Candace surveyed every 10th student that walked onto campus. She asked them if they were planning to read any books over the summer. She ended up surveying 50 people. 15 of them said yes. If there are 1000 students at her school, predict about how many will be reading over the summer. ​

Answer:

16) r = C/(2·π)

17)  [tex]r^2 = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]

18) x = (9 - 3·y)/2

19) Please find attached the required graph of the inequality x ≤ 4 created with MS Excel

20) z ≥ 1

Solve each inequality and graph the solution

21) n ≤ 1

22) p > -5

23) -3 ≤ q ≤ 2/5

24) x > 1/5

25) x < -11

26) 7

Step-by-step explanation:

Solving for the indicated variable

16) C = 2·π·r for r

Dividing both sides by 2·π gives;

C/(2·π)  = 2·π·r/(2·π)  = r

∴ r = C/(2·π)

17) [tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h \ for \ r^2[/tex]

Dividing both sides by [tex]\left( \dfrac{1}{3} \cdot \pi \cdot h \right)[/tex] gives;

[tex]\dfrac{V}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)} = \dfrac{ \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)}[/tex]

[tex]\therefore r^2 = \dfrac{V}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)} = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]

[tex]r^2 = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]

18) 2·x + 3·y = 9 for x, gives;

x = (9 - 3·y)/2

19) Please find attached the required graph of the inequality x ≤ 4 created with MS Excel

20) Solve each inequality

z - 3 ≥ -2

z ≥ -2 + 3 = 1

∴ z ≥ 1

Solve each inequality and graph the solution

21) 3·n  + 5 ≤ 2·n + 6

n ≤ 1

22) 10·p + 20 - p > p + 3 - 23

9·p + 20  > p - 20

8·p > -40

p > -5

23) -1 ≤ 1 - 5·q ≤ 16

∴ 2/5 ≥ q ≥ -3

-3 ≤ q ≤ 2/5

Solve each word problem

24) Let x represent the number, we have;

2·x + 3·(x + 2) > 17

5·x + 6 > 7

∴ x > 1/5

The numbers are numbers larger than (1/5)

Solve each inequality

25) 2·(x - 5) + 3·x < 4·(x - 6) + 3

2·x - 10 + 3·x < 4·x - 24 + 3

x < -11

26) -2 - [-4 - (3 - 2)] = -2 + 4 + 3 - 2 = 7

Answer:

1/6=6

Step-by-step explanation:

Conversion a mixed number 2 1/

4

to a improper fraction: 2 1/4 = 2 1/

4

= 2 · 4 + 1/

4

= 8 + 1/

4

= 9/

4

To find new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/

4

= 8/

4

b) Add the answer from previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 4.

Two and one quarter is nine quarters

Divide: 9/

4

: 3/

8

= 9/

4

· 8/

3

= 9 · 8/

4 · 3

= 72/

12

= 12 · 6/

12 · 1

= 6

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/

8

is 8/

3

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 12 gives 6/

1

.

In words - nine quarters divided by three eighths = six.

Answer:

Infinite points

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

-24x - 4y = -164

y = 41 - 6x

Step 2: Solve for x

Here we see that -164 does indeed equal -164.

∴ We have an infinite amount of solutions.

Answer:

C. 1

Step-by-step explanation:

angle L and angle N are equal so the length of ML and MN should be equal too (isosceles triangle)

4x = x + 3 subtract x from both sides

3x = 3 divide both sides by 3

x = 1

Answer:

y = -3

Step-by-step explanation:

the length from directrix to vertex is equal to the length from focus to the vertex.

Answer: y=-3

Step-by-step explanation: y = -3 Step-by-step explanation: the length to vertex is equal

Answer:

79.4%

Step-by-step explanation:

the volume of a cylinder is as for any other regular 3D object

base area × height

the base area is for a cylinder a circle.

so, it is

pi×r² × height

the radius (r) is always half of the diameter.

so, volume of cylinder A is

Va = pi×(10/2)² × 8 = pi×25 × 8 = 200pi ft³

the volume of cylinder B is

Vb = pi×(12/2)² × 7 = pi×36 × 7 = 252pi ft³

therefore, in a volume of 252pi ft³ we have 200pi ft³ filled with water.

252pi = 100% filling

1% = 100%/100 = 252pi/100 = 2.52pi

how many % are 200pi ?

as many as times 1% fit into 200pi :

200pi/2.52pi = 200/2.52 = 79.36507937... ≈ 79.4%

=========================================================

Explanation:

Draw a horizontal line to cut the figure into a rectangle on top and a triangle down below.

The rectangle has length and width of 6 and 4 (horizontal and vertical components respectively). The area of this rectangle is 6*4 = 24 square units.

The triangle has a base of 6 and a height of 4. The base and height of any triangle are always perpendicular.

The area of the triangle is base*height/2 = 6*4/2 = 24/2 = 12 square units. If you were to cut out half of the triangle and rearrange things, you'll find that a rectangle can be formed. This rectangle is half in area that of the first rectangle we found. This is why we divide by 2 when finding the area of the triangle.

Once you know the two sub-areas, we add them up to get the overall area: 24+12 = 36 square units.

Answer:

D. 27

Step-by-step explanation:

sum of exterior angles = 360

2x + 56 + 57 + 85 + 4x = 360

6x + 198 = 360

6× = 360 - 198

6× = 162

× = 27

Answer:

26%

Step-by-step explanation:

Answer:

1/10 if its is in the group

Step-by-step explanation:

but if its as the whole thing it would be 1/200 because he has 10  and 10 of 2000 is 1/200

The probability that the winning ticket belongs to Neil is 5%.

It is a branch of mathematics that deals with the occurrence of a random event.

There are a total of 2,000 tickets, and Neil and his 9 friends bought 10 tickets each, so they bought a total of 100 tickets (10 tickets/person x 10 people = 100 tickets).

The probability of Neil's group winning the car is equal to the number of tickets they bought divided by the total number of tickets sold:

Probability = Number of tickets bought by Neil's group / Total number of tickets sold

Probability = 100 / 2000

Probability = 0.05 or 5%

Therefore, the probability that the winning ticket belongs to Neil is 5%.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ5

Answer:

perimeter of the garden=2(length+width)

=2(7√13+√13)

=2(8√13)

=16√13

Answer:

Step-by-step explanation:

take 60 degree as reference angle

using cos rule

cos 60=adjacent/hypotenuse

1/2=80/x

x=80*2

x=160

=======================================================

Explanation:

There are A = 13 hearts and B = 4 copies of "7"

The count A+B = 13+4 = 17 may seem like it's the count of hearts or "7" cards, but we're double counting the 7 of hearts. So the true count is actually 17-1 = 16

There are 16 cards we want (either a heart or a "7") out of 52 total. Therefore, the probability is 16/52 = (4*4)/(4*13) = 4/13

Answer:

The vertex is (-2,10)

Step-by-step explanation:

The vertex is the maximum point on a downward facing parabola

The maximum is (-2,10)

The vertex is (-2,10)

Answer:

the value of x is 2^9/4 then 2^3x-4=2^11/4

Answer:

20

h(x) = 2x - 20

Step-by-step explanation:

f(x) = ¹/₂ x + 10

First, isolate x, like so:

f(x) - 10 = ¹/₂ x

x = 2(f(x) - 10)

x = 2f(x) - 20

Now, simply switch f(x) with x and x with h(x), like so:

h(x) = 2x - 20

Answer:

the answer is 20

Step-by-step explanation:

took the test on edge

Answer:

-21

Step-by-step explanation:

f(-3) = -4(-3)² + 15 = -4(9) + 15 = -36 + 15 = -21

Answer:

f(-3) = -21

Step-by-step explanation:

f(x) = −4x²+ 15

f(-3) = -4(-3)² + 15

f(-3) = -4(9) + 15

f(-3) = -36 + 15

f(-3) = -21

Answer:

1/10

Step-by-step explanation:

7 is one number in a 10 sided die

Answer:

x=11

Step-by-step explanation:

The equation for the problem is 4x-2=42. The angle (4x-2) is equal to 42 degrees because it is vertical to the angle with 42 degrees. If angles are vertical, they are equal to each other.

Add 2 to both sides of the equation.

4x+2=4x     42+2=44

Simplify.

4x=44

Divide 4 by both sides.

4x/4=x     44/4=11

Simplify to get the final answer.

x=11

Answer:

[tex]\boxed {\boxed {\sf d= \sqrt{34}}}[/tex]

Step-by-step explanation:

We want to find the distance between two points, so the following formula is used.

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

Where (x₁, y₁) and (x₂, y₂) are the points we are finding the distance between.

We are given the points (-2, -1) and (3,2). If we match the corresponding value and variable we see that:

Substitute the values into the formula.

[tex]d= \sqrt {(-2-3)^2+(2--1)^2[/tex]

Solve the parentheses.

[tex]d= \sqrt{(-5)^2+(3)^2[/tex]

Solve the exponents.

[tex]d= \sqrt{25+9}[/tex]

Add.

[tex]d= \sqrt{34}[/tex]

This radical cannot be simplified, so the distance between the two points is √34 and choice 3 is correct.

Answer:

X²–49

Step-by-step explanation:

(x+7)(x-7)

x²+7x-7x-49

x²-49

Step-by-step explanation:

I think its similar

Answer: Unlock code = 76

==========================================================

Explanation:

Use a factor tree to find the prime factorization of each value

22 = 2*11

30 = 2*3*5

Both values have '2' in common and this is the largest such value. Therefore, the GCF of 22 and 30 is 2.

So E = 2

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

Since 3 and 8 have no factors in common (other than 1), this means the LCM is 3*8 = 24

We can say that F = 24.

If the numbers had some larger number in common, then we'd have to do a bit more work to find the LCM.

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

As the hint suggests, we'll use the distributive property to show that

3*(7+10) = G + 30

3*7 + 3*10 = G + 30

21 + 30 = G + 30

21 = G .... subtract 30 from both sides; they cancel and go away

G = 21

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

Use the same idea for the other equation as well

5*(3 + H) = 15 + 45

5*3 + 5*H = 15 + 45

15 + 5H = 45

5H = 45 ............ subtract 15 from both sides; they go away

H = 45/5 ......... divide both sides by 5

H = 9

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

The unlock code is

E+F+G+H = 2+24+21+29 = 76

Answer:

The hypotenuse is sqrt ( 2x^2)

Step-by-step explanation:

Given a right angled triangle, we can find the hypotenuse of a triangle using the Pythagorean theorem which says that c^2 = a^2 + b^2, where a is the length, b is the perpendicular height and c is the hypotenuse. The length of the triangle (l) is x and the height of the triangle is also x. By substituting the values,

c^2 = x^2 + x^2 = 2x^ 2

There are two possible answers to c but the hypotenuse cannot be negative.

Hence,

c = Sqrt (2x^2)

Answer:

two hundred nineteen and 44

OR

two hundred nineteen point 44

Step-by-step explanation:

do not say AND before nineteen. saying AND represents a decimal point. Both can be used (point or and)

Answer:

its 93.4

Step-by-step explanation:

just multiply 46.7 by 2

Answer:

Step-by-step explanation:

pythagoras theorem

a^2+b^2=c^2

24^2+10^2=x^2

576+100=x^2

676=x^2

[tex]\sqrt{676[/tex]=x

26=x

Answer:

x = -6

Step-by-step explanation:

8 + 4x = -16

4x = -16 - 8

4x = -24

x = -24/4

x = -6

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 6}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

[tex]\:8 + 4x = - 16[/tex]

➺[tex] \: 4x = - 16 - 8[/tex]

➺[tex] \: 4x = - 24[/tex]

➺[tex] \: x = \frac{ - 24}{4} [/tex]

➺[tex] \: x = - 6[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]\:8 + 4x = - 16[/tex]

➼[tex] \: 8 + 4( - 6) = - 16[/tex]

➼[tex] \: 8 - 24 = - 16[/tex]

➼[tex] \: - 16 = - 16[/tex]

➼[tex] \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]