A cube has an edge length of 8 meters. What is its volume, in cubic meters?

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:

<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:

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:

Dilation

Step-by-step explanation: im doing this in k-12 in math now

Dilation is NOT an isometry transformation.

We have to give that,

All the transformations are,

A.) Rotation

B.) Reflection

C.) Translation

D.) Dilation

Since, An isometry, such as a rotation, translation, or reflection, does not change the size or shape of the figure.

Dilation is not an isometry since it either shrinks or enlarges a figure.

Hence, Dilation transformations are NOT an isometry.

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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:

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:

5/12

1/6+1/4=5/12

To determine the fraction of puppies that are black or white, you add 1/6 and 1/4, which gives you 5/12 when using a common denominator of 12. Therefore, 5/12 of the puppies are either black or white.

To find out what fraction of the puppies in the pet store are black or white, we simply add the fractions that represent the black puppies and the white puppies together. Since 1/6 of the puppies are black and 1/4 are white, we can write:

[tex]\(\frac{1}{6} + \frac{1}{4}\)[/tex]

To add these fractions, we need a common denominator. The least common multiple of 6 and 4 is 12, so we convert each fraction to have a denominator of 12:

[tex]\(\frac{1}{6} = \frac{2}{12}\) and \(\frac{1}{4} = \frac{3}{12}\)[/tex]

Now, we add the fractions:

[tex]\(\frac{2}{12} + \frac{3}{12} = \frac{5}{12}\)[/tex]

Therefore, 5/12 of the puppies are either black or white.

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:

17

Step-by-step explanation:

Pythagorean formula

a²+b²=c²

in other words, sidea²+sideb²=hypotenuse

8²+15²=c²

64+225=c²

289=c²

√289=√c²

17=c

Answer:

17

Step-by-step explanation:

Pythagorean formula

a²+b²=c²

in other words, sidea²+sideb²=hypotenuse

8²+15²=c²

64+225=c²

289=c²

√289=√c²

17=c

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:

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

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.

Step-by-step explanation:

53-5 is 48

48/6 is 8

X=8

therefore it's 8

Answer:

x=8

Step-by-step explanation:

[tex]6x+5=53\\6x+5-5=53-5\\6x=48\\\frac{6x}{6}=\frac{48}{6} \\x=8[/tex]

Answer: There is no diaphragm below

Step-by-step explanation: Please add picture

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:

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:

[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:

60

Step-by-step explanation:

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:

B.

Step-by-step explanation:

proof below

Answer:

B

it is very simple as that

Step-by-step explanation: Here, we want to find the mean, median, and mode for the data set. Let's begin by finding the mean.

The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set. So to find the mean of the data set shown here, let's begin by adding the numbers.

So we have

120 + 140 + 164 + 158 + 161 + 292 + 128 + 145 + 163 + 127 + 159 + 155.

This will be divided by how many numbers are in the set which is 12.

[tex]So[/tex] [tex]we[/tex] [tex]have[/tex] [tex]\frac{120 + 140 + 164 + 158 + 161 + 292 + 128 + 145 + 163 + 127 + 159 + 155}{12}[/tex].

Adding the numbers, we get 1,912.

1,912 is divided by the number of numbers in the set or 12.

1,912 divided by 12 is about 159.3333.

So the mean of the set of data shown here is about 159.3333.

Next, let's find the median.

The median is the middle number in the data set when the data set is written from least to greatest. So let's write our data set from least to greatest.

So we have 120, 127, 128, 140, 145, 155, 158, 159, 161, 163, 164, 292.

In this data set however, notice that there is no one middle number. When there is no middle number in a data set, we take the two numbers that are in the middle and we take the average of those numbers.

In this set, the two middle numbers are 155 and 158 because if we group these numbers together, there are five numbers on either side of them.

Now, to find the average of 155 and 158, we simply add them together and divide by 2. So we have 155 + 158 which is 313. Now, 313 ÷ 2 is 156.5.

So the median of the data set is 156.5.

Finally, let's find the mode.

The mode is the number that appears most frequently in a data set.

Notice that each number in our data set appears only once so there is no mode.

Answer:

120, 140, 164, 158, 161, 292, 128, 145, 163, 127, 159, 155

List the following data from least to greatest:

120, 127, 128, 140, 145, 155, 158, 159, 161, 163, 164, 292

Median: 156.5  

Mode: There are no mode in the following data set.

Mean: 120 + 127 + 128 + 140 + 145 + 155 + 158 + 159 + 161 + 163 + 164 + 292 = 1,912/12 = 159.3

Answer:2.2

Step-by-step explanation:

Boo

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

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

[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:

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 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:

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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