In each diagram, one square unit represents 10 square centimeters. Find the area of each figure. Round to the nearest tenth if necessary.

The length of the rectangle with the above information is calculated as: 7 feet.

Let the length of the rectangle be l and the width be w. Then, we know that:

Perimeter = 2(l + w) = 18 feet

Area = lw = 14 square feet

We can use the first equation to solve for one of the variables in terms of the other:

l + w = 9

l = 9 - w

Substituting l = 9 - w into the equation for the area, we get:

(9 - w)w = 14

w² - 9w + 14 = 0

Factorize

(w - 2)(w - 7) = 0

Therefore, w = 2 or w = 7. Since the length of the rectangle must be larger than its width, we choose w = 2 and l = 9 - w = 7.

Thus, the length of the rectangle is 7 feet.

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In 1973, the batting average of .350 of Rod Carew is more impressive as it has a higher z-score of 2.81

To establish which batting average was more spectacular, we must compare it to the mean and standard deviation of 1970s hitting averages. The case of Jackie Robinson,

z = (x - μ) / σ

z = (.342 - .261) / .0317

z = 2.56

For Rod Carew,

z = (x - μ) / σ

z = (.350 - .261) / .0317

z = 2.81

A higher z-score indicates a more impressive performance relative to the mean. As a result, Rod Carew's .350 batting average was more spectacular, as it had a higher z-score of 2.81 than Jackie Robinson's z-score of 2.56.

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Answer:

1:8

Step-by-step explanation:

The original volume of the box can be calculated by multiplying the length, height, and width:

V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches

If each of the dimensions is reduced by half, the new dimensions become:

Length = 20 inches

Height = 4 inches

Width = 10 inches

The volume of the new box can be calculated as follows:

V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches

The ratio of the volume of the new box to the volume of the original box is:

V_new / V = 800 / 6,400 = 1/8

Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.

Answer:

I think it's 1 : 8

Step-by-step explanation:

if you don't understand, you can ask me

#CMIIW

Answer:

A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.

B. Yes, it is possible. By the Triangle Inequality Theorem:

15 + 15 > 20, and 20 + 15 > 15

Jim's rate of savings (slope): 3

Cassie's rate of savings (slope): 3

Jim's y intercept: 3

Cassie's y intercept: 12

Jim's Savings Equation: y = 3x + 3

Cassie's Savings Equation: y = 3x + 12

Number of weeks it will take to Cassie to save $27: 5

Number of weeks it will take to Jim to save $27: 8

Yes, Jim and Cassie's rates parallel.

Cassie will be able to buy the hat first.

We know that the slope intercept form of a straight line is,

y = mx + c, where m is the slope of the line and c is the y intercept.

For the straight line for Cassie:

The line passing through the points (0, 12) and (1, 15).

So the slope = (15 - 12)/(1 - 0) = 3

The y intercept is = 12.

Equation of the straight line is: y = 3x + 12 ....... (i), where y represents earning in dollars and x represents the time in weeks.

For the straight line for Jim:

The line passing through the points (0, 3) and (1, 6).

So the slope = (6 - 3)/(1 - 0) = 3

The y intercept is = 3

Equation of the straight line is: y = 3x + 3 .......... (ii), where y represents earning in dollars and x represents the time in weeks.

Since the slope of both are equal so the rates of both are parallel.

Substituting the value y = 27 in equation (i) and (ii) we get,

equation (i): 3x + 12 =27

3x = 27 - 12

3x = 15

x = 15/3

x = 5

So Cassie needs 5 weeks to save $27.

Equation (ii): 3x + 3 = 27

3x = 27 - 3

3x = 24

x = 24/3

x = 8

So Jim needs 8 weeks to save $27.

Hence Cassie will be able to buy the hat first.

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The question is incomplete. The complete question will be -

Answer:

Step-by-step explanation:

The sampling distribution of the sample mean for samples of size n is approximately normal with mean μ and standard deviation σ/sqrt(n), where μ is the mean of the population, σ is the standard deviation of the population, and sqrt(n) is the square root of the sample size.

In this case, the population mean is μ = 112 and the population standard deviation is σ = 22. We are interested in the sampling distribution of the sample mean for samples of size n = 16.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is μ = 112.

The standard deviation of the sampling distribution of the sample mean is σ/sqrt(n) = 22/sqrt(16) = 5.5.

Therefore, the sampling distribution of the sample mean for samples of size 16 is approximately normal with mean 112 and standard deviation 5.5.

The solution to the equation is x = 33/5.

We can start by simplifying both sides of the equation using the distributive property and combining like terms:

4/3 (x + 6) = 2x - 3 + x

4/3 x + 8 = 3x - 3

Next, we can isolate the variable x on one side of the equation by subtracting 4/3 x and adding 3 to both sides:

4/3 x - 3x = -8 - 3

-5/3 x = -11

Finally, we can solve for x by dividing both sides by -5/3:

x = -11 / (-5/3)

x = 33/5

Therefore, the solution to the equation is x = 33/5.

Answer:

Step-by-step explanation:

1/3 is greater.

The calculated area of the triangle B is 1.8 square units

From the question, we have the following parameters that can be used in our computation:

Triangle A and B

Where

Area of A = 1/2 base * height

Sp, we have

Area of A = 1/2 * 2 * 5

Next, we have

Area of B = Area of A * Scale factor^2

Using the above as a guide, we have the following:

Area of B = 1/2 * 2 * 5 * (3/5)^2

Evaluate

Area of B = 1.8

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Answer:

symbols V

The symbols V L and D are not written to the left of a symbol that has greater value

The number of acres pollinated by the bees in 18 beehives is 48 acres.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

x: number of beehives.

y: number of acres.

From the table, the constant is obtained as follows:

3k = 8

k = 8/3

Hence the equation is of:

y = 8x/3.

The number of acres that will be pollinated by 18 beehives is then given as follows:

y = 8(18)/3

y = 48 acres.

Therefore, the number of acres pollinated by the bees in 18 beehives is 48 acres.

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The measure of the side length x is 15.04.

The figure in the image is a right triangle.

Angle θ = 43 degrees

Adjacent to angle θ = 11

Hypotenuse = x

To determine the measure of the side length x, we use the trigonometric ratio.

Note that: cosine = adjacent / hypotenuse

Plug in the values:

cos( 43° ) = 11 / x

Solve for x

x = 11 / cos( 43° )

x = 15.04

Therefore, the value of x is 15.04 units.

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Answer:5.25cm

Step-by-step explanation:

1)look back at your question

2)look after the 6th word

Answer:  The value of the test statistic to 2 d.p is z= 1.65

Step-by-step explanation:

P cap= 0.72

n= 170

P= 0.66

q= 1- p

q= 1- 0.66

q= 0.34

Z=( p cap - p)/√(p*q)/n

Z= (0.72- 0.66)/√(0.66*0.34)/170

Z= 0.06/0.036332

Z= 1.65

Answer:

3. radius = 9.4

4. radius = 22.6

5. diameter = 13.3

Step-by-step explanation:

The diameter of a circle = 2 * radius

For problem 3 and 4,  you need to multiply the given radius by 2 to get the diameter.

For problem 5, you need to divide the diameter by 2 to get the radius.

The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

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Therefore, 4,000 centimeters are equivalent to 40 meters. Hence, the answer is A) 4,000 cm.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

Since there are 100 centimeters in one meter, we can convert meters to centimeters by multiplying the length in meters by 100.

So, to convert 40 meters to centimeters, we can multiply 40 by 100:

40 meters = 40 x 100

= 4,000 centimeters

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Answer:

13.3333333333 or 13.3

Step-by-step explanation:

yeah :3

Answer: 16 pounds

Step-by-step explanation:

12/3=4 and 4x4=16

The perimeter of the rug is 36ft

Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.

Perimeter of a rectangle is expressed as ;

P = 2(l+w)

The area of the rug is 81ft²

area = l× w

length = 9ft

width of the rug = 81/9 = 9ft

Therefore the perimeter of the rug will be

P = 2(l+w)

P= 2( 9+ 9)

P = 2 × 18

P = 36 ft

therefore the perimeter of the rectangular rug is 36ft

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Roger and Trish can complete 11/30 of the math homework in 1 hour if they work together.

What is an expression?

An expression is a sentence that has at least two numbers/variables and at least one math operation.

According to the given information:

Let the total amount of work in the math homework is 1.

In one hour, Roger can finish 1/6 of the work, and Trish can finish 1/5 of the work.

If they work together for 1 hour, then the total amount of homework they can finish is the sum of the parts each of them can finish in one hour:

1/6 + 1/5 = 5/30 + 6/30 = 11/30

So together they can finish 11/30 of the homework in one hour.

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To find the mean time it takes for Diane and her friends to complete the obstacle course, we added up the time taken by each person and divided by the total number of people. The mean time is 13.0 minutes.

Add up the time taken by each person

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16

Total time = 12 + 14 + 10 + 16 = 52 minutes

Count the total number of people:

Diane and three friends, so the total number of people = 4

Divide the total time by the total number of people to find the mean time

Mean time = Total time / Total number of people

Mean time = 52 / 4

Mean time = 13.0 minutes

Therefore, the mean time it takes for Diane and her three friends to complete the obstacle course is 13.0 minutes.

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--The given question is incomplete, the complete question is given

" Diane is a camp counselor she designs a new obstacle course in testicles with three friends. The plot data shows the time it takes them to complete the obstacle course. What is the mean of time

the plot data for the time taken by each person in minutes is as follows

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16 "--

for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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for KW 1 calculation output are 15,17,19,21,23for KW 2 calculation output are 61,63,65  for KW 3 calculation are   16,23,30,37,114,121,128,  just by substituting to equation we can get answer

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written using an equal sign (=) between the two expressions. An equation can contain variables, which are symbols that represent unknown values.

In the given question,

for table 1 calculation is as below

output x=0 is  15+2x=15+2*0=15

output x=1 is  15+2x=15+2*1=17

output x=2 is  15+2x=15+2*2=19

output x=3 is  15+2x=15+2*3=21

output x=4 is  15+2x=15+2*4=23

for table 2 calculation is as below

output x=1 is  60+2x=60+2*1=61

output x=2 is   60+2x=60+2*2=63

output x=3 is   60+2x=60+2*3=65

for table 3 calculation is as below

output x=0 is 16+7x=16+7*0=16

output x=1 is  16+7x=16+7*1=23

output x=2 is 16+7x=16+7*2=30

output x=3 is  16+7x=16+7*3=37

output x=14 is 16+7x=16+7*14=114

output x=15 is 16+7x=16+7*15=121

output x=16 is 16+7x=16+7*0=128

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Answer:

<2  = 30°

Step-by-step explanation:

Let angle 1 = x

Let angle 2 = y

x + y = 95

x = 35 + y  Substitute 35 + y for x in x + y = 95

x + y = 95

35 + y + y = 95  Subtract 35 from both sides

y + y = 60    Combine like terms

2y = 60  Divide both sides by 2

y = 30

Helping in the name of Jesus.

The initial temperature of the soda is 18 degrees Celsius.

Its temperature after 20 minutes is 2.73 degrees Celsius.

In Mathematics, an exponential function can be modeled by using this mathematical expression:

f(x) = a(b)^x

Where:

When time, t = 0, the initial value can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]

C(0) = 18(1)

C(0) = 18 degrees Celsius.

When time, t = 0 = 20, the temperature can be calculated as follows;

[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]

C(20) = 2.73 degrees Celsius.

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Complete Question:

A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.

[tex]C(t)=18(0.91)^{t}[/tex]

Find the initial temperature of the soda and its temperature after 20 minutes?

a) We are given that f(x) = x^3 - 10x^2 + 19x + 30 and x - 6 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x - 6 to get the other factor(s):

 6 │ x^3 - 10x^2 + 19x + 30

     x^3 - 6x^2

     -------------

          -4x^2 + 19x

          -(-4x^2 + 24x)

          ---------------

                     5x + 30

                     5x - 30

                     -------

                            0

Therefore, we can write:

f(x) = (x - 6)(x^2 - 4x + 5)

The quadratic factor x^2 - 4x + 5 cannot be factored further using real numbers.

b) We are given that f(x) = x^3 + 6x^2 + 5x - 12 and x + 4 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x + 4 to get the other factor(s):

-4 │ x^3 + 6x^2 + 5x - 12

     -x^3 - 4x^2

     --------------

              2x^2 + 5x

              2x^2 + 8x

              ------------

                     -3x - 12

                     -3x - 12

                     --------

                            0

Therefore, we can write:

f(x) = (x + 4)(x^2 + 2x - 3)

The quadratic factor x^2 + 2x - 3 can be factored further using the product-sum method:

x^2 + 2x - 3 = (x + 3)(x - 1)

Therefore, we have:

f(x) = (x + 4)(x + 3)(x - 1)

Answer:

3rd choice:  when b>1

Step-by-step explanation:

For this function, a is the starting value (initial amount).  b is the decay or growth factor.  If b>1, then the function is a growth function.

FYI, if 0 < b < 1, then it is a decay function.