add at the park there's a pool shaped like a circle with a diameter 22 yards. A ring shaped path goes around the pool. it's width is 5 yards.

Answer:

0

Step-by-step explanation:

Because finding mean is adding the numbers, then dividing by the number of numbers. They are both 2.5. So 2.5 - 2.5 =0

Bella: 2.5

Isaac: 2.5

The difference in their mean score is 0.

The mean is the arithmetic average of a set of given numbers.

Bella and Isaac take a weekly quiz in their math class.

Their grades on each of the ten first quarter quizzes are shown below.

The Bella grades are;

100, 90, 70, 80

The mean of Bella's grades is;

[tex]\rm Mean =\dfrac{Sum \ of \ all \ values}{Number \ of \ values}\\\\Mean =\dfrac{100+90+70+60}{4}\\\\Mean =\dfrac{320}{4}\\\\Mean =80[/tex]

The Isaac grades are;

100, 90, 80, 50

The mean of Isaac's grades is;

[tex]\rm Mean =\dfrac{Sum \ of \ all \ values}{Number \ of \ values}\\\\Mean =\dfrac{100+90+80+50}{4}\\\\Mean =\dfrac{320}{4}\\\\Mean =80[/tex]

The difference in their mean score is;

Difference = Bella's grades - Isaac's grades

Difference = 80 - 80

Difference = 0

Hence, the difference in their mean score is 0.

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#SPJ2

Answer:

A=138

Step-by-step explanation:

First you would multiply 18 times 8, which equals 144. Then you would subtract 6, which equals 138. So A=138.

Answer:

A = 138

Step-by-step explanation:

[tex] \frac{a + 6}{8} = 18 \\ a + 6 = 18 \times 8 \\ a + 6 = 144 \\ a = 144 - 6 \\ a = 138[/tex]

Answer: x= -2; y = 3

Step-by-step explanation:

y=-2x – 1

y = 8x + 19   -  

replacing "y"

-2x – 1 = 8x + 19

-2x - 8x = 19 + 1

-10x = 20

x = 20/-10

x= -2

y=-2x – 1

y= -2.(-2) - 1

y= 4 - 1

y = 3

Answer:2.2

Step-by-step explanation:

Boo

Answer:

  corresponding angles are listed in the same order

Step-by-step explanation:

Corresponding angles are listed in the same order in the triangle names. Corresponding angles are congruent.

  ∠D ≅ ∠Z

  ∠E ≅ ∠X

  ∠F ≅ ∠Y

_____

This is why you have to carefully choose the names of triangles that you say are congruent. The sequence of the letters in the name carries significant information.

Answer: There is no diaphragm below

Step-by-step explanation: Please add picture

Here we know that at 3:17 pm you started to bake the cake. The total revolution the minute hand on the clock makes is:

[tex]\frac{5}{8}+\frac{13}{24}=\frac{7}{6} \ revolutions[/tex]

We know that:

[tex]1 \ revolution ----------- 60min \\ \\ 7/6 \ revolutions -----------x[/tex]

Solving for x:

[tex]x=\frac{7}{6}\times 60=70 minutes[/tex]

So it takes 70 minutes after you put the cake in the oven. But:

[tex]70minutes=1h \ 10min[/tex]

Adding this to the initial time:

[tex]3:17pm+1h \ 10min=4:27pm[/tex]

Finally, the cake is done at 4:27 pm, option C.

Answer:

  w > 20

Step-by-step explanation:

Perhaps you want the solution to the inequality 2w+5>45.

Subtract 5:

  2w > 40

Divide by 2:

  w > 20 . . . . this is the solution

_____

Comment on solving inequalities

An inequality is solved in virtually the same way that an equation is solved: undo what is done to the variable. The only difference is that when you perform an operation that reverses the ordering, you need to reverse the ordering symbol.

Multiplying or dividing by a negative number will reverse the ordering. Consider, for example, ...

  2 > 1

Multiplying both sides by -1, we get ...

  -2 < -1 . . . . . the > sign needs to be reversed to a < sign to keep the inequality true

Answer:

The width is 12 inches, the length is 24 inches, and the height is 16 inches

Step-by-step explanation:

Please see the attached photo, it provides full information we need to solve this problem

We know that:

So the vomume fomula is = LWH = (36 -w)*w*(w+4)

<=> [tex]32w^{2}[/tex] + 114w - [tex]-w^{3}[/tex] - 4608

<=> w = 32 and w =  12 and w= -12

Disregard w= -12, because the width cannot be negative, and we also know that length is more than 10 inches so w =  12 is fit with the requirement.

=> Length = 36 -12 = 24

Width = 12 and Hight = 12 + 4 = 16

The length, width, and height of the terrarium that has a shape of a rectangular prism is:

Volume of rectangular prism = length × width × height.

Given the dimensions of the terrarium in the shape of a rectangular prism as:

Volume = 4,608 cubic in.

Length = (36 - w) in

Width = w in.

Height = (w + 4) in.

Plug in the values:

4,608 = (36 - w)(w)(w + 4)

4,608 = (36 - w)(w² + 4w)

4,608 = 36(w² + 4w) -w(w² + 4w)

4,608 = 36w² + 144w - w³ - 4w²

36w² + 144w - w³ - 4w² - 4,608 = 0

-w³ + 32w² + 144w - 4,608 = 0

Factorize

w = −12 or w = 12 or w = 32

Since we know the length is more than 10 inches and cannot be negative, therefore, w = 12.

Plug in the value of w

Length = (36 - 12) = 24 in

Width = 12 in.

Height = (12 + 4) = 16 in.

Therefore, the length, width, and height of the terrarium that has a shape of a rectangular prism is:

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Answer:

B.

Step-by-step explanation:

proof below

Answer:

B

it is very simple as that

Answer:

1 3/7

Step-by-step explanation:

10/7 is same as 7/7 + 3/7

7/7 equals to 1

Therefore, 1 + 3/7

Answer:  1 3/7

Answer:

About 13

Step-by-step explanation:

There's no equation shown, but you can guesstimate and say it's between 10 and 20, so about 13 makes sense

Answer:

[tex]d=6\sqrt{2}\ ft[/tex]

Step-by-step explanation:

step 1

Find the length side of the square

we know that

The area of the square is given by the formula

[tex]A=b^2[/tex]

where

b is the length side of the square

we have

[tex]A=36\ ft^2[/tex]

substitute

[tex]36=b^2[/tex]

solve for b

[tex]b=6\ ft[/tex]

step 2

Find the diagonal length of the table top

Let

d ----> the diagonal length of the table top

Applying the Pythagorean Theorem

[tex]d^2=b^2+b^2[/tex]

substitute the value of b

[tex]d^2=6^2+6^2[/tex]

[tex]d^2=72[/tex]

[tex]d=6\sqrt{2}\ ft[/tex]

Answer:

√143

4π

√79+√63

Step-by-step explanation:

√143 gives 11.958

4π = 4 times 22/7 = 12.57

√79+√63 gives 16.825

In ascending order, i.e from the least to the greatest, we have

11.958

12.57

16.825

Which is same as

√143

4π

√79+√63

Answer: p=-2

Step-by-step explanation:

0.5(2p+4)x10=-4x10-2px10

5(2p+4)=-40-20p

10p+20-20=-40-20p-20

10p=-20p-60

10p+20p=-20p-60+20p

30p=-60

30p/20=-60/30

p=-2

Time taken by the car to cover 260 km is 2.6 hrs

Step-by-step explanation:

Speed = Distance/Time = 150/1.5 = 100 km/hr

Time = Distance/Speed = 260/100 = 2.6 hrs

Answer:

Explanation:

1. Call A the event of selecting a student who takes Spanish and P(A) the corresponding probability:

2. Call B the event of selecting a student who takes biology and P(B) the corresponding probability:

3. The joint probability, P(A∩B), is the probability that a student takes Spanish and biology:

4. By the properties of probabilities, the probability of the event A or B is:

Final answer:

To find the probability of a student taking Spanish or Biology, you need to consider the students taking each subject and those taking both, applying the principle of inclusion-exclusion. The simplified probability is [tex]\frac{17}{28}[/tex].

Explanation:

The probability that a student selected at random takes Spanish or Biology can be calculated using the principle of inclusion-exclusion.

Find the total number of students taking Spanish or Biology: 550 + 700 - 400 (students taking both) = 850.

Calculate the probability: P(Spanish or Biology) = Number of students taking Spanish or Biology ÷ Total number of students = [tex]\frac{850 }{ 1400} = \frac{17}{28}[/tex].

Answer:

Step-by-step explanation:

Let w be the width

Length = w + 3

Perimeter = 40 m

2*(length + width) = 40

2*(w+3 + w) = 40

2* (2w + 3) =40

2w + 3 = 40/2

2w + 3 = 20

2w = 20-3

2w = 17

w = 17/2 = 8.5 m

w = 8.5 m

Length = w + 3 = 8.5 + 3 = 11.5m

[tex]3.15*10^{12}[/tex]  would be 3.15 trillion in scientific notation. When putting a number into scientific notation, move the decimal point until you have a number between 1 and 10.

To convert 3.15 trillion to scientific notation, express it as 3.15 × 10¹². This involves moving the decimal point 12 places to the left. Scientific notation helps manage very large or very small numbers efficiently.

To convert the number 3.15 trillion to scientific notation, follow these steps:

Scientific notation is particularly useful in fields where dealing with extremely large or small numbers, such as astronomy and other sciences, is common.

Answer: James will save $3 for 18 weeks before he can buy the telescope

Step-by-step explanation:

Answer:18weeks

Step-by-step explanation:

54/3=18

He will save up for 18weeks to buy the telescope

Answer:

Step-by-step explanation:

they were exchanged for iron, guns, gunpowder, mirrors, knives, cloth, and bead

Answer:

The answer should be [tex]14x^{2} - 56 x + 51 = 0[/tex]

Step-by-step explanation:

Step 1: First, you add 51 to both sides

−56x + [tex]14x^{2}[/tex]+ 51= 0

Step 2: then you fix the order.

[tex]14x^{2} - 56 x + 51 = 0[/tex]

10 to the second power = 100

Since powers of TEN is 10 multiplied by itself, multiply 10 by 10 TWO times, because its 10 to the SECOND power

10x10=100

By the way do not multiply 10 by 2 at ALL IT IS WRONG!!!

For example, 10 to the 3rd power is 10x10x10 not 10x3

Answer: +100

Explanation: 10 raised to the 2nd power means the same thing as 10 squared and any number squared is that number times itself.

So 10² is just 10 · 10 or +100.

Answer:

1) P(A) = 0.20

2) P(B) = 0.80

3) P(A and B) = 0.15

4) P(A or B) = 0.85

Step-by-step explanation:

Total number of customers = 20

Customers with enough cash = 4

Customers with credit card = 16

Customers with enough cash and credit card = 3

Part 1) Customer has enough cash

Probability is defined as the ratio of favorable outcomes to total number of outcomes. Here the favorable outcome will be the customers with enough cash which are 4 in number and total number of outcomes will be the total number of customers which is 20.

Therefore, the probability that a customer has enough cash will be:

[tex]P(A)=\frac{4}{20}=\frac{1}{5}=0.20[/tex]

Part 2) Customer with a credit card

Using the same formula we used in previous part. However, in this case the number of favorable outcomes will be the number of customers with a credit card i.e. 16

Therefore, the probability that a customer has a credit card will be:

[tex]P(B)=\frac{16}{20} =\frac{4}{5} =0.8[/tex]

Part 3) Customer has enough cash and a credit card

Using the same formula once again. However, in this case the number of favorable outcomes will be the customers with enough cash and a credit card which is 3.

Therefore, the probability that a customer has enough cash and a credit card will be:

[tex]P(A \cup B)=\frac{3}{20}=0.15[/tex]

Part 4) Customer has enough Cash or a Credit Card

We need to find union of two events i.e. P(A or B). The union of two events is defined as:

P(A or B) = P(A) + P(B) - P(A and B)

We calculated all these values in the previous parts. Substituting the values in above formula, we get:

P(A or B) = 0.2 + 0.8 - 0.15

P(A or B) = 0.85

Therefore, the probability that a customer has enough cash or a credit card is 0.85

Answer:

<QRT = 130°

X = 135

<QRS = 180°

Step-by-step explanation:

1. A straight line is 180°.

180° - 50° = 130°

<QRT = 130°

2. x - 5 = 130°

130° + 5° = 135°

3. As stated before, a straight line is 180°.

Answer:

5 hundreds

Step-by-step explanation:

5 is the hundreds place.  So, there are 5 hundreds

Answer:

5 hundreds

Step-by-step explanation:

500 divided by 100 = 5

so, there are 5 hundreds in the number 5

Answer:

Step-by-step explanation:

Enter a problem...

Algebra Examples

Popular Problems Algebra Solve for x 64^(4x)=16^(x+1)

64

4

x

=

16

x

+

1

Create equivalent expressions in the equation that all have equal bases.

4

3

(

4

x

)

=

4

2

(

x

+

1

)

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

3

(

4

x

)

=

2

(

x

+

1

)

Solve for

x

.

Tap for fewer steps...

Multiply

4

by

3

.

12

x

=

2

(

x

+

1

)

Simplify

2

(

x

+

1

)

.

Tap for fewer steps...

Apply the distributive property.

12

x

=

2

x

+

2

⋅

1

Multiply

2

by

1

.

12

x

=

2

x

+

2

Move all terms containing

x

to the left side of the equation.

Tap for fewer steps...

Subtract

2

x

from both sides of the equation.

12

x

−

2

x

=

2

Subtract

2

x

from

12

x

.

10

x

=

2

Divide each term by

10

and simplify.

Tap for fewer steps...

Divide each term in

10

x

=

2

by

10

.

10

x

10

=

2

10

Cancel the common factor of

10

.

Tap for fewer steps...

Cancel the common factor.

10

x

10

=

2

10

Divide

x

by

1

.

x

=

2

10

Cancel the common factor of

2

and

10

.

Tap for fewer steps...

Factor

2

out of

2

.

x

=

2

(

1

)

10

Cancel the common factors.

Tap for fewer steps...

Factor

2

out of

10

.

x

=

2

⋅

1

2

⋅

5

Cancel the common factor.

x

=

2

⋅

1

2

⋅

5

Rewrite the expression.

x

=

1

5

The result can be shown in multiple forms.

Exact Form:

x

=

1

5

Decimal Form:

x

=

0.2

Answer:

The dryer costs $350

Step-by-step explanation:

Step 1:  Make a system of equations

w + d = 652

w = d - 48

Step 2:  Plug in the know w into the first equation

d - 48 + d = 652

2d - 48 + 48 = 652 + 48

2d / 2 = 700 / 2

d = 350

Answer:  The dryer costs $350