A cereal box's length is 25 cm, height is 30 cm and width is 10 cm.

Answer:

The intensity on a screen 70 ft from the light is 1.728 foot candle.

Step-by-step explanation:

Given that,

The magnitude of  intensity [tex]I[/tex] of light varies inversely as the square of the magnitude of distance D from the source.

That is

[tex]I\propto \frac{1}{D^2}[/tex]

Then,

[tex]\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}[/tex]

Given that,

The magnitude of intensity of illumination on a screen 56 ft from a light is 2.7 foot-candle.

Here,

[tex]I_1[/tex]=2.7 foot-candle, [tex]D_1[/tex]= 56 ft

[tex]I_2[/tex]=?, [tex]D_2[/tex]= 70 ft.

[tex]\frac{I_1}{I_2}=\frac{D_2^2}{D_1^2}[/tex]

[tex]\Rightarrow \frac{2.7}{I_2}=\frac{70^2}{56^2}[/tex]

[tex]\Rightarrow \frac{I_2}{2.7}=\frac{56^2}{70^2}[/tex]

[tex]\Rightarrow {I_2}=\frac{56^2\times 2.7}{70^2}[/tex]

[tex]\Rightarrow {I_2}=1.728[/tex] foot-candle

The intensity on a screen 70 ft from the light is 1.728 foot candle.

Answer:

in expanded form the summation is

2 + 4 + 6 .... upto 20 + 2 y^6 × 10

= 110 + 20y^6

Answer:

No

Step-by-step explanation:

Say the price of 1 apple is x and the price of 1 orange is y. Then, we can write the two equations:

4x + 4y = 10

6x + 6y = 15

We can try to solve this by elimination, which means getting rid of one variable so that we're left with only 1 variable to solve for. Multiply the top equation by 3 and the bottom equation by 2:

3 * (4x + 4y) = 10 * 3  ⇒  12x + 12y = 30

2 * (6x + 6y) = 15 * 2  ⇒  12x + 12y = 30

Subtract the bottom equation from the top:

  12x + 12y = 30

-  12x + 12y = 30

______________

   0   +   0   =   0

Since we result in 0 = 0, that means any values of x and y we put into the equations will work, so we cannot find a unique price.

Hope this helps!

Answer:

No

Step-by-step explanation:

4A + 4O = 10

6A + 6O = 15

The second equation is just a multiple of the first one, so we don't have two distinct equations to solve for the prices

Answer:

No, This is not a valid Probability Distribution

Step-by-step explanation:

Probability [Neighbour walks with Beagle] = 20%

Probability [Neighbour walks with Golden Retriever] = 70%

Probability [Neighbour walks alone] = 30%

Disjoint Events are the events that have zero probability of occurring together. If all the three above items are disjoint, it means that it can never happen that two of them happen together.

The total (summed) probability of a valid probability distribution, with disjoint sets = 1 . In given case, total probability = 0.2 + 0.7 + 0.3 = 1.2 ; i.e > 1.

So, this probability distribution with stated disjoint events is not a Valid Probability distribution.

Final answer:

The given percentages (20% with the beagle, 70% with the golden retriever, 30% walking alone) add up to 120%, which exceeds the total probability of 100%. Thus, they do not constitute a valid probability distribution.

Explanation:

The situation described about the neighbor walking with her pets and alone presents individual probabilities of different events. If these events are indeed disjoint, meaning they cannot happen at the same time, then to determine if the given percentages represent a valid probability distribution, they must satisfy two main conditions: the sum of all probabilities must be equal to one (100%), and each individual probability must be between 0 and 1 inclusive.

Calculating the sum of the given probabilities: 20% (for walking with the beagle) + 70% (for walking with the golden retriever) + 30% (for walking alone) equals 120%, which exceeds 100%. This indicates that the given percentages do not contain a valid probability distribution because they do not sum to one, violating one of the fundamental characteristics of a probability distribution.

Step-by-step explanation:

Given diameter (d) = 28 inches

π = 3.14

Radius (r) = 28/2= 14 inches

Now

Area of the circle

= πr²

= 3.14 * 14²

= 615.44 inch ²

9514 1404 393

Answer:

  a^2·b^3

Step-by-step explanation:

Factors of both terms include 'a' to some power, and 'b' to some power. The greatest common factor will use the lowest power of each of these variables.

  powers of 'a' are a^2, a^3. Greatest common power is a^2

  powers of 'b' are b^5 and b^3. Greatest common power is b^3

The highest common factor of both terms is a^2·b^3.

__

Additional comment

When that is factored out of the sum, you have ...

  a^2b^5 +a^3b^3 = a^2·b^3(b^2 +a)

The remaining two terms (b^2+a) have no common factors—as it should be.

Answer: A

A= 1/2 x b x h

1/2(1)(1 sq rt 3)= .866

Sq rt 3 /2 = .867

Step-by-step explanation:

The cost of an apple is 0.7 dollars and the cost of a banana is 0.35 dollars.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, Two apples and five bananas cost £4.20.

Assuming no. of apples to be x and no. of bananas to be y.

∴ 2x + 5y = 4.20...(i) and,

Three apples and seven bananas cost £5.95.

∴ 3x + 7y = 5.95...(ii)

Now multiplying eqn(i) by 3 and eqn(ii) by 2 to cancel out x in both equations.

So, 6x + 15y = 12.6...(iii) and 6x + 14y = 11.9...(iv)

Subtracting eqn(iv) from eqn(iii) we get y = 0.7 and substituting value of y in eqn(iv) we get x = 0.35

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Given:

Given that the standard golf ball has a diameter of 1.68 inches.

Radius of the golf ball is 0.84 inches.

The material used to make the golf ball weighs 0.6523 ounces per cubic inch.

We need to determine the weight of one golf ball.

Volume of the golf ball:

The volume of the golf ball can be determined using the formula,

[tex]V=\frac{4}{3} \pi r^3[/tex]

Substituting r = 0.84, we get;

[tex]V=\frac{4}{3} (3.14)(0.84)^3[/tex]

[tex]V=2.481\ in^3[/tex]

Thus, the volume of one golf ball is 2.481 cubic inches.

Weight of one golf ball:

The weight of one golf ball can be determined by multiplying the volume of the golf ball with 0.6523 ounces per cubic inch.

Thus, we have;

[tex]Weight=2.481 \times 0.6523[/tex]

[tex]Weight = 1.62[/tex]

Thus, the weight of one golf ball is 1.62 ounces.

Final answer:

To find the weight of a golf ball, calculate its volume using its diameter, then multiply the volume by the weight of the material. The weight of one golf ball is approximately 1.80 ounces.

Explanation:

To find the weight of one golf ball, we first need to calculate its volume. The diameter of the golf ball is given as 1.68 inches, so the radius is 0.84 inches. Using the formula for the volume of a sphere, V = (4/3)πr³, we find the volume to be approximately 2.759 cubic inches.

Next, we calculate the weight of the golf ball by multiplying the volume by the weight of the material per cubic inch. Given that the material weighs 0.6523 ounces per cubic inch, multiplying this by the volume of the golf ball gives us the weight. Therefore, the weight of one golf ball is approximately 1.80 ounces.

Answer:

[tex]t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33[/tex]    

Step-by-step explanation:

Data given and notation  

[tex]\bar X=67[/tex] represent the sample mean

[tex]s=12[/tex] represent the sample standard deviation

[tex]n=16[/tex] sample size  

[tex]\mu_o =60[/tex] represent the value that we want to test

t would represent the statistic (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 60, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 60[/tex]  

Alternative hypothesis:[tex]\mu > 60[/tex]  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{67-60}{\frac{12}{\sqrt{16}}}=2.33[/tex]    

Answer:

151.43 meters

Step-by-step explanation:

We can use ratios to solve

1.75m             265m

--------------- = -----------

1 m                   x meters

Using cross products

1.75x = 265*1

Divide each side by 1.75

1.75x/1.75 = 265/1.75

x =151.4285714

151.43 meters

Answer:

151.429m

Step-by-step explanation:

This is a proportion problem.

1.75m/1m = 265m/ Xm

1.75m= 265m/ Xm

Xm = 265m/1.75m = 151.429m

Answer:

12 years old

Step-by-step explanation:

16 = m+4

-4   -4

12 = m

Answer:

12 years

Step-by-step explanation:

j = m + 4

j = 16

16 = m + 4

m = 16 - 4

m = 12

Answer:

4 adults 3 children

Step-by-step explanation:

Final answer:

To solve the problem, we set c as the number of children, and deduced that a = c + 1 for the number of adults, leading to 3 children and 4 adults going to the movies.

Explanation:

The question is about solving a basic algebra problem involving a small group of people going to the movies. To find out how many adults and children went to the movies, we can set up an equation based on the information provided. Let c represent the number of children. Since the number of adults is one more than the number of children, we have a = c + 1 for the number of adults. Together, they total seven people, so we can write the equation c + (c + 1) = 7. Simplifying this equation gives us 2c + 1 = 7. Solving for c, we subtract 1 from both sides to get 2c = 6, and then divide by 2 to find c = 3. This means there were 3 children. Since there is one more adult than children, a = 3 + 1 = 4, which gives us 4 adults. Therefore, there were 3 children and 4 adults that went to the movies.

Answer:

A

Step-by-step explanation:

Hi!

This one's a bit hard to explain! IF you want explanation, just comment.

Using the data given, we can conclude that [tex]\boxed{A}[/tex] is the correct answer.

Hope this helps!

Answer:

(x+2)(x+1)

Step-by-step explanation:

it factors to (x+2) and (x+1) then the answers are -2 and -1

Answer:

Isolating a variable means rearranging an algebraic equation so that a different variable is on its own. The goal is to choose a sequence of operations that will leave the variable of interest on one side and put all other terms on the other side of the equal sign.

Step-by-step explanation:

Answer:

Sam's description = [tex]3x+3[/tex], Kim's description =  [tex]5x-7[/tex]

Step-by-step explanation:

Given:

Kim and Sam were each given the same pair of numbers.

Sam's description of the two numbers was:

The larger number is 3 more than three times the smaller number.

Kim's description of the two numbers was:

Five times the smaller number decreased by 7 is the larger number.

Question asked:

Which equation represents the situation?

Solution:

Let smaller number = [tex]x[/tex]

According to Sam's description of the two numbers, the equation will be:-

Larger number = 3 more than three times the smaller number

                         = [tex]3x+3\ (eq1)[/tex]

According to Kim's description of the two numbers was, the equation will be:-

Larger number = Five times  decreased by 7

                         = [tex]5x-7\ (eq2)[/tex]

By equating  both equation:-

[tex]5x-7=3x+3\\ \\ Subtracting\ both\ sides\ by \ 3x\\ \\ 5x-3x-7=3x-3x+3\\ \\ 2x-7=3\\ \\ Adding\ both\ sides\ by\ 7\\ \\ 2x-7+7=3+7\\ \\ 2x=10\\ \\ Dividing\ both\ sides\ by\ 2\\ \\ x=5[/tex]

Smaller number = [tex]x[/tex] = 5

Larger number = [tex]3\times5+3=15+3=18[/tex]

Therefore, equations represents the situation are [tex]3x+3[/tex] and [tex]5x-7[/tex]

Answer:

10 Packages

Step-by-step explanation:

The rectangular vegetable garden has a dimension of Length 20 feet and Width 40 feet.

Perimeter of a Rectangle=2(L+W)

=2(20+40)=2(60)=120 feet

Since the store sells fencing in 4-yard packages, let us convert our perimeter to Yards.

1 Yard= 3 Foot

x Yard =120 Feet

Cross Multiply

3x=120

x=40 Yards

The Perimeter =40 Yards

Therefore the number of Packages which Troy and his Mom needs:

Perimeter of the Garden÷Length Per Package

=40÷4

=10 Packages

Troy and his mom would need 20 Packages of Fencing.

To be able to conclude, we conver

Answer:

y-intercepts (0,-12)

Step-by-step explanation:

Answer:

The length is 20 in

Step-by-step explanation:

Use Pythagorean Theorem to solve for the length

15^2 + b^2 = 25^2       Simplify

225 + b^2 = 625

-225           - 225          Subtract 225 from both sides

b^2 = 400                     Take the square root of both sides

b = 20 in

If this answer is correct, please make me Brainliest!

Answer: no

Step-by-step explanation: it is not lower than 12% this year because the Sam model was not used this year which can lead to variation in the calculation of data

Answer:

[tex]x^2+y^2=81[/tex]

Step-by-step explanation:

The standard form of the equation of a circle of radius r, with centre (h, k) is given as:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We are required to write an equation in standard form for the circle with radius 9 centered at the origin.

Substituting these values into the Standard form of the equation of a circle given above:

[tex](x-0)^2+(y-0)^2=9^2\\x^2+y^2=81[/tex]

The standard form is: [tex]x^2+y^2=81[/tex]

The equation of the circle whose center is at (0,0) and the radius is 7 is [tex]\rm x^2+y^2=49[/tex] and the equation of the circle whose center is at (0,0) and the radius is 9 is [tex]\rm x^2+y^2=81[/tex].

Given :

The circle with a radius 9 is centered at the origin.

The following steps can be used in order to determine the equation in standard form for the circle:

Step 1 - The generalized equation of the circle is given below:

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]    --- (1)

where (h,k) represents the coordinates of the center of the circle and r is the radius of the circle.

Step 2 - According to the given data, the center of the circle is at (0,0) and the radius of the circle is 9.

Step 3 - Substitute the values of all the known terms in equation (1) in order to determine the equation of the circle.

[tex]\rm x^2+y^2=81[/tex]

Step 4 - Now, the equation of the circle whose center is at (0,0) and the radius is 7 is given by:

[tex]\rm x^2+y^2=49[/tex]

For more information, refer to the link given below:

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Answer:

19 %

Step-by-step explanation:

380 : 2000 = 0.19

0.19 X 100%= 19 %

Answer:

C. 3/$5.79 = 13/x

Step-by-step explanation:

We can write the fact that 3 markers cost $5.79 as a proportion:

3/$5.79

Let x represent the unknown cost of 13 markers. Since 13 markers cost x, we have the following proportion:

13/x

The cost changes along with the number of markers purchased, and so the two proportions are equivalent.

3/$5.79 = 13/x

Answer:

x = -5

Step-by-step explanation:

You're asking for the solution?  the x value that makes the equation true?

First perform the multiplication:  5 - 10x + 8x = 15

Combining like terms, we get -10 = 2x.

Dividing both sides by 2 yields x = -5.

Answer:

D

Step-by-step explanation:

Area of rectangle= length × breadth

Area of figure

[tex] = ( \sqrt{15x}) ( \sqrt{10x} ) \\ = \sqrt{(10x)(15x)} \\ = \sqrt{150 {x}^{2} } \\ = \sqrt{6(25 {x}^{2}) } \\ = (\sqrt{6} )( \sqrt{( {5x})^{2} } ) \\ = ( \sqrt{6} )(5x) \\ = 5x \sqrt{6} [/tex]

Answer:

5

Step-by-step explanation:

4,2,5,6,3

cancel one on each side ou till you have 1 number left

Answer:

Mean: 4

Median: 4

Mode: 4, 2, 5, 6, 3

Minimum: 2

Maximum: 6

Range: 4

Count: 5

Sum: 20

Step-by-step explanation:

Answer:

x = 119

Step-by-step explanation:

Solution:-

- The number of students in a marching band = x

- When they Line up in "twos" there is 1 left over, That if we mathematically  express it:

                   Division: x / 2 , Remainder = 1

- When they Line up in "threes" there is 2 left over, That if we mathematically  express it:

                   Division: x / 3 , Remainder = 2

- When they Line up in "fours" there is 3 left over, That if we mathematically  express it:

                   Division: x / 4 , Remainder = 3

When they Line up in "fives" there is 4 left over, That if we mathematically  express it:

                   Division: x / 5 , Remainder = 4

When they Line up in "sixes" there is 5 left over, That if we mathematically  express it:

                   Division: x / 6 , Remainder = 5

When they Line up in "sevens" there are no left over, That if we mathematically  express it:

                   Division: x / 7 , Remainder = 0

- It means that the total number of "x" students are perfectly divisible by 7. If it is not divisible by 2, then it is an odd number.

- So,

                  x = 7 * a

Where,       x > 7 and exclude derivative multiples of (5, 4 , 6)

- So from trial and error, a = 17

                  x = 119  

Using multiples and remainder of divisions, it is found that there were 119 students there.

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

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

Shortening the possibilities, we look at odd multiples of 7, which are: {7, 21, 35, 49, 63, 77, 91, 105, 119, ...}

Thus, 119 is the number of students.

A similar problem is given at https://brainly.com/question/21644206