Write the exponential function that describes the situation.
The initial amount of the function is 12​, and then it decreases by a factor of 7/9
with each unit increase in x.

Answer: 1 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Make it a mixed number then simplify if you can. I hope this helps.

Answer:

(x + 7)(x - 3) = 75 square feet.

Step-by-step explanation:

Given that x represents the side length of the mural in Ashwin's classroom, the hallway mural's length is x + 7 feet and its width is x - 3 feet. The area of the hallway mural can be found by multiplying these two binomials, (x + 7)(x - 3), to get x^2 + 4x - 21.

If each side of the classroom mural is 8 feet long, the hallway mural would have sides of 15 feet and 5 feet, so its area would be 75 square feet, which is the answer.

The third side is between 7 and 17 inches long.

This theorem states that for any triangle, the sum of the lengths of the first two sides will always be greater than the length of the third side.

A triangle's two sides have lengths of 5 and 12 inches.

According to the triangle Inequality (theorem), any triangle's two sides must add up to more than its third side.

The length of the third side will be,

5 + 12 = 17 inches

It is to be noted that the difference between the two sides cannot be less on the third side.

The third side must be greater than,

12 – 5 = 7 inches.

As a result, the third side's length ranges from 7 to 17 inches.

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4.1. The boys' masses range from a minimum of 32 kg to a maximum of 82 kg.

4.2. The girls' masses range from a minimum of 35 kg to a maximum of 67 kg.

5: To create the frequency table, we need to tally the number of male and female learners in each mass interval. Here are the tallies:

Mass interval Tally

40 - 49,9 kg |||| (4 females)

50 - 59,9 kg ||||||| (7 females)

60 - 69,9 kg ||||| (5 females)

70-79,9 kg || (2 males)

80 - 89,9 kg || (2 males)

Note: The vertical lines represent the tallies, with each line representing one learner.

6: By looking at the frequency table, we can compare the number of male and female learners in each mass interval. We can see that there are more female learners in the lower mass intervals (40-49.9 kg, 50-59.9 kg, and 60-69.9 kg) compared to male learners. On the other hand, there are more male learners in the higher mass intervals (70-79.9 kg and 80-89.9 kg) compared to female learners

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Answer: 54 is 18.24% of 296

Step-by-step explanation:

54:296*100 =

(54*100):296 =

5400:296 = 18.24

Now we have: 54 is what percent of 296 = 18.24

Question: 54 is what percent of 296?

Percentage solution with steps:

Step 1: We make the assumption that 296 is 100% since it is our output value.

Step 2: We next represent the value we seek with x

Step 3: From step 1, it follows that 100% = 296

Step 4: In the same vein, x% = 54

Step 5: This gives us a pair of simple equations:

100% = 296 (1)

x% = 54 (2)

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left-hand side) of both equations have the same unit (%); we have

100% over x% = 296 over 54

Step 7: Taking the inverse (or reciprocal) of both sides yields

x% over 100% = 54 over 196

x=18.54

The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°

A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.

When the two diagonals of a rhombus are known,

The perimeter = 2√p² + q²

where 'p' and 'q' are the diagonals.

Given data ,

Let the rhombus be represented as JKLM

where MK and JL are the diagonals and N is the midpoint of intersection

The measure of MK = 24

The measure of JL = 20

The measure of NK = 12

The measure of ∠MJL = 50°

Now , the diagonals of a rhombus bisect each other , so

NK = MK/2 = 12

And , NL = JL / 2 = 10

Now , to calculate the measure of ML ,

In triangle MNL, ∠N = 90°

MN = NK = 12 , NL = 10

Using Pythagorean theorem of triangles , we get

ML² = MN² + NL²

ML² = 12² + 10²

ML² = 244

ML = √244

On simplifying the equation , we get

ML = 2√61 = 15.62

The measure of ML = measure of JM = 15.62 ( all sides are equal )

The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )

∠KJL = ∠MJL (diagonals bisect angles)

The measure of ∠KJL = 50°

∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°

∠MJK = ∠MLK (opposite angles are equal)

The measure of ∠MLK = 100°

∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)

50 + 90 + ∠JKM = 180

The measure of ∠JKM = 40°

∠JKL = 2 x ∠JKM (diagonal bisect angle)

The measure of ∠JKL = 2 x 40

The measure of ∠JKL = 80°

∠JKL = ∠JML (opposite angles are equal)

The measure of ∠JML = 80°

Hence , the measures of rhombus is solved

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Answer:

4/23

Step-by-step explanation:

I Did The Quiz :)

Answer:  Choice D

Explanation:

The notation [tex]-\infty < \text{x} < \infty[/tex] says x is anything between negative infinity and positive infinity. Basically x is any real number. This is because the curve stretches forever to the left and right. Any number can be the x input.

The indirect speech version of the given sentence would be:

She said that her mother was cooking food.

Indirect speech (also known as reported speech) is a way of expressing what someone else said, without using their exact words. In indirect speech, we usually report the statement or question using a reporting verb like "say", "tell", "ask", or "explain", followed by a conjunction such as "that". We also need to change the tense and sometimes the pronouns to reflect the new context.

Indirect speech is often used in writing and speaking to convey someone else's message, opinion or idea. It helps us to paraphrase or summarize what someone else said, without quoting them directly. It is important to learn how to use indirect speech correctly, as it is a common feature of both formal and informal communication.

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Step-by-step explanation:

inscribed angles subtended by the same arc are equal.

the angle FGH is "based" on the same arc (FH) as the angle FJH.

so, FGH = FJH = 56°.

Answer:

Step-by-step explanation:

To solve this system of linear equations, we need to find the values of x and y that make both equations true at the same time. One method to solve this is to use elimination or substitution.

First, let's rearrange the first equation:

y = 2x

Next, we can substitute y = 2x into the second equation:

-7x + 3y = 2

-7x + 3(2x) = 2

-7x + 6x = 2

-x = -2

So, x = 2.

Finally, we can use the first equation to find y:

y = 2x

y = 2 * 2

y = 4

So, the solution to the system of equations is (x, y) = (2, 4).

4x³ + 9x² - x - 6 is a volume of the container.

What does volume mean in plain terms?

Any three-dimensional solid's volume is just the amount of space it takes up. These solids can have the shape of a cube, cuboid, cone, cylinder, or sphere.

                                The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called the cubic meter (m3) serves as the SI unit of volume.

= (4x-3) . (x+1) . (x+2)

= [ 4x .x + 4x . 1 - 3x - 3] . ( x + 2)

= ( 4x² + 4x - 3x - 3 ) ( x + 2 )

= ( 4x² + x - 3 ) ( x+ 2 )

= 4x³ + x² - 3x + 8x² + 2x - 6

 = 4x³ + 9x² - x - 6

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Answer:

The flagpole is 15 ft tall.

Step-by-step explanation:

In this problem, we are asked to create a proportion of similar triangles to solve for the height of a flagpole.

We are given an equation with the proportion:

[tex]\dfrac{h}{6\text{ft}}=\dfrac{\square}{\square}[/tex]

We can fill in the blanks as follows:

[tex]\dfrac{h}{6\text{ft}}=\dfrac{25 \text{ft}}{10 \text{ft}}[/tex]

Notice that the heights of the triangles compared are both in the numerator, and the lengths of both triangles are in the denominator.

Then, to solve for the height of the flagpole, we can isolate the variable h in the proportion.

[tex]\dfrac{h}{6}=\dfrac{25}{10}[/tex]

↓ multiply both sides by 6

[tex]h = \dfrac{150}{10}[/tex]

↓ simplify the fraction

[tex]h = 15 \text{ ft}[/tex]

So, the flagpole is 15 ft tall.

The equation for the perimeter will be (4/5)d + 18d = 282. The value of d is 15.

The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a trapezoid, the perimeter will be the sum of all the sides of the trapezoid.

Given that the four sides of the figure are,

12d + 4

4/5d -9

2d

4d - 6

The perimeter of the figure is 271. The equation can be written as:-

(4/5)d - 9 +12d + 4 + 4d - 6 + 2d = 271

(4/5)d + 12 d + 4d + 2d -15 + 4 = 271

(4/5)d + 18d = 282

94d = 282 x 5

d = 15

Therefore, the perimeter will be calculated as (4/5)d + (18d) = 282. D has a value of 15.

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The answer is given below:

Binomial distribution is a discrete  probability distribution in which it gives two values that is either success or failure.

A local donut shop began putting an extra donut in some of the boxes.

The shop owner claimed that one in seven boxes had an extra donut.

Nine customers each bought one box of donuts at the shop.

Probability of success fixed is, [tex]p=\frac{1}{7}[/tex]

A value of n fixed, n=9.

We can use binomial distribution to solve this problem,

The probability mass function for the Binomial distribution is given as:

Assume  X is a binomial distribution, [tex]B(n=9,p=\frac{1}{7}=1.143)[/tex].

[tex]P(X)=(nCx)(p)^{x} (1-p)^{n-x}[/tex]

The mean is given by:

[tex]E(X)=np=9*\frac{1}{7}=1.29\\[/tex]

The variance is given by,

[tex]Var(X)=np(1-p)=9*\frac{1}{7}(1-\frac{1}{7} )[/tex]=1.1094

From variance, the standard deviation is given by, [tex]std(X)=\sqrt{1.1094}[/tex]=1.05.

Two of the nine customers buy a box of donuts with an extra donut. Compute P(X ≥ 2) and use the result to justify your answer.

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)][/tex]

And if we find the individual probabilities we got,

[tex]P(X=0)=(9C0)(0.143)^{0} (1-0.143)^{9-0}=0.249\\P(X=1)= (9C1)(0.143)^{1} (1-0.143)^{9-1}=0.374[/tex]

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)]\\[/tex]

                      = 1-[0.249+0.374]

                       = 0.377

Hence, [tex]P(X\ge2)=[/tex] 0.377.

This case makes sense the claim since the probability is higher or equal than the expected with the claim.

Corrected question:

To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.A. Is X a binomial random variable? Explain.B. What is the mean and standard deviation of X? Provide an interpretation for each value in context.C. Two of the nine customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer.

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The given sequence appears to be an arithmetic sequence, as the difference between consecutive terms is 9. To find the 43rd term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_n is the nth term, a_1 is the first term (11 in this case), n is the term number (43 in this case), and d is the common difference (9 in this case).

Plugging in the values, we get:

a_43 = 11 + (43 - 1) * 9

a_43 = 11 + 42 * 9

a_43 = 11 + 378

a_43 = 389

So the 43rd term of the sequence is 389.

The Cupcake Café’s recipe for cheesecake calls for 2/3 cup of cream cheese.42 cups of cream cheese does the café use to make 63 cheesecakes.

What is word problem?

A word problem is a mathematical problem or puzzle that is presented in the form of a written description or narrative, rather than as a simple equation or formula. It typically involves a scenario or situation that requires mathematical calculations or problem-solving skills to arrive at a solution. Word problems can be found in a variety of settings, including in math textbooks, standardized tests, and real-life situations. They often require the reader to identify and interpret relevant information, apply mathematical concepts and formulas, and use critical thinking skills to arrive at a correct answer.

To make 63 cheesecakes, the Cupcake Café would use:

(2/3 cup of cream cheese per cheesecake) x (63 cheesecakes)

= 42 cups of cream cheese.

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The standard deviation of the number of lemons used is equal to 14.7.

Mathematically, the mean for these set of data would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 47 + 45 + 61 + 44 + 16

F(x) = 213.

Mean = 213/5

Mean = 42.6

Next, we would calculate the standard deviation of this data set by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × (47 - 42.6)² + (45 - 42.6)² + (61 - 42.6)² + (44 - 42.6)² + (16 - 42.6)²)

Standard deviation, SD = √(1073.2/5)

Standard deviation, SD = 14.7.

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The three consecutive odd integers are 47, 49, and 51. The third number is 51, so the answer is (d) 51.


Let's represent the first odd integer as x. Then, the next two consecutive odd integers would be x + 2 and x + 4.

According to the problem, the sum of these three consecutive odd integers is 147:

x + (x + 2) + (x + 4) = 147

We simplify and solve for x, which gives us the value of the first integer.

Simplifying and solving for x, we get:

3x + 6 = 147

3x = 141

x = 47

So the three consecutive odd integers are 47, 49, and 51. The third number is 51, so the answer is (d) 51.

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The answers include the following below:

This is referred to as the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Parallel lines refers to the type of lines that never cross one another and are the same distance apart at all times.

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Answer:

Step-by-step explanation: (a) To expand (1 + e^x) + (e^3x) in ascending powers of x to the term x^2, we can use the Taylor series expansion.

The Taylor series expansion for e^x is given by:

e^x = 1 + x + x^2/2! + x^3/3! + ...

So,

e^x = 1 + x + x^2/2! + x^3/3! + ...

and

e^3x = 1 + 3x + 9x^2/2! + 27x^3/3! + ...

Now, we can substitute these expansions into the original equation to get:

(1 + e^x) + (e^3x) = 1 + (1 + x + x^2/2! + x^3/3! + ...) + (1 + 3x + 9x^2/2! + 27x^3/3! + ...)

Expanding, we get:

(1 + e^x) + (e^3x) = 2 + x + 4x + x^2/2! + 9x^2/2! + ...

So, to the term x^2, the expansion becomes:

(1 + e^x) + (e^3x) = 2 + x + 4x + (x^2/2! + 9x^2/2!) + ...

which simplifies to:

(1 + e^x) + (e^3x) = 2 + x + 4x + 11x^2/2! + ...

(b) The coefficient of x^2 in the expansion is 11/2!. So, n = 11/2! = 11/2.

Answer:

Step-by-step explanation:

You want to know the slope of the line segment between (-4, -3) and (3, -3), and its relation to the x-axis.

The slope of a line between two points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (-3 -(-3))/(3 -(-4)) = 0/7 = 0

The slope of the line segment is zero.

The line segment has the same slope as the x-axis. It is parallel to the x-axis.

__

Additional comment

The equation of the line segment is ...

  y = -3 . . . for -4 ≤ x ≤ 3

The equation of the x-axis is ...

  y = 0

The steps to set up the study and the limitations that would be faced are explained below .

The Steps to setup the study are  :

(i) Recruit a large and diverse group of participants who are willing to stick to the prescribed diets for the duration of the study.

(ii) Divide the participants randomly into two or more groups. One group would be given a diet high in trans fats, and the other group(s) would be given a diet low in trans fats.

(iii) Monitor the health status of the participants closely throughout the study .

(iv) At the end of the study, compare the health outcomes of the different groups of participants to determine whether there is a significant difference in health outcomes .

The Limitations of this type of study include :

⇒ the difficulty of controlling all aspects of participants' diets, since participants may consume other foods outside of what is provided to them.

⇒ the study may not be long enough to detect long-term effects of trans fats on health.

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The given question is incomplete , the complete question is

One way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. For example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. In this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. Throughout the study, the health status of the participants is monitored closely.

Suppose that you are a researcher designing an experimental feeding trial. How would you set up your study and what limitations would you face ?

a)  The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.

A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.

In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.

If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.

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The complete question is:

A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.

a) What chance of a Type I error was the test designed for, if H0 were true?

b) What judgement would you draw on this test (reject or fail to reject)?

c) What kind of error, if any, was there as a result of this test?

The frequency of each class interval 103 - 107, 108 - 112 and 113 - 117 are 2, 2 and 4 respectively.

A grouped frequency distribution is the distribution of data into various classes with equal width with the frequency being the number of outcomes in that class.

Given are the hottest recorded temperatures (in °F) for eight cities throughout North America.

113   110   108   104   117   116   113   103

The class intervals are 103 - 107, 108 - 112 and 113 - 117.

In the distribution, the frequency of a class is the number of temperatures that class.

The temperatures in the class 103 - 107 are 103 and 104.

Frequency of 103 - 107 = 2

The temperatures in the class 108 - 112 are 108 and 110.

Frequency of 108 - 112 = 2

The temperatures in the class 113 - 117 are 113, 113, 116 and 117.

Frequency of 113 - 117 = 4

Hence the frequency are 2, 2 and 4 for the intervals 103 - 107, 108 - 112 and 113 - 117 respectively.

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Answer:

D

Step-by-step explanation:

[tex]100(1 + \frac{016}{12}) ^{12(20)}[/tex]

331.02

Answer:

D. $220.00

Explanation :

Pt(1+r/n) n