Find the area. The figure is not drawn to scale.

A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.

Answer:

Star is is further away

3.995 x [tex]10^{7}[/tex]

Step-by-step explanation:

(4 x [tex]10^{7}[/tex]) - ( 5 x [tex]10^{4}[/tex]) To subtract we need to have the same powers of 10

(4 x [tex]10^{7}[/tex]) - (.005 x [tex]10^{7}[/tex])

(4  - .005)x [tex]10^{7}[/tex]

3.995 x [tex]10^{7}[/tex]

The scale factor of the dilation of the given object is 4.

The scale factor of dilation:

The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.

Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.

The basic formula to find the scale factor of a dilated is:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

[tex]SD=\frac{32cm^2}{4cm^2}[/tex]

SD=4

Thus, the scale factor of the dilation of the given object is 4.

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Jamal will have the amount of $5132.10 in the account after 10 years.

As per the given data:

Jamal deposited the principal amount of $4000 into an account.

P = $4000

Amount brought with 2. 5% interest which is compounded quarterly.

Convert the rate percent to the decimals.

We get:

2. 5% = [tex]$\frac{25}{100}[/tex]

2. 5% = 0.025 = r

Also given that no withdrawals are made.

Here we have to determine that how much will he have in the account after 10 years.

t = 10 years

As the interest is compounded quarterly the value of n is 4

n = 2

Compound interest is the type of interest that is added to the principle amount before the next compounding period begins.

According to compound interest formula:

[tex]$ A=P\left(1+\frac{r}{n}\right)^{n t} \\[/tex]

[tex]$\Rightarrow & A=4000\left(1+\frac{0.025}{4}\right)^{4 \times 10} \\[/tex]

[tex]\Rightarrow \quad & A=4000(1+0.00625)^{40} \\[/tex]

[tex]\Rightarrow \quad & A=4000 \times(1.00625)^{40} \\[/tex]

A = 4000 × 1.2830268206

A = 5132.1072824

A = 5132.10 (After rounding to the nearest cent)

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If he bake 3 loave pf banana bread. Since 23 1/3 wants a lot of bread, Erin's banana bread is not enough.

These are the specified parameters:

Erin's number of guests = 20 people.

Each guet to have 1 1\6 of a loaf.

If he bake 3 loave pf banana bread.

Much to be desired bread

= number of guests × bread per guest

= 20 × 1 1/6

= 20 × 7/6

= 70/3

= 23 1/3

He baked 3 banana loaves, whereas the desired number of loaves was 23 1/3.

Thus Erin's banana bread is not enough for the guest.

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When 0.36 is expressed as a common fraction in lowest terms, the numerator is 9 and the denominator is 25. The sum of the numerator and denominator is 34.

To calculate the sum of the numerator and denominator when 0.36 is expressed as a fraction in lowest terms, follow these steps:

In this case, 0.36 can be expressed as 9/25. The greatest common factor of 9 and 25 is 1, so the fraction is already in its lowest terms. The sum of the numerator and denominator is 9 + 25 = 34.

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Answer:
The solution to the system of linear inequalities x <= 8 and y > -3, represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x=8 and above the line y=-3 .

Step-by-step explanation:

The solution to the system of linear inequalities x <= 8 and y > -3 can be represented on a coordinate plane as a region that satisfies both inequalities.

To graph the solution, we first plot the line x = 8 on the coordinate plane. Since x <= 8, this line represents the boundary of the solution. Everything to the left of the line x = 8 is included in the solution.

Next, we plot the line y = -3. Since y > -3, everything above the line y = -3 is included in the solution.

The final graph will be a half-plane formed by the line x=8 and above the line y=-3 .

Suppose that 20% of people own dogs, if you pick two people at random,  the probability that they both own a dog is 0.04.

Suppose that 20% of people own dogs.

So the probability of selecting own dogs = 0.20

The probability that a population unit will be included in a sample obtained through probability sampling is known as probability of selection. Each subset of a population has a probability of being chosen in the sample, which is determined by the sampling design.

If you pick two people at random, then the probability that they both own a dog = 0.20 × 0.20

If you pick two people at random, then the probability that they both own a dog = 0.04

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Answer:

X>3

Step-by-step explanation:

So we're solving for X

Since it's an inequality, let's make it = 27 instead

4x+15=27

Now we can subtract 15

4x = 12

x = 3

Now that it's saying > 27, that means the same for x, it's has to be > too, concluding x>3... all x's greater than 3

The average rate of change from x = -2 to x = 0 of the function f(x) = 3x² - 2x + 5 is -8.

The average rate of change from -2 to 0 is;

f(0) - f(-2) / 0 - (-2)

Given the quadratic equation in question;

f(x) = 3x² - 2x + 5

Plug in the values;

[ ( 3(0)² - 2(0) + 5 ) - ( 3(-2)² - 2(-2) + 5  ) ]/ 0 - (-2)

[ ( 0 - 0 + 5 ) - ( 12 + 4 + 5  ) ]/ 0 - (-2)

[  5 - 21 ] / 0 - (-2)

[  -16 ] / 2

-16/2

-8

Therefore, the average rate of change is -8.

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The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.

What is a function ?

Function can be defined as which relates an input to output.

Given,

Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms.

Height = b

Volume V = 6³-6b²+9b.

Length of each side (s) :

V = 6³-6b²+9b.

s^2 b  = b (b^2 - 6b + 9 )

s^2 = b^2 - 6b + 9

(a - b ) ^2 = a^2 + b^2 -2ab

s^2 = (b-3) ^2

s = b-3

height is 18 inches and height is given as b

Hence, b = 18

s= b-3 (from i)

= 18 - 3

s = 15

Therefore volume:

volume of rectangle = l x b x h

V= 18 x15 x15= 4,050

(If height = 15

then, b = 15

b -15 = 0

Definition of remainder theorem:

we divide a polynomial P(x) by a factor ( x – a); to find a smaller polynomial along with a remainder. The factor doesn't have to be a part of the polynomial.

b^3 - 6b^2 + 9b  /  b-15  = 2160

Therefore Volume with b = 15 is 2160

Therefore, The expression for side of square bottom = b - 3, volume of rectangle is 4050 and the volume of a cage with a height of 15 inches is 2160.

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Answer:

C

Step-by-step explanation:

Hi there and welcome to brainly!

By looking at the number line, we want to identify which point represents the approximate value of 5π

We know that π has an approximate value of 3.14 so the approximate value of 5π = 5 × 3.14 = 15.7

Looking at the number line, 15.7 falls in between 15 and 16 which correlates to point C

The graph shows that f is not continuous at x=-4 and x=4. This is because the graph does not have a continuous line at those points.

A graph is a visual representation of data that uses dots, lines, or bars to show how different elements of a set of data are related. Graphs are typically used to show patterns or trends in data over time, or to compare different sets of data. Graphs can also be used to show the relationships between different variables.

At x=-4, there is a large gap between the left side and the right side of the graph. At x=4, the graph has a sharp corner, which shows that the graph is not continuous.

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When a = 2, b = 4, c = -5, and d = -5, the expression for 1/4b^3 - 1/5d^3 is 11.

How do you evaluate this expression?

When a = 2, b = 4, c = -5, and d = -5, the expression becomes:

1/4 * 4^3 - 1/5 * (-5)^3

= 1/4 * 64 - 1/5 * -125

= 16 - 25/5

= 16 - 5

= 11

So the expression evaluates to 11.

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I think "E" it's the most close answer for me

Answer:

52

Step-by-step explanation:

Using the exterior angle theorem, [tex]112+x=164 \implies x=52[/tex]

a. The percentage of GMAT scores is 647 or higher approximately 15.9%

b. The percentage of GMAT scores that are 747 or higher (to 1 decimal) is approximately 2.3%.

c. The percentage of GMAT scores between 447 and 547 is approximately 84.1%.

d. The percentage of GMAT scores between 347 and 647 (to 1 decimal) is approximately 98.0%.

a. The GMAT score of 647 is 100 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 647-547/100 = 1.

Using a standard normal table, we can find that the percentage of GMAT scores that are 647 or higher is approximately 15.9%.

b. The GMAT score of 747 is 200 points above the average score of 547. Using the standard deviation of 100, we can calculate the standard score (z-score) as 747-547/100 = 2.

Using a standard normal table, we can find that the percentage of GMAT scores that are 747 or higher is approximately 2.3%.

c. The GMAT scores between 447 and 547 are 100 points below and 100 points above the average score of 547, respectively.

Using the standard deviation of 100, we can calculate the standard score (z-score) as (447-547)/100 = -1 and (547-547)/100 = 0.

Using a standard normal table, we can find that the percentage of GMAT scores that are between -1 and 0 is approximately 84.1%.

d. The GMAT scores between 347 and 647 are 200 points below and 100 points above the average score of 547, respectively.

Using the standard deviation of 100, we can calculate the standard score (z-score) as (347-547)/100 = -2 and (647-547)/100 = 1.

Using a standard normal table, we can find that the percentage of GMAT scores that are between -2 and 1 is approximately 98.0%.

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The complete question is -

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

a. What percentage of GMAT scores are 647 or higher?

b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?

c. What percentage of GMAT scores are between 447 and 547 ?

d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

Answer: The initial amount (a) in the exponential function is 5, and the decay factor (b) is 0.5.

Step-by-step explanation: :D

Answer:

24

Step-by-step explanation:

18/3=6 6*4=24

The value of x for the similar triangles is equal to 24.

The triangles are similar, this implies that the length x cm of the bigger triangle is similar to the length HJ = 18 cm of the smaller triangle

and the length DF = 16 cm of the bigger triangle is similar to the length JG = 12 cm of the smaller triangle

so;

x/18 = 16/12

12x = 18 × 16 {cross multiplication}

12x = 288

x = 288/12 {divide through by 12}

x = 24 cm

Therefore, the value of x is equal to 24 cm for the similar triangles.

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Answer:

The answer assumes that the density of glass is 3 g/cm^3, not 3 g/cm^2.

The mass of the paperweight is 270 grams.

Step-by-step explanation:

Lets calculate the volume of a sphere having a radius of 3.5cm, and then divide that by 2 to get the volume of the hemisphere (half a sphere).  The sphere has a diameter of 7cm (therefore, a radius of 3.5cm).

Vol (sphere) = (4/3)πr^3

Vol = (4/3)(3.14)(3.5cm)^3

Vol = 180 cm^3

Half of this (the hemisphere) will be 90 cm^3

We know the volume, and we know the density of glass (3 g/cm^3), so multiply the two to obtain the mass of the paperweight.

 (90 cm^3)*(3g/cm^3) = 270 grams

well, we know there are 60 minutes in 1 degree, so 24' is 24/60 = 0.4°, so 61°24' is really 61.4°,  now, we also know that there are 180° in π radians, so

[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 61.4&x \end{array}\implies \cfrac{180}{61.4}~~ = ~~\cfrac{\pi }{x} \\\\\\ 180x=61.4\pi \implies x=\cfrac{61.4\pi }{180}\implies x=\cfrac{307\pi }{900}\implies x\approx 1.07~radians[/tex]

Span {u1, u2} = P, and we have found two vectors in u1 = (1, 0, -a/c) and u2 = (0, 1, -b/c) in R3 that span the plane P.

Given: "Find two vectors in u1 and u2 in R3 so that span {u1, u2} = P", where P is a plane in R3.

To find the vectors u1 and u2, we need to find two linearly independent vectors that lie in the plane P.

One possible method to find these vectors is to choose a point on the plane and find a normal vector to the plane. We can then use the point and the normal vector to parameterize the plane.

For example, let's choose a point on the plane as (x0, y0, z0) and a normal vector to the plane as n = (a, b, c).

Then, the equation of the plane can be written as:

ax + by + cz = d

where d = a * x0 + b * y0 + c * z0

We can then choose two linearly independent vectors in the plane by taking partial derivatives with respect to x and y, respectively.

Let's choose u1 = (1, 0, -a/c) and u2 = (0, 1, -b/c). These two vectors lie in the plane and are linearly independent.

Therefore, span {u1, u2} = P, and we have found two vectors in u1 and u2 in R3 that span the plane P.

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The concept is Data Analysis,  which is the process of totally applying statistical tools to dissect data. The answer is options B, C, and D.

To help you consider data limitations, critically dissect correlations, examine the environment, and understand tool strengths and sins. Data analysis applies statistical and/ or logical ways to describe, illustrate, epitomize, and estimate data.

Data analysis helps individualities and associations make sense of data. Data analysts typically analyze raw data for insights and trends.

Limitations include:

Question

You're preparing a question-and-answer session that will follow your donation. Which styles help you to consider data limitations? elect everything that suits you.

A) exclude the outliers

B) Understand the strengths and sins of the tools

C) Critically dissect the correlations

D) Look at the environment

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Answer:

[tex]\left(\dfrac{14}{3}\;, \;\dfrac{16}{3}\right)[/tex]

Step-by-step explanation:

We have two points A(2, 4) and B(10, 9)

P divides the segment AB, it is located 1/3 of the distance from A to B

Lets use the following notation

[tex]\textsf {x_{AB}$= x-distance from A to B}[/tex]
This is the absolute difference between the x-coordinates of A and B

[tex]\textsf {y_{AB}$= y-distance from A to B}[/tex]
This is the absolute difference between the y-coordinates of A and B

[tex]\textsf {x_{AP}$= x-distance from A to P}[/tex]
This is the absolute difference between the x-coordinates of A and P

[tex]\textsf {y_{AP}$= y-distance from A to P}[/tex]
This is the absolute difference between the y-coordinates of A and P

To find the coordinates of P:

Answer: The coordinates of point P are:
[tex]\left(\dfrac{14}{3}\;, \;\dfrac{16}{3}\right)[/tex]

If you actually calculate the distances AB and AP using the distance formula:   [tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

you will find
AB has length 8.944272 and AP has length 2.9829

2.9829/8.944272 ≅ 0.333 which is 1/3

W satisfies both conditions and is closed under addition and scalar multiplication.

In mathematics, a vector space is a fundamental concept in linear algebra.

It is a mathematical structure that consists of a set of objects called vectors, along with operations for vector addition and scalar multiplication.

These operations follow certain axioms, which define the properties of a vector space.

The statement "W is the set of all nonnegative functions in C(−∞, ∞)" does not specify the vector space C(−∞, ∞) correctly.

To determine if W is a subspace of a given vector space, we need to define the vector space correctly.

However, assuming C(−∞, ∞) refers to the set of all continuous functions defined on the interval (−∞, ∞), we can analyze whether W is a subspace of this vector space.

To be a subspace, W must satisfy two conditions:

W must be closed under addition.

W must be closed under scalar multiplication.

Let's evaluate these conditions for W, the set of all nonnegative functions in C(−∞, ∞):

W is closed under addition:

If we take two nonnegative functions from W, their sum will also be nonnegative.

Thus, the sum of any two functions from W will remain in W. Therefore, W is closed under addition.

W is closed under scalar multiplication:

If we multiply a nonnegative function from W by a positive scalar, the result will still be a nonnegative function.

Thus, scalar multiplication by a positive scalar preserves the nonnegativity of the function.

Therefore, W is closed under scalar multiplication.

Based on the above analysis, W satisfies both conditions and is closed under addition and scalar multiplication.

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The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Rita the mentor has two independent exercise designs that she offers her clients: Plan An and Plan B. Every client does it is possible that either (not both). On Friday there were 5 clients who arranged A and 3 who arranged B. On Saturday there were 2 clients who arranged A and 6 who arranged B. Rita prepared her Friday clients for a sum of 10 hours and her Saturday clients for a sum of 10 hours.

The length of each Plan A workout is given as,

Rate = (5 + 2) / 10

Rate = 7 / 10

Rate = 0.70 per hour

The length of each Plan B workout is given as,

Rate = (3 + 6) / 10

Rate = 9 / 10

Rate = 0.90 per hour

The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.

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C(x) = 16x – 63, where x is the number of thousands of bottles, gives the cost of producing bottled spring water.

The formula R(x) = - x2 + 326x – 7463 calculates the total amount (revenue) from the sale of these bottles.

Bottles sold will yield the highest profit.

Profit maximization

Profit after selling 245 thousand bottles

C(x) = 16x – 63

R(x) = – x² + 326x – 7463.

Revenue – Cost = Profit

P(x) = R(x) – C (x)

= – x² + 326x – 7463 – (16x – 63) (16x – 63)

= – x² + 310x – 7400

Choice c)

Profit = x2 minus 310x minus 7400

P(x) = – x² + 310x – 7400

P’(x) = -2x + 310

P’(x) = 0 => -2x + 310 = 0 => x = 155

P’’(x) = - 2 < 0

As a result, profit is greatest at x = 155.

The highest profit will be generated if 155 bottles are sold.

Alternative b)

Profit maximization at x = 155

P(x) = – x² + 310x – 7400

= -(155)² + 310(155) – 7400

= Rs 16625

The highest possible profit is Rs 16625.

Alternative b)

Profit after selling 245 thousand bottles

X = 245

−(245)2 + 310(245) – 7400 = profit

= 8525

Alternative (a) Rs 8525

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The Recommended daily amount of fiber from the expression 8x is 32g.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given Fiber in one serving of cereal=8gm which is 25% of one day need.

Let 8x be the fiber in cereal where x is multiple of 25%.

So, for one day need fiber needed is 100% i.e. x=4.

Therefore, Fiber needed =8*4=32g

Hence,

          The Recommended daily amount of fiber is 32g.

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Answer:

C and D

Step-by-step explanation:

3x + 1 and 1 + 3x are the phrase for 'Thrice a number more than 1.

they can simplify to get the same answer.