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Answer:

A. -9, -6, 8, 13

B. -4/5, -1/2, -.2, .25

C. -8/3, -2 1/2, 9/2, 4.75

D. -8, -3, -1, 4

E. -1/2, -1/4, .5, 3/4

F. -3/2, -5/4, -4/5, 1.5

Step-by-step explanation:

The easiest thing to do is to put them all in the same format. Fractions are just division problems, so just divide. 4/5 is 4 divided by 5, which is .8.

Remember, the farther a negative number is from 0 on the number line, the smaller it is. So, -8 is smaller than -5. -5 is smaller than -2, etc.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

[ log 5 = 0.69 ]

[ log 26 = 1.41 ]

The formula for log [tex]x^n[/tex] = n log x

The value of x is 0.043

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

[tex]5^{2x + 1} - 26(5^x) + 5 = 0[/tex]

[tex]5^{2x + 1} + 5 = 26(5^x)[/tex]

The formula for log [tex]x^n[/tex] = n log x

Taking logs on both sides.

log [tex](5^{2x + 1} + 5)[/tex] = log [tex]26(5^x)[/tex]

log [tex]5^{2x + 1}[/tex] + log 5 = log 26 + log [tex]5^{x}[/tex]

(2x + 1) log 5 + log 5 = 1.41 + x log 5

[ log 5 = 0.69 ]

[ log 26 = 1.41 ]

(2x + 1) x 0.69 + 0.69 = 1.41 + 0.69x

1.39x + 0.69 + 0.69 = 1.41 + 0.69x

0.70x = 1.41 - 1.38

x = 0.03 / 0.70

x = 0.043

Thus,

The value of x is 0.043

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The inequality that represents the bid for the artwork is A. b ≥ 25,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.

Let the minimum bid be b. This will be b ≥ 25,000.

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The equations using any method for the given situation illustrated that:

The equation for Jordan: 225 + 45w

The equation for RayAnn: 150 + 60w

Let the number of weeks be represented by w. Jordan saved $225 and continues to save $45 each week. The equation for this will be:

= 225 + (45 × w)

= 225 + 45w

RayAnn saved $150 and continues to save $60 each week. The equation will be:

= 150 + (60 × w)

= 150 + 60w

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7.82 % is probability that all reservation holders who show will be accommodated.

What is probability in math?

If 236 are booked.

and there is only room of 213.

if 214 or 215 or 216 ............  etc

all the way to 236

there won't be enough seats.

P( X = 214 ) = ²³⁶C₂₁₄ * ( 0.9005 ) ²¹⁴   * ( 0.995 )²²

P( X = 214 ) = 0.08439109

                   = 8.44 %

P( X = 215 ) =  ²³⁶C₂₁₅ *  ( 0.9005 ) ²¹⁵   * ( 0.995 )²¹

                    = 0.0781522

                     = 7.82 %

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The equivalent equation of the equation, [tex]\frac{5x+6}{2}=3-(4x+12)[/tex] is 5x + 6 = -18 - 8x

Two equations are said to be equivalent when they have the same solution set.

Equivalent equations are algebraic equations that have identical solutions or roots.

Therefore, let's find the equivalent equation of the equation.

[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]

Let's open the bracket on the right side

[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]

[tex]\frac{5x+6}{2}=3 - 4x - 12[/tex]

[tex]\frac{5x+6}{2}=(-9-4x)[/tex]

cross multiply

5x + 6 = 2(-9 - 4x)

5x + 6 = -18 - 8x

5x + 8x = -18 - 6

13x = - 24

divide both sides by 13

x = - 24 / 13

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Answer:

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example

You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).

Step-by-step explanation:

The point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

What is equation of line ?

  A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Here the given point ,

=> [tex](x_1,y_1)=(5,1)[/tex]

Slope m = [tex]\frac{1}{5}[/tex]

Here using equation formula

=> [tex]y-y_1 = m ( x- x_1)[/tex]

=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

Hence the point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

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64 is the standard deviation and the width of the confidence interval are both doubled .

What is standard deviation in math?

Margin of error(E)=0.5

Standard deviation(σ)=1.55

Significance level(α)=100%-99%=1% or 0.01

From Z distribution Critical value table

the Critical value(Zc)=2.58 at significance level=0.01

we know formula for the Margin of error

 E = Zc  * σ/√n

0.5 = 2.58 * 1.55/√n

√n = 2.58 *  1.55/0.5

 √n = 3.999/0.5

  √n = 7.998

  n = ( 7.998)²

 n = 63.968004

Aproximately

  n = 64

the realtionship between the sample size and margin of error is inversly proportional.

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Answer:

2

Step-by-step explanation:

y² = 4²= 16 (in substitution way)

16÷8= 2

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Answer:

2

Step-by-step explanation:

y^2/8

4^2/8

16/8

2

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Answer:2.86

Step-by-step explanation:

3.5(x +2) = 17

3.5x + 7 = 17

3.5x =17 - 7

3.5x =10

x = 10/3.5

x = 2.86

With a net change of +0.72 yesterday's closing price was 19.81 and stock dividend yield for yesterday's closing price is 7.2%.

How to calculate the Dividend Yield?

To calculate dividend yield, all you have to do is divide the annual dividends paid per share by the price per share.

Dividend Yield = Annual Dividends Paid Per Share / Price Per Share

According to the given question:

Net change = today's price - yesterday's price

0.72 = 19.09 - yesterday's price

∴ Yesterday's price = 19.81

Stock dividend yield

= (1.43/19.81) x 100

= 7.2%

Therefore the stock yield of yesterday's closing price is 7.2%

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The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

The correct option is (A).

What is the average rate of change of a function?

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

Using function notation, we can define the Average Rate of Change of a function f from a to b as:

                                     [tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]

The given function is  [tex]g(x) = 5(2)^{x}[/tex],

Now calculating the average rate of change of function from x = 1 to x = 2.

                               [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]

Now, calculate the average rate of change of function from x = 3 to x = 4.

                                 [tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]

The jump from m = 10 to m = 40 is "times 4".

So option (A) is correct.

Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.

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Answer:

x intercept = (-3/4, 0)

y intercept = (0, 3/7)

Step-by-step explanation:

just ask :))

Answer: x=3

Step-by-step explanation:

5x+2=7x-4
-5x +4    -5x +4
2x=6
divide both sides by 2
x=3

Answer:

Gift aid  68.38 £

Step-by-step explanation:

Proportion:

273.50 £  -    100%

X £            -      25%

Gift aid:

X = 273.50·25% / 100% = 273.50 / 4 ≈ 68.38 £

x-intercept

The x-intercept is where y=0.

[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]

y-intercept

The y-intercept is where x=0.

[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]

Answer:

70%

Explan your answer :

200-130=70 and 70% of 100 = 30% so

Answer: 65

Step-by-step explanation:

0.65

×

100

=

0.65×100=

65

%

65%

The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The area of a triangle is given as (1/2) × base × height.

The given area of the triangle = 12 feet².

Thus,

12 =  (1/2) × base × height

Base × height = 12 × 2

Base × height = 24

The combination of two quantities gives 24 by multiplying will be (12,2),(8,3), and (4,6).

For example, the triangle with dimensions (4,6) is attached below.

Hence "The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6)".

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The value of the correlation coefficient is 0.60.

There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.

R² is the coefficient of determination, which measures how much variation can be explained by the regression line.

This means that, the R² value of the data is 36%

R² = 36% = 0.36

Correlation coefficients measure the strength of relationships between variables in the form of square roots.

That is ; R = √R²

R = √0.36

Hence, the correlation Coefficient, R is 0.60

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Answer:

y=-4x-4

Step-by-step explanation:

we know the slope so put it in the slope intercept form

y=-4x

Now fill it in to find y intercept with the coordinates

0=-4(-1)

0=4

We need to subtract 4 to make this equation true so the y intercept is -4

The equation will become

y=-4x-4

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The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given,

Let's say the cost per pound of strawberry taffy is "s" and the cost per pound of banana taffy is "b".

Then, the cost of 8 pounds of strawberry taffy and 3 pounds of banana taffy will be,

8s + 3b = 66

And,

The cost of 10 pounds of strawberry taffy and 3 pounds of banana taffy will be,

10s + 3b = 78

By solving both above equations,

2s = 12

s = $6

3b = 78 - 10(6)

b = $6

Hence, "The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6".

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Answer: angle 1 and 4

Step-by-step explanation:

The difference between the distance between the two cities if of 14.842 latitudes.

The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.

Therefore, the earth has 181 latitudes.

Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.

Hence the distance covered by all 181 latitudes = 2 X radius of the Earth

= 2 X 6378 km

= 12756

Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be

12756/181

= 70.475 km

Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.

Therefore the difference in latitudes between the two cities is

1046/70.475

= 14.842 latitudes

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The cost of 4.5 tonnes of rock is $56.25

Given,

cost of 1 tonne of rock=$12.50

then

to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,

cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25

Thus ,the cost of 4.5 tonnes of rock is $56.25.

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The solution of the inequality that determines how far Dev can travel over the weekend is -

x ≤ 400 miles.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Dave who is planning a car trip for weekend.

Assume that [x] represents the number of miles Dev can travel.

We can write the inequality as -

18 - 0.04x ≤ 2

0.04x ≤ 16

x ≤ 400 miles

Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -

x ≤ 400 miles.

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The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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Answer:

16(2z-3) or GCF: 16

Step-by-step explanation:

32z-48 has a GFC of 16

16(2z-3)

Answer:

$16(2z-3)

Step-by-step explanation:

Prime factorization:

32: 2*2*2*2*2

48: 2*2*2*2*3

Notice any similarities:

2*2*2*2=16

$32z-$48 = $16(2z-3)

The product of a number minus 17 and 5 are equivalent to: 5 (n - 17) .

X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.

the sum of a number less than 17 and five

If x is an ambiguous number,

The sign for minus is -

A number less than 17 is denoted by x-17.

The multiplication is the product.

Add x-17 and (x-17)5 to get the answer.

In this case, the expression is 5 (n - 17).

When two numbers are multiplied together, the outcome is known as the product.

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