A garden table and a bench cost $703 combined. The garden table costs $47 less than the bench. What is the cost of the bench?

Answer:

Step-by-step explanation:

Sue is older than Ria, but Ria is younger than Jill. Ria is the middle of the three. Paula is the youngest. So the order would be Paula, Ria, Michelle, Jill, and Sue. Hope this was correct and hoped it helped. :)

Using the exponent's rule we know that x = 5.

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bn and is pronounced as "b to the n."

A number's exponent indicates how many times to multiply that particular number.

It appears as a little number above and to the right of the basic number.

For instance, 82 = 8 x 8 = 64.

(The exponent "2" instructs us to multiply by two and use the number eight.)

Another illustration is 53 = 5 * 5 * 5 = 125.

So, we have: 2ˣ = 32

We know that:

2 * 2 * 2 * 2 * 2 = 32

2 is multiplied 5 times which means:

2⁵ = 32

Hence, x = 5.

Therefore, using exponents we know that x = 5.

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No matter how they are expressed, fractions, decimals, and percentages can all have the same value.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

Here,

It is possible to have fractions, decimals, and percentages that have the same value regardless of how they are expressed.

These fractions, decimals, and percentages are said to be equivalent.

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Answer:

His rate is a whopping $231.47 per hour.

:)

Step-by-step explanation:

We can conclude that.

[tex]r*t_1=p_{reg}[/tex]   is the gross pay from his regular hours.

[tex]1.5r*t_2=p_{ovt}[/tex] is the gross pay from his overtime hours.

So all together we can say

[tex](r*t_1)+(1.5r*t_2)=p[/tex]

We are looking for his hourly rate.

Lets solve for [tex]r[/tex].

Multiply the terms in the parenthesis.

[tex]rt_1+1.5rt_2=p[/tex]

Factor [tex]r[/tex] out of [tex]rt_1[/tex].

[tex]r(t_1)+1.5rt_2=p[/tex]

Factor [tex]r[/tex] out of [tex]1.5rt_2[/tex].

[tex]r(t_1)+r(1.5t_2)=p[/tex]

Factor [tex]r[/tex] out of [tex]r(t_1)+r(1.5t_2)[/tex].

[tex]r(t_1+1.5t_2)=p[/tex]

Divide each term in [tex]r(t_1+1.5t_2)=p[/tex] by [tex]t_1+1.5t_2[/tex] and simplify.

[tex]\frac{r(t_1+1.5t_2)}{t_1+1.5t_2} =\frac{p}{t_1+1.5t_2}[/tex]

Simplify the left side.                                                                              Cancel the common factor of [tex]t_1+1.5t_2[/tex]

[tex]r=\frac{p}{t_1+1.5t_2}[/tex]

Now we have an equation to find his regular hourly rate.

We are given

[tex]p=16203[/tex]

[tex]t_1=40[/tex]

[tex]t_2=20[/tex]

Lets plug these numbers into our equation for [tex]r[/tex].

[tex]r=\frac{16203}{40+1.5*20}[/tex]

[tex]r=\frac{16203}{70}[/tex]

[tex]r=231.47[/tex]

1) The differential equation is: dP/dt=kP

2) P(t)=8000[tex]e^{-0.28t}[/tex]

3)  The solution at the specified value of the independent variable is 1490.991

In practical contexts, derivatives frequently represent the rates of change of physical quantities, and the differential equation establishes a relationship between the two. As a result of the frequent occurrence of these correlations, differential equations are widely employed in a wide range of disciplines, including engineering, physics, economics, and biology.

Only the simplest differential equations can be resolved explicitly, but many aspects of a given differential equation's solutions can be determined without doing an exact calculation.

1) The differential equation is: dP/dt=kP

Here k is the proportionality constant

2) Now, we have to solve the differential equation on dP/dt=kP

∫dP/P=∫kdt+lnP₀

lnP₀=kt+lnP₀

lnP/P₀=kt

P=P₀[tex]e^{kt}[/tex]

Here P₀ is the constant of integration.

P(t)=P₀[tex]e^{kt}[/tex]

And they have given that,

P(0)=8000=P₀e⁰

P₀=8000

P(1)=5200

5200=8000[tex]e^{k}[/tex]

k=-2log(2)+log(3)≈ -0.28

Therefore, the required function is:

P(t)=8000[tex]e^{-0.28t}[/tex]

3) Now, we have to put t=6 in the above equation:

P(6)=8000[tex]e^{-0.28*6}[/tex]

P(6)=1490.991

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The number of servings of juice in the bottles on the shelf is 135

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

Bottles = 9

Serving of juice per bottle = 15

This means that

The number of servings of juice in the bottles on the shelf = Bottles x Serving of juice per bottle

So, we have

The number of servings of juice in the bottles on the shelf = 9 * 15

Evaluate

The number of servings of juice in the bottles on the shelf = 135

Hence, the servings is 135

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Complete question

There are 9 bottles of juice on a shelf. Each serving of juice is 15 of a bottle.

How many servings of juice are there in the bottles on the shelf?

Answer:

x = In(26)/In(27)

Step-by-step explanation:

26=27^(x)

take the logarithm of both sides

x = In(26)/In(27)

Answer:

This is a bit late but I believe the answer is

Step-by-step explanation:

x = In (26)/3In (3).

Im very sorry if this turns out to be wrong.

According to the given statement the greatest common factor is -1(x+10).

Examples involving linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3. The concept of linear equations, the including that for linear equations involving one parameter, two independent variables, or three variables, and examples of each will all be explored in detail in this article.

A linear equation has the slope-intercept form y = mx + b. When x is 0, the integers m and b provide the line's slope (m) and also the value of y. (b). It y-intercept is indeed the value that y has when x is 0 because (0,y) is the point at which the line crosses the y-axis.

= -x – 10

= -1(x+10)

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so, to find the answer you times  the 2 bottom rows together so in this picture is is 4 x 7 which equals 28

hope this helps :)

Answer:

(-5, 0)

|z| = 5

Step-by-step explanation:

Complex numbers can be represented on an Argand diagram.

The x-axis is called the real axis and the y-axis is called the imaginary axis.

The complex number  z = x + iy  is represented on the diagram by the point  P(x ,y), where x and y are Cartesian coordinates.

Therefore, the complex number z = -5 can be represented on the Argand diagram by the point:

The absolute value of a complex number is the magnitude of its corresponding vector.

For a complex number  z = x + iy,  the absolute value is given by:

[tex]|z|=\sqrt{x^2+y^2}[/tex]

Therefore, the absolute value of complex number z = -5 is:

[tex]\implies |z|=\sqrt{(-5)^2+(0)^2}[/tex]

[tex]\implies |z|=\sqrt{25+0}[/tex]

[tex]\implies |z|=\sqrt{25}[/tex]

[tex]\implies |z|=5[/tex]

The linear model would be a better model for the given function.

What are linear models?

A response variable can be described in terms of a linear combination of predictor variables using linear models. The response ought to be continuous and at least roughly regularly distributed. Although these models are widely used, they are unable to handle clearly discrete or skewed continuous data.

In the table, we see that as x increases, y values change in a steady manner. The slope of this function is approximately 1860.

We use straight lines to visually illustrate linear relationships. Typically, a linear model has two parameters: the slope, also known as the growth factor or rate of change, and the y-intercept, often known as the beginning value. The linear model can be expressed as a linear function, y = mx + b or y=mx+b, where m is the slope and b is the y-intercept.

So, we get the slope as 1860.

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Answer:

AA similarity theorem.

Step-by-step explanation:

As per the concept of vector, the subspace of the vector is < 3, 4, 5>

The term vector is defied as the geometric entity that has both magnitude and direction.

Here we have to find the given vector <1, 2 , 3> and < 3, 4, 5> subspaces by using the vector formula.

Let us consider V = R³ and let H be the subset of V of all points on the plane 7x+4y+6z=0.  

By looking into the given equation, we have identified that H is a non empty set.

And here be looking into the given vector, the second one is always the subspace. Based on this, the resulting subspace is written as,

=> < 3, 4, 5>

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The value of the given sum after the execution of code segment is equal to 16.

As given in the question,

Using attached code segment.

Given values are:

num1 = 6

num2 =4

num3 =10

Value of sum after execution of code segment is given by:

num1 < num2

⇒ 6< 4 which is false.

Else num3 = num2

⇒ num3 = 4

num2≥ num3

⇒4 ≥ 4

True as 4 =4

num1 = num2 + num3

         = 4 + 4

         = 8

Final sum = num1 + num2 + num3

                = 8 + 4 + 4

                 = 16

Therefore, using code segment the value of the sum is equal to 16.

The given question is incomplete, I answer the question in general according to my knowledge:

What is the value of sum after the code segment is executed?

code segment is attached:

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By using the concept of stretch, it can be concluded that -

When 0 < b < 1, the graph of y = [tex](bx)^2[/tex] is stretched horizontally by a factor of b

What is stretch?

Stretch is a mathematical transformation in which an object enlarges in one direction only.

y = [tex](\frac{1}{2}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 2

y = [tex](\frac{1}{3}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 3

y = [tex](\frac{1}{4}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 4

So when 0 < b < 1, the graph of y = [tex](bx)^2[/tex] is stretched horizontally by a factor of b

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Answer:

No more than 10 dollars

Step-by-step explanation:

Facts!

Hello,

I hope you and your family are doing well!

To solve this problem, you need to set up a proportion using the information given in the problem. Let x represent the number of miles the family will travel during the next 4 hours. The proportion will look like this:

318 miles / 6 hours = x miles / 4 hours

To solve for x, you can cross-multiply and solve the equation:

318 miles / 6 hours = x miles / 4 hours

6 hours * 318 miles = 4 hours * x miles

1848 miles = 4x miles

x = 462 miles

Therefore, if the family continues at the same rate, they will travel a total of 462 miles during the next 4 hours.

---

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Happy Holidays!

The value of ∠ A = 40°,∠C = 70° and AC = 12

What is value ?

Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. Consider the number 45, for example. Here, the fourth digit is in the tens column.

If triangle is isosceles it means the two sides and angles are equal

∴ BC = AC

 AC = 8 cm

A + B + C = 180

A = 180 - 70 -70

∠A = 40°

∠C = 70°

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The value of the test statistic rounded to two decimal places is equal to 5.05.

In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

For a claim that most adults would erase all of their personal information online if they could, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p ≤ 0.5.

Ha: p > 0.5.

Mathematically, the test statistic for the z-test of a population proportion can be calculated by using this mathematical expression;

[tex]z=\frac{\hat{p} \;- p}{\sqrt{\frac{p(1\;-p)}{n } } }[/tex]

Where:

Substituting the given parameters into the formula, we have;

z = (0.61 - 0.5)/√(0.5(1 - 0.5)/526)

z = (0.11)/√(0.5(0.5)/526)

z = (0.11)/√(0.25/526)

z = 0.11/0.0218

z = 5.05.

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For the given function, f(x)=0.48 ln (x+2)+27. The distance is 6.004 from the eye is the pressure of 28 inches of mercury.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that the function is, f(x)=0.48 ln (x+2)+27

f(x)=28

28 = 0.48 ln (x+2)+27

0.48 ln(x+2)=28-27

ln(x+2)=1/0.48

ln(x+2)=2.08

[tex]\rm x+2 = e^{2.08}[/tex]

x+2 = 8.004

x=8.004 - 2

x=6.004

Thus, for the given function, f(x)=0.48 ln (x+2)+27. The distance is 6.004 from the eye is the pressure of 28 inches of mercury.

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The option that best describes the data is B; The data is univariate and numerical.

This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In this case, the one variable is World History scores exam

Since we are given vertical box plot is titled world history exams, with a minimum of 54, a maximum of 94, a lower quartile of 70, a median of 83, and an upper quartile of 88.

A numerical data is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.

Numerical data, also known as quantitative data, that is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.

Hence, the correct one is B; The data is univariate and numerical.

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Answer:

it is univariate and numerical

Step-by-step explanation:

univariate vs bivariate thsi is univariate because it only deals with one varialbe and its numberical because it is numbers ( that parts a litle clear)

hope i helped a litle i tried to explain it bc i know how tought this class can be (this is flvs from 4.09 from lesson4.05  incase that helps)

The true statements that satisfy ΔPQR ≅ ΔSTU are PQ = ST, m∠R = m∠U, and m∠Q = m∠T.

What is congruence?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Here, we have

Given

ΔPQR is congruent to ΔSTU

We have to find a true statement that satisfies the given condition.

We concluded that PQ = ST, m∠R = m∠U, and m∠Q = m∠T.

Hence, the true statements that satisfy ΔPQR ≅ ΔSTU are PQ = ST, m∠R = m∠U, and m∠Q = m∠T.

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Answer:

Look at images

Step-by-step explanation:

it doesn't let me put the full image

Answer

2617.

Step-by-step explanation

To estimate the number of people that can fit into a circular arena with a diameter of 100 yards, we first need to find the area of the arena. To do this, we can use the formula for the area of a circle, which is equal to pi times the radius squared. Since the diameter of the arena is 100 yards, the radius would be half of that, or 50 yards. Plugging this value into the formula for the area of a circle, we get:

Area = pi * 50^2

Since pi is approximately equal to 3.14, we can plug this value into the equation to get:

Area = 3.14 * 50^2

This simplifies to:

Area = 3.14 * 2500

Which gives us an area of approximately 7850 square yards.

Since one person requires a personal space of 3 square feet, we can divide the total area of the arena by 3 to find the number of people that can fit in the arena. This gives us:

7850 square yards / 3 square feet/person = 2616.666... people

Rounded to the nearest whole number, this means that approximately 2617 people could fit in the circular arena with a diameter of 100 yards.

Answer:

5.89 green jelly beans or we would round down to the nearest whole jellybean, 5.

Step-by-step explanation:

I am assuming that the ration is 36:32 pink:green so we need 7:?

36/32

7/ (36/32) =5.8947

Number of years it will take for the amount to double is 23 years

The principal amount = $900

The interest rate = 3%

The interest is compounded monthly

The given equation is

S = 900(1.0025)^12t

Where S is the final amount

t is the time period in years

The final amount is the double of principal amount

Final amount = 2 × 900

= $1800

Substitute the values in the equation

1800 = 900(1.0025)^12t

1.0025^12t = 1800/900

1.0025^12t = 2

Then value of t = ln(2) / 12ln (1.0025)

Divide the numbers

= 23.13b years

Therefore, the time period is 23 years

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Answer: $60.00

Step-by-step explanation: If we want to find how much money she makes in 12 hours, we must use the information we got for how much she makes in 1 hr, and apply that to make a proportional relationship. So, it would look like this:

[tex]\frac{5}{1}[/tex] = [tex]\frac{?}{12}[/tex]

Now, using cross multiplying, we multiply 1 x 12 and 5 x 12 to get $60. I hope this helped.

Answer:

a) 23,1 milions

b) en 2013 - 2014

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-6}{2 +1} \implies \cfrac{ -6 }{ 3 } \implies \text{\LARGE -2}[/tex]

Answer:

The slope is 2

Step-by-step explanation:

To find the slope you divide the rise by the run. Rise being how many units it goes up or down) (run being how many units it goes to the side).

In this case the rise is -2 and the run is -1.

See in the picture, for every 2 units the line goes down, it moves one unit to the right.

so, -2/-1= 2

Answer:

-9

Step-by-step explanation:

(y2-y1)/(x2-x1)

[tex]\frac{(-1--10)}{(-6--5)}[/tex]=-9