therefore, if you connect two semicircles, you get a circle

If you cut them in half or divide the circumference of the circle by 2, you will get a semi-circle. Area of ​​semicircle The area of ​​the semicircle is half the area of ​​the circle. Because the area of ​​the circle is πr2. Therefore, the area of ​​the semicircle is 1/2 (πr2). Where r is the radius. The value of π is 3.14 or 22/7.

Semi-circular area = 1/2 (πr2)

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Answer:

16

Step-by-step explanation:

You replace m with 14. 2 + 14 = 16.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Assuming equation:}[/tex]

[tex]\mathsf{\dfrac{m}{2} + m}[/tex]

[tex]\huge\textsf{If so, let's solve for your equation:}[/tex]

[tex]\mathsf{\dfrac{m}{2} + m}[/tex]

[tex]\mathsf{= \dfrac{14}{2} + 14}[/tex]

[tex]\mathsf{= 7 + 14}[/tex]

[tex]\mathsf{= 21}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{21}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]