What is the image of Q for a dilation with the center (0,0) and a scale factor of 0.5?

A.) (0.5, 2.5)
B.) (2, 10)
C.) (1, 2.5)
D.) (10, 2)

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].

The front wheel turns around approximately 300 times.

To determine how many times Gia's bicycle wheel turns around during her 1,884 feet ride, we need to calculate the circumference of the wheel and then divide the total distance traveled by the circumference.

The diameter of the wheel is 24 inches. To find the circumference (C), we use the formula C = pi x d, where d is the diameter, and (pi) is approximately 3.14159.

C = 3.14159 x 24 inches = 75.39816 inches.

Next, we need to convert the distance Gia rode her bike from feet to inches because the circumference is in inches. There are 12 inches in a foot, so

1,884 feet x 12 inches/foot = 22,608 inches.

Now we divide the total distance traveled in inches by the circumference of the wheel to find out how many full revolutions there are:

22,608 inches / 75.39816 inches/revolution ≈ 300 revolutions.

To the nearest whole number, Gia's front bicycle wheel turns all the way around 300 times.

Answer:

Step-by-step explanation:

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

Answer: There is no diaphragm below

Step-by-step explanation: Please add picture

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:

  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:

17=p+8

Step-by-step explanation:

Start by setting the equation equal to 17 on either the right or left side. Now, on the opposite side of the equation read out what the question is saying.

"8 more than a number (p)" the variable would be p, and 8 more than p is 17. Now that you have that in mind, write 17 is equal to p plus 8.

17=p+8

If the question asks you to solve this equation for p, subtract 8 from both sides to get 9 for p.

I hope this is easy to understand.

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

Answer:

1 5/6 is on the twelfth line/tick mark. 2 1/3 is on the 15 line/tick mark.

Step-by-step explanation:

Go to the 1 and count up five lines. (5/6) For the 2nd one convert the 1/3 into 6ths. You now have 2 2/6. go to the 2 and count up 2 lines.

Answer:2.2

Step-by-step explanation:

Boo

[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:

15,825

Step-by-step explanation:

Because it is a square divide 63,300 by 4.

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:

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:

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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Answer:

the answers are A) 18p^3r and D) 54p^3

Good luck! :)

Answer:

A) 18p³r

D) 54p³

Step-by-step explanation:

The term 6p³ multiplies into (or goes into) both 18p³r and 54p³.

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:

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]

Answer: answer is D, descriptive, because the scientists are writing down observations but not making comparisons

Step-by-step explanation:

According to the question, the scientists were making individual notes on their observation about shape, colour, size and other characteristics of the living cells. We do not have enough information to show that they were making comparisons.

I hope this helps.

Answer:

anwser D

Step-by-step explanation:

discreptive because scientist are writing dow explanations

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

The ratio of boys to girls will be 15 : 13.

There are 28 students in all.

The fraction of the students are girls will be 13/28.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

A class contains 13 girls and 15 boys.

Now,

Since, A class contains 13 girls and 15 boys.

Hence, Number of total students = 13 + 15

                                                   = 28

So, The ratio of boys to girls = Number of boys : Number of girls

                                             = 15 : 13

Hence, Number of total students = 13 + 15

                                                   = 28

And, The fraction of the students are girls is;

= Number of girls / Number of students

= 13 / 28

Thus, The ratio of boys to girls = 15 : 13.

Total number of students = 28

And, The fraction of the students are girls = 13/28.

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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

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:

√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:

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

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:

[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]