What is the area of the rectangle shown on the coordinate plane?



Enter your answer in the box. Do not round at any step.

Answer:x=-3

Step-by-step explanation:

if you were to plug in -3 for f(x) you would get, f(-3)=1/3(-3) +2, which then equals f(-3)=-1+2, so f(-3)=1

Now you do the same thing for g(x), so you would get g(-3)=2^(-3+3), meaning you first add -3 and 3 leaving you with g(-3)=2^0, which is equal to 1.

f(-3)=1=g(-3)

The integer has a greater value is -2

An integer is a whole number (rather than a fraction) that can be positive, negative, or zero. Positive numbers, negative numbers, and zero are all examples of integers. 'Integers include both whole and negative numbers. This means that if we add negative numbers to whole numbers, we get a set of integers.

An integer is a number that has no decimal or fractional part and can be negative or positive, including zero. In this case, the numbers are -5 and -2. It should be noted that -2 is more than -5.

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The area under the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].

Consider the following parametric equations:[tex]$$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$[/tex]

The objective is to find area enclosed by the curve using the formula.

The area under the curve is given by parametric equations x=f(t), y=g(t),  and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:

[tex]$$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$[/tex]

The curve has intersects with y-axis. so x=0

[tex]$$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$[/tex]

Now we have to draw the graph,

Let f(t)=[tex]t^2-3 t, g(t)=\sqrt{t}$[/tex]

Differentiate the curve f(t) with respect to t.

[tex]f^{\prime}(t)=2 t-3[/tex]

Now, find the area under the curve use the above formula.

[tex]\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$[/tex]

[tex]& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right][/tex]

[tex]$\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}[/tex]

Therefore,  the area of the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].

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Answer:

By using the given ratio, we will see that there are 15 boys and 12 girls.

How we can find the number of boys and girls in the class?

The given information is:

There are 3 more boys.

There are 5 boys for every 4 girls.

Now, notice that in the ratio we have a difference of 1 boy, so if we want to have a difference of 3 boys, we must multiplicate it by 3, then we get:

3*15 boys for every 3*4 girls (remember that you can multiply both quantities on the ratio and it does not change).

15 boys for every 12 girls.

Now the difference is 3.

15 - 12 = 3

So we can conclude that there are 15 boys and 12 girls.

Step-by-step explanation:

The percentage of children are born from pregnancies lasting less than 274 days are 0.02.

The percentage of children are born from pregnancies lasting less than 246 days are 0.02.

What is normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution in statistics.

The normal distribution describes a symmetrical plot of data around its mean value, with the standard deviation serving as the determinant of the curve's width. The "bell curve" is used to visually represent it.

Given:

Lengths of pregnancies of women are normally distributed with a mean of 266 days and a standard deviation of 16 days.

⇒  μ = 266,   σ = 16

Consider, the normal distribution formula

f(x) = (1 / σ√2π) e^(-1/2)(x - μ/ σ)^2

For x = 274,

f(274) = (1 / 16√2π) e^(-1/2)(274 - 266/16)^2

f(274) = 0.02

Hence, the percentage of children are born from pregnancies lasting less than 274 days are 0.02.

For x = 246

f(246) = (1/16√2π) e^(-1/2)(246 - 266/16)^2

f(246) = 0.02

Hence, the percentage of children are born from pregnancies lasting less than 246 days are 0.02.

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She'll need 4 gallons of 15% ethanol gasoline and 5 gallons of 78% ethanol gasoline.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

Here,

The number of gallons required of both kind would be as follows:

4 gallons having 15% ethanol

5 gallons having 78% ethanol

Given that,

The 2 kinds of gases are:

One with 15% ethanol

Other with 78% ethanol

Given that,

The gases(ethanol and gasoline) are diluted in a such a manner that it involves a total of only 50% ethanol.

Number of gallons she wants to use = 9

This shows that only 50% of 9 gallons i.e. 4.5 gallons of ethanol can be used.

Assuming x being the gasoline's measure that is diluted with 15% ethanol.

Now,

The gasoline's measure that is diluted with 78% ethanol would be = 9 - x gallons

Therefore,

x × 15% + (9-x) × 78% = 4.5

On solving, we get

x = 4 gallons

Thus,

The measure of gallons having 15% ethanol = 4

The measure of gallons having 78% ethanol = (9 - x)

= (9 - 4)

= 5 gallons

She will use 4 gallon of 15% ethanol gas and 5 gallon of 78% ethanol gas.

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Answer:

8[tex]x^{2} \\[/tex] + 24x

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The required amount of the ribbon, when split into half, is 57 / 20. Option A is correct.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
A family member has two and one-fourth yds of ribbon, and you add three-fifths yds to it,
So,
= 2 1/4 + 3 / 5
= 9 / 4 + 3 / 5
= 57 / 20

Now,

Half of the ribbon = [57 / 20] × [1/2] = 57 / 40

Thus, the required amount of the ribbon, when split into half, is 57 / 20. Option A is correct.

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19% of people have a dog,24% of people have a cat , and 14% percentage of people have both 62% of people have either a dog or a cat.

To find the percentage of people that have either a dog or a cat, we need to add the percentage of people that have a dog to the percentage of people that have a cat.

19% + 24% = 43%

Therefore, 62% of people have either a dog or a cat.

43% of people have either a dog or a cat, but do not have both. We can find this by subtracting the percentage of people that have both a dog and a cat from the total percentage.

43% - 14% = 29%

Therefore, 29% of people have a dog or a cat, but not both.

The complete question is:

Suppoe that 19% of people have a dog,24% of people have a cat , and 14% of people have both dog and cat.

What percentage of people have either a dog nor a cat?

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Answer:

(5 + 2x + 4 + 3)/4 = 5

(12 + 2x)/4 = 5

3 + 1/2x = 5         (multiply by 2

6 + x = 10

x = 4

The numbers are 5, 8, 4 and 3.

Step-by-step explanation:

The value of x in the solution set of the inequality -2(3x + 2) > -8x + 6 is 6.

Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-2(3x + 2) > -8x + 6

-6x - 4 > -8x + 6

8x - 6x > 6 + 4

2x > 10

x > 5

x = (5, +∞)

Hence, the solution set of the given inequality is the set of numbers greater than 5. Among the given choices, only 6 is greater than 5. Therefore, the value of x is 6.

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Answer:

6

Step-by-step explanation:

edge on

What value of x is in the solution set of the inequality –2(3x + 2) > –8x + 6?

6

The only kind of data generated by observational research is correlations or patterns in the data that have been observed. By using correlations, one variable's value can be used to predict the value of another.

Explanation:

Accurate predictions using data correlation can be ensured by using a variety of methods. Firstly, it is important to ensure that the data is free from errors and is of high quality. This can be done by cleaning and validating the data to remove any inconsistencies and outliers. Secondly, it is important to analyze the data thoroughly and identify any patterns or trends. Furthermore, it is beneficial to use appropriate statistical tests and algorithms such as linear regression, logistic regression, and decision trees to identify the predictive relationships between the variables. Finally, it is important to evaluate the model’s performance to determine the accuracy of the predictions.

The most effective methods for ensuring accurate predictions using data correlation are:

1. Perform Exploratory Data Analysis: Exploratory data analysis is an essential step in any predictive modeling process. It involves exploring the data to identify patterns, trends, and relationships within the data. This helps to identify any potential issues or biases within the data that could affect the accuracy of predictions.

2. Use Statistical Tests: Statistical tests can be used to measure the strength of the relationship between two variables. These tests can help to identify which variables are most strongly correlated with each other and can help to determine which variables should be used in a predictive model.

3. Use Machine Learning Algorithms: Machine learning algorithms can be used to create predictive models that can identify and learn patterns in the data. These algorithms are particularly effective at identifying complex relationships between variables that may not be identified by statistical tests.

4. Validate Predictions: Predictions should always be validated to ensure that they are accurate and reliable. This can be done by comparing the predictions against known outcomes or by testing the model on a separate data set.

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Answer:

See Answer

Step-by-step explanation:

8/3 or 2 2/3 cups of milk are needed for 16 servings.

What is the unitary method?

The unitary method is a technique for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.

Given that 3/4 cups of milk needs to make 4 1/2 servings

Converting mixed fraction into improper fraction:

or,  3/4 cups of milk needs to make 9/2 servings.

To make 9/2 servings, needs  3/4 cups of milk

Applying unitary method:

To make 1 servings, needs  (3/4)/(9/2) cups of milk.

To make 16 servings, needs  [(3/4) × 16]/(9/2) cups of milk.

Simplify the numerical expression:

[(3/4) × 16]/(9/2)

=  [3 × 4]/(9/2)

=  [3 × 4 × 2] /9

= 8/3

Convert  improper fraction into mixed fraction:

=(6 + 2)/3

= 6/3 + 2/3

= 2 2/3

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The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3 and the slope of AD is -2/7. The Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel in a parallelogram.

The vertices of Quadrilateral ABCD are A(−5, 1) , B(−2, 5) , C(5, 3) , and D(2, −1) .

The slope between 2 points is:- m=(y2-y1) / (x2-x1)

The slope of AB :

m= (5-1) / (-2-(-5))

m= 4/3                 ........................(1)

The slope of BC :

m= (3-5) / (5-(-2))

m= -2/7                 ..........................(2)        

The slope of CD :

m= (-1-3) / (2-5)

m= 4/3                  ............................(3)

The slope of AD :

m= (-1-1) / (2-(-5))

m= -2/7                  .............................(4)

Therefore,

The slope of AB is (1) 4/3, the slope of BC is (2) -2/7, the slope of CD is (3) 4/3, and the slope of AD is (4) -2/7.

Quadrilateral ABCD is a (5) parallelogram because (6) both pairs of opposite sides are parallel.

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They have a 0.77 chance of finishing within 10 minutes of each other.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

mean of the difference between their times is the difference of the expected (or mean) times for each person,

=20-18

=2

standard deviation,

=√((6.4)²+(4.8)²)

=8

The probability,

=0.77

The probability that they finish within 10 minutes of each other is 0.77.

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Answer:

[tex]\frac{5}{13}[/tex]

Step-by-step explanation:

If you have studied trigonometry, you will know that [tex]cos(\theta )=\frac{adjacent}{hypotenuse}[/tex], where the adjacent is the side with both the right angle and the angle θ, and the hypotenuse is the diagonal side.

We know here that the hypotenuse is 26.

We know do not know that adjacent where both angle R and the right angle are, but we can find it using Pythagoras' Theorem, something else which you may have studied.

[tex]a^2=c^2-b^2\\a^2=26^2-24^2\\a^2=100\\a = \sqrt{100}=10[/tex]

We now know that the adjacent is equal to 10.

Therefore, we substitute them into the cos ratio, and simplify the fraction.

[tex]cos(R)=\frac{10}{26} =\frac{5}{13}[/tex]

Answer:

The length of the hypotenuse is 25 cm.

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse.

Pythagorean theorem states

[tex]a^2+b^2=c^2[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the legs or sides of the triangle.

The hypotenuse is [tex]c[/tex].

We can solve for [tex]c[/tex] by taking the square root of both sides of the equation.

[tex]c=\sqrt{a^2+b^2}[/tex]

We are given

[tex]a=7\\b=24[/tex]

Lets evaluate [tex]c.[/tex]

[tex]c=\sqrt{7^2+24^2}[/tex]

[tex]c=\sqrt{49+b^2}[/tex]

[tex]c=\sqrt{49+576}[/tex]

[tex]c=\sqrt{625}[/tex]

[tex]c=25[/tex]

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The builder will be able to execute his idea based on the other measurements in the illustration.

In the traditional system of measurement, one inch can be referred to as a unit of length. Inches of length are either denoted by in or by ". 5 inches, for instance, can be expressed as 16 inches or 16".

Initially, 1 inch was equal to the breadth of a man's thumb. In the 14th century, King Edward II of England decreed that 3 grains of barley laid end to end and lengthwise made up 1 inch.

Historically, there have been many different standards for what an inch is exactly, but since the international yard was adopted in the 1950s and 1960s, the inch has been based on the metric system and defined as precisely 25.4 mm.

Building codes prohibit the construction of homes that are taller than 35 feet.

The building is 22 feet tall in the diagram.

                  = 35 - 22

                  = 13 feet

so the builder is allowed to carry out is plan

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The lower and the upper limit for a 99% confidence interval would be approximately 37.51 and 50.03

Here,

Mean = 43.77

Standard deviation (s)= 12.43655

n= 30

So,

   CI= mean ± t (s/√n)

      = 43.77±2.756(12.43655/√30)

      = 43.77±6.26

      = 37.51,50.03

So, the lower and upper limit would be 37.51 and 50.03

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Answer:

4) (5, -1)

Step-by-step explanation:

To find the midpoint, we must average the x coordinates to find the x-coordinate of the midpoint and average the y-coordinates to find the y-coordinate of the midpoint.

Thus, we do:

x-coordinate: [tex]\frac{2 + 8}{2}[/tex] = [tex]\frac{10}{2}[/tex] = [tex]5[/tex]

y-coordinate: [tex]\frac{-5 + 3}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = [tex]-1[/tex]

This means the midpoint has an x-coordinate of 5 and a y-coordinate of -1. This can be expressed as the point (5, -1), which is option 4

This athlete should aim to lift approximately 70-80% of their 1RM for ten repetitions, which would be approximately 360-410 lbs (163-186 kg).

When determining the weight an athlete should lift for a given set of repetitions, it is important to consider the athlete's 1RM. 1RM stands for one-repetition maximum and is the most weight an athlete can lift for one repetition. Generally, when lifting for a set of repetitions, athletes should aim to lift 70-80% of their 1RM. In this case, the athlete has a 1RM of 515 lbs (234 kg). If this athlete was performing ten repetitions per set, they should aim to lift approximately 360-410 lbs (163-186 kg). This is a good starting point for the athlete and can be adjusted as needed depending on how it feels.

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The formula used to gain information about an individual data value when the variable is normally distributed is called the z-score formula.

It is used to calculate how many standard deviations a value lies above or below the mean of the data set. The formula is:

z-score = (x - μ) / σ

where x is the data value, μ is the mean of the data set, and σ is the standard deviation of the data set.

To find the z-score of an individual data value when the variable is normally distributed, use the z-score formula. This formula subtracts the mean (μ) from the data value (x) and divides by the standard deviation (σ). This calculation will give you the number of standard deviations the data value lies above or below the mean.

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The percentile rank of the score 71 on the test is 26.7.

The value that a specific percentage falls under is known as the percentile. Ben, for instance, is the fourth-tallest child in a group of 20, and eighty percent of the kids are shorter than you.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

[tex]Percentile = n / N \times 100[/tex]

Here, n is the number of scores below 71 and N is the total number of scores,

Percentile = 4 / 15 × 100

Percentile = 0.267 × 100

Percentile = 26.7 percentile

Therefore, the percentile rank of the score 71 on the test is 26.7

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Answer:

x = 4.083

Step-by-step explanation:

6(2x+5)+19=0

12x+30+19=0

12x+49=0

12x=-49

x=4.083

Answer:

f(2x + 5) = 6x + 19

= 6(2x + 5) + 19

= 12x + 30 + 19

= 12x + 49

f(2) = 12x + 49

= 12(2) + 49

= 73

Step-by-step explanation:

the null hypothesis is rejected for an observed p-value of at 0.07 at a significance level of 0.05.

At a significance level of 0.05, the p-value of 0.07 indicates that the observed value is not statistically significant. As a result, the null hypothesis cannot be disproven.In other words, the observed value is not strong enough to prove that the null hypothesis is false. Therefore, the null hypothesis is not rejected for an observed p-value of 0.07 at the significance level of 0.05.

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The linear function of  f(-10)= 4.5,f(-2)=4.5 is y = 4.5.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the linear function of f(-10)= 4.5, f(-2)=4.5 can be represented as follows:

Using y = mx + b

4.5 = -10m + b

4.5  = -2m + b

b = 4.5 + 10m

Hence, using substitution,

4.5  = -2m + 4.5 + 10m

4.5 - 4.5 = 8m

m = 0

Let's find b

4.5 = -10(0) + b

b = 4.5

Therefore, the linear function is y = 4.5

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