What is the value of x in the equation 0.04x + 0.3 = 0.42

Answer:

Henry is correct

Step-by-step explanation:

add 4 to each sides of the equation

2x=16

Divide each side of the equation by 2

X=8

2x - 4 = 12

add 4 to both sides:

2x - 4 + 4 = 12 + 4

2x = 16

divide both sides by 2:

2x/2 = 16/2

x = 8

so Henry is correct.

The area of a rectangle with length of 4 ft. and width of 9 ft. is 36 ft²

An equation is an expression that shows the relationship between two or more numbers and variables.

The area of a figure is the amount of space occupied in a two dimensional shape or object.

The area of a rectangle is the product of its length and width. Hence:

Area = length * width

From the diagram:

Area = 4 ft. * 9 ft. = 36 ft²

The area is 36 ft²

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Answer:

Perimeter: 26 ft

Step-by-step explanation:

To find perimeter, you add all the side measurements together.

Since the left side (4 ft) is congruent to the right, the right side is also 4 ft. Add both and you get 8 ft.

Since the bottom side (9 ft) is congruent to the top, the top side is also 9 ft. Add both and you get 18 ft.

8 + 18 = 26

So the perimeter is 26 ft.

By using unitary method it is obtained that Jennifer is at a distance of 8 km to her destination

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here unitary method is used

The scale on a map is stated as 1: 100 000

So 1 cm on the map is equivalent to 100000 cm on the ground

8 cm on the map is equivalent to 100000 [tex]\times[/tex] 8 cm on the ground

8 cm on the map is equivalent to 800000 cm on the ground

8 cm on the map is equivalent to [tex]\frac{800000}{1000 \times 100}[/tex] km on the ground

8 cm on the map is equivalent to 8 km on the ground

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Hailey's estimation is reasonable, because she can make 25 centerpieces using 430 flowers

Number of flowers in each centerpieces = 17 flowers

The total number of flowers that she has = 430 flowers

She estimates that she can make between 20 and 30 complete centerpieces

Number of centerpieces that she can make = The total number of flowers that she has / Number of flowers in each centerpieces

Substitute the values in the equation

Here we have to use division

Number of centerpieces that she can make = 430 / 17

= 25.29

≈ 25 centerpieces

Hence, Hailey's estimation is reasonable, because she can make 25 centerpieces using 430 flowers

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The required length of the diagonal  AC is given as 56 units.

Given that,
In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = 7x -21, and CE = 4x.

A parallelogram is a quadrilateral consisting of pairs of parallel sides.

Here,
in a parallelogram, diagonals bisecting each other means that a diagonal intersects another diagonal at a midpoint.
So,
AE = CE
7x - 21 = 4x
x = 7
Now,
CE = 4 {7} = 28
AC = 28 + 28 = 56

Thus, the required length of the diagonal  AC is given as 56 units.

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Answer:56

Step-by-step explanation: TRUST ME

The angle of elevation is 18. 43 degrees

Angle of elevation can be described as an angle formed between a horizontal line and the line of sight above the line.

From the information given, we have that;

Using the tangent identity, we have;

tan θ = opposite/ adjacent

tan  θ = 1/ 3

Divide the values

tan θ =0. 3333

Find the tan inverse of the value to determine  θ

θ = tan^-1(0. 3333)

θ = 18. 43 degrees

Hence, the value is 18. 43 degrees

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The given statement is false.

Statistics is a science concerned with developing and studying methods of collecting, analyzing, interpreting, and presenting empirical data. Statistical research is applicable to virtually all scientific disciplines, and research challenges in various scientific disciplines motivate the development of new statistical methods and theories. Statisticians use a variety of mathematical and computational tools to develop methods and study the theory behind methods.

The given statement is false: A p-value is the probability of obtaining a sample statistic less extreme than the one observed under the assumption that the statement in the null hypothesis is true.

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The problem and solution are:

(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) The person will have $33 after 6 months.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation is y = 5x + 3.

(a) Problem: I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) Solution: The person gets $5 every month, therefore, he will have $5x after x month.

The person has $3 initially, therefore, the total money he will have after x month is:

y = 5x + 3

To find how much money will the person have after 6 months, substitute x=6 into the above equation:

y = 5(6) + 3

y = 30 + 3

y = 33

The person will have $33 after 6 months.

Hence, the problem and solution are:

(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) The person will have $33 after 6 months.

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Step-by-step explanation:

First we need to write down something

X*x+8*x+6*x=240msquares

X2+14x=240

X2+14x-240=0

So now we use discriminant formula

196-4(1*240)=-44

-14-+(root of 44)

_____________. = answer

2

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance([tex]\sigma[/tex])= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) [tex]=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]

So n [tex]=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2[/tex]

where n=sample size

We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of [tex]z_{\alpha /2}[/tex].

Te given interval is 99%=99/100=0.99

The value of [tex]\alpha[/tex] =1−0.99

The value of [tex]\alpha[/tex] =0.01

Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005

From the standard table of z

[tex]z_{0.005}[/tex] =2.58

Now putting in the value in formula of sample size.

n[tex]=(2.58\times\frac{1.55}{0.25})^2[/tex]

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance([tex]\sigma[/tex])= 2×1.55

Standard deviation of resistance([tex]\sigma[/tex])= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n[tex]=(2.58\times\frac{3.1}{0.5})^2[/tex]

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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The final balance after 1 year with initial value $1000 if the interest is compounded quarterly will be $1215.5

What is compound interest?

Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. The power of compound interest is the creation of "interest on interest."

We are given that she initially invested $1000 and that she get 5% and interest is compounded quaterly.

After 3 months the interest will be

I = 1000*(5/100)

I = 50

So the total amount becomes

$1050 after 3 months

Now after 3 months again 5% interest will be credited

Hence the amount becomes

I1 = 1050*(5/100)

I1 = 52.5

Hence the total amount becomes

1102.5 after 6 months

After 9 months the interest will be

I2 = 1102.5*(5/100)

I2 = 55.12

Hence the total amount becomes

$1157.62 after 9 months

After 1 years the interest will be

I3 = 1157.62*(5/100)

I3 = 57.88

Hence the total amount becomes $1215.5

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Answer: I don't know if I'm 100% spot on but I belive it may be 6.32.

There are calculators for this online, try get home (unless it's a test) and use them.

Answer:

2 4/7 is the correct answer

Answer:    

Step-by-step explanation:

7x2=14=2

18-14=4

So 18/7 equals 2 4/7

Slope intercept form is y = mx + b

Y = the y-value [ for example, in the pair (9, 8), 8 would be the y-value

M = slope [ to find slope, use the equation (y2-y1)/(x2-x1) ]

X = the x-value [ for example, in the pair (9, 8), 9 would be the x-value

B = the y-intercept; when x is 0, whatever y is, that's your y-intercept

Now that you know what the variables mean, plug them into your equation.

Answer:

9 peppers

Step-by-step explanation:

A dozen is 12

so 3t + t = 12

4t=12  /3

t=3

He planted 9 peppers

Answer:

tomatoes are T so T3 is how many peppers he planted.

PS: if you are looking for a direct question you need to give the number of tomatoes or peppers.

Step-by-step explanation:

Answer:

area = base x height

Step-by-step explanation:

You multiply the base of the square and the height of the square and you get the area of it.

Step-by-step explanation:

8m + 20 - 6m - m + 7

We combine 8m and -6m to get 2m. Now we combine 2m and -m to get m.

This gives us:

m + 20 + 7.

We combine 20 and 7 to get 27.

This gives us the answer of

m + 27

The total distance traveled by him is 60 ft

In this question, apply the Pythagorean relationship

Let's assume, the climbing, sliding and walking back to the base form a right-angle triangle

The tower height = the height of the triangle, h=10f

The sliding lane= the hypotenuse of the triangle=?

The distance covered to the base= base of the triangle=24f

Applying the relation ;

a²+b²=c²

10²+24²=c²

100+576=c²

676=c²

[tex]\sqrt{626}[/tex]=c

26=c

Distance traveled in all=26+24+10=60 feet

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The expression equivalent to the given expression  -2(3x + 5y) is

given that

-2(3x + 5y)

expanding the parenthesis

-6x - 10y = 0

10y = 6x

y = 6x/10

y = 3x / 5

we can conclude that y = 3x/5 is equivalent to  -2(3x + 5y)

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Answer:

1. 2x + 3y

2. 15m -6n

Step-by-step explanation:

Combine like terms.

Answer:

1) 2x+3y

2) 15m-6n

Step-by-step explanation:

Lets first simplify 1.

1) open parentheses

9x+3y-7x

2)combine like terms

2x+3y

Simplify 2.

1) open parentheses

8m-6n+7m

2) combine like terms

15m-6n

The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment.

What is a Perpendicular bisector?
A line that divides another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to draw a perpendicular bisector. When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.
So, In the given question, We can say that A bisector that divides the line segment into two parts is called a perpendicular bisector;
We can also, find the proof of it: as: It divides AB into two equal halves or bisects it. It makes right angles with (or is perpendicular to) AB.
Every point in the perpendicular bisector is equidistant from points A and B.A ruler and compass are needed. The process for creating a line segment's perpendicular bisector is as follows:

Draw the first segment of the line PQ.

Step 2: Set the compass to a length that is a little longer than half of PQ's length.

Draw arcs above and below the line by positioning the compass pointer at point P in step 3.

Step 4: Set the compass pointer at point Q while maintaining the same length. Draw two arcs above and below the line, in the same manner, maintaining the compass's pointer at Q.
Hence, The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment

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Answer:

I think it is 671

Step-by-step explanation:

The 2 sides are the same length because of those dashes on them so 61 + 61 = 122.

144 - 122 = 22 which is the base

Area is  "Base times height divided by two"

The height is 61

so the area is (22 x 61) / 2

22 x 61 = 1,342

1,342 divided by 2 is 671

I think this is right, im sorry if it is wrong.

11) The pre-image, R at the point (-2, 3) on the grid shown produces an image following the reflection across the line y = 2·x - 3 as follows;

I. The line [tex]\overline{RR'}[/tex] which is obtained from the image R' following a reflection across the line y = 2·x - 3, is perpendicular to the line y = 2·x - 3, because the points R and R' are vertically opposite each other, therefore, the slope is the negative inverse of the slope of y = 2·x - 3, which is -0.5

II. Please find attached the graph made using MS Excel showing the points R and R'

A reflection transformation is one in which a point is reflected across a line such that the distances of the image and the pre-image from the line are the same and the line acts like a mirror producing an image of the object.

The coordinates of point R = (-2, 3)

The equation of the line of reflection is; y = 2·x - 3

The coordinates of the image of a point, (x₁, y₁) reflected across a line, a·x + b·y + c = 0, is found as follows;

The image of is found using the formula;

[tex]\dfrac{x - x_1}{a} =\dfrac{y-y_1}{b} = -\dfrac{2\cdot (a\cdot x_1+b\cdot y_1+c)}{a^2+b^2}[/tex]

The equation, y = 2·x - 3, can be expressed in the form a·x + b·y + c = 0, as follows;

y = 2·x - 3

0 = 2·x - 3 - y

Therefore;

a = 2, b = -1, and c = -3

(x₁, y₁) = (-2, 3)

[tex]\dfrac{x - (-2)}{2} = -\dfrac{2\times (2\times (-2)- 3-3)}{2^2+(-1)^2}=4[/tex]

[tex]\dfrac{x +2}{2} = 4[/tex]
x = 2× 4 - 2 = 6

x = 6

[tex]\dfrac{y-3}{-1} = 4[/tex]

y = 4 ×(-1) + 3 = -1

The coordinates of the image, (x, y) = (6, -1)

The slope of the line is -(1/2)

The equation of the perpendicular line is therefore;

(y - 3) = -0.5·(x - (-2)) = -0.5·x - 1

y = -0.5·x - 1 + 3 =  -0.5·x + 2

Equation of the perpendicular line through R; y = -0.5·x + 2

The intersection point is therefore;

-0.5·x + 2 = 2·x - 3

2.5·x = 5

x = 5 ÷ 2.5 = 2

y = 2×2 - 3 = 1

y = 1

The point is therefore, (2, 1)

The difference in the x-values = 2 - 2 = 4

The difference in the y-value = 1 - 3 = -2

Therefore, 4 is added to the x-value of the point (2, 1) and 2 is subtracted to get the image as follows;

(x, y) = (2 + 4, 1 - 2) = (6, -1)

The slope of [tex]\overline{RR'}[/tex] = (3 - (-1))/(-2 - 6) = -0.5

b. Graphically, the equation of the line [tex]\overline{RR'}[/tex] can be used to find the point R', by adding the horizontal distance and subtracting the vertical distance of the point R from the the point of intersection of the two lines.

Please find attached the graph showing R and the image R' created with MS Excel.

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Answer: I think the answer is 71.98

Step-by-step explanation:

Answer:

r = -37

Step-by-step explanation:

Step 1: Write out what is known

Step 2: Set up an equation to solve for r

Step 3: Solve for r

Answer:

  x ≈ 30.8

Step-by-step explanation:

You want the value of x if the measure of an interior angle of a regular octagon is (4x +12)°.

The sum of interior angles of an n-gon is 180°×(n -2), where n is the number of sides. An octagon has 8 sides, so the sum of angles is ...

  180°×(8 -2) = 1080°

The angles of a regular n-gon are congruent, so one interior angle of a regular octagon is ...

  1080°/8 = 135°

The given angle expression is equal to 135°, so we have ...

  (4x +12)° = 135°

  4x = 123 . . . . . . . divide by ° and subtract 12

  x = 30.75 . . . . . . divide by the coefficient of x

The value of x is about 30.8.

The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.

What is distribution?

Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.

Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.

Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.

So we need to use the mean of non-normal distribution.

Hence the answer will be the mean of the original non-normal distribution.

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The image point of the given parent point (-8,-6) after the transformation R 90° and T-4,-4 is (10, -12).

For the given question.

Let the given point be;

P --> (-8, -6)

Translation the function by  T-4,-4.

P'--> (-8 - 4, - 6-4)

P'--> (-12, - 10)

Now, rotation the function by 90 degrees.

The new coordinates be-

P' (x, y) ----> P''(-y, x)

P''(-y, x) = (10, - 12)

Thus, the image point of the given parent point (-8,-6) after the transformation R 90° and T-4,-4 is (10, -12).

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600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.

Given:

standard deviation σ = 0.01

margin of error e = 0.0008

For 95% confidence interval:

z value = 1.96

we know that:

e = z * σ/[tex]\sqrt{n}[/tex]

0.0008 = 1.96*0.01/[tex]\sqrt{n}[/tex]

0.0008 = 0.0196/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex] = 0.0196/0.0008

= 24.5

n = 24.5^2

n = 600.25

Therefore 600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.

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The answer is no, and the below explanation is given with a counter-example.

An integer is a number that includes both negative and positive numbers, including zero. It has no decimal or fractional parts. Here are a few examples of integers: -5, 0, 1, 5, 8, 97, and 3,043

P(n) is a condition that is true for P(0), P(1), and P(2), but P(3k) is true when P(k) is true for all numbers k0.

P(n) is thus not always true for all nonnegative integers n because 4 is not a multiple of 3.

For example, consider the property P(n): "n is 0 or 1, or n is a multiple of 3." Then P(0), P(1), and P(2) are trivially true, however, P(3k) is true for all numbers k because 3k is a multiple of 3. However, P(4) is false because 4 is not a multiple of 3.

As a result, no.

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The complete question is:

"Suppose P(n) is a property such that 1. P(0), P(1), P(2) are all true, 2. for all integers k≥0, if P(k) is true, then P(3k) is true. Must it follow that P(n) is true for all integers n≥0?

If yes, explain why; if no, give a counterexample".