Is the sum of any 2 consecutive prime numbers also prime?

Answer:

24.6 units

Step-by-step explanation:

\(tan \: 72 \degree = \frac{x}{8} \\ \\ 3.0776835372 = \frac{x}{8} \\ \\ x = 3.0776835372 \times 8 \\ \\ x = 24.6214683 \\ \\ x \approx \: 24.6 \: units\)

Answer: The answer is D

Step-by-step explanation:

I took the quiz

We want to solve the following equation finding the value of k:

Since both sides are equal we can multiply each side by 10:

dividing both sides by 9:

Simplifying the answer dividing both sides by 3:

A line of best fit guides a line through a scatter plot of data points that best describes the association between those points.

A line of best fit guides a line through a scatter plot of data points that best describes the association between those points. Statisticians typically utilize the least squares approach to arrive at the geometric equation for the line, either through manual computations or regression analysis software.

A line of best fit can be approximately specified utilizing an eyeball the method by marking a straight line on a scatter plot so that the numeral of points above the line and below the line stands about equal (and the line passes via as many points as possible).

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By using the facts given, 60.5 cm is 0.605 m or 0.605 meters.

Given: Convert 60.5 cm to meters

And the facts are as follows:

1000 milli-meters (mm) - 1 meter (m)

100 centimeters (cm) - 1 meter (m)

10 decimeters (dm) - 1 meter (m)

1 deka-meter (dam) -10 meters (m)

1 hectometer (hm) - 100 meters (m)

1 kilometer (km) - 1000 meters (m)

What is the length?

Length is the measurement of something from one point to another point.

Length can also be the distance between two points.

The shortest length between two times is known as displacement.

There are different ways to measure the length between two points or objects.

The SI unit of length is metered (m)

Also, kilometers or miles are used to measure large distances.

How to convert from centimeters (cm) to meters (m)?

1 meter or 1 m is equivalent to 100 centimeters or 100 cm. So let us apply the unitary method.

100 cm = 1 m

So 1 cm = 1 / 100 m

Therefore, x cm will be x / 100 m

Let’s solve the problem.

Given 60.5 cm to show in meters

So 100 cm = 1 m

1 cm = 1 / 100 m

60.5 cm = 60.5 / 100 m

60.5 cm = 0.605 m

Hence by using the facts given 60.5 cm is 0.605 m or 0.605 meters.

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The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.

First, let's calculate the margin of error:

Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055

Next, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%

Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%

Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).

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The coordinates of the image are -2P

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

Ry = -2(P)

To calculate the coordinate of the image, we simply open the bracket

So, we have

Ry = -2(P)

Solving further, the equation can be represented as

Ry = -2 * P

Evaluate the product

So, we have the following representation

Ry = -2P

Hence, the image has an coordinate or ordered pair of -2P

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Answer:

4 2/3

Step-by-step explanation:

hope this helps you in any way

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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The answer to the given question is option A that is only the first equation is an identity.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

Sin θ = 1/Csc θ or Csc θ = 1/Sin θ

Cos θ = 1/Sec θ or Sec θ = 1/Cos θ

Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

1) LHS : 8 sec θ sin θ = 8 X 1/ cos θ X sin θ = 8 tan θ

RHS : 8 X sin^2 θ/ cos^2θ X cosθ / sin θ = 8 tan θ

Thus LHS = RHS and it is given above so 1st equation is an identity.

2) LHS:  11 X cot^2 θ/ cosec θ X sec^2 θ = 11 cos^2θ /sin θ

and RHS : 11 cosec^2 θ

since LHS ≠ RHS because the second equation us not an identity.

thus the correct option is A that is Only the first equation is an identity.

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Answer:

the segment bisector should be the line n

the length of XY= 6

Step-by-step explanation:

since segment, XY is bisected, we know that each side is equal to the other

so in order to find the length of the segment, you need to set each side equal to the other

5x+8=9x+12

8=4x+12

-4=4x

x=-1

then, you plug -1 into both functions

5(-1)+8=3

9(-1)+12=3

then simply add these two numbers together to get 3+3=6

Answer:

12/20

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

Given expression is \(\sqrt[3]{64a^6b^7c^9}\)

By simplifying this expression,

\(\sqrt[3]{64a^6b^7c^9}=\sqrt[3]{(4)^3(a^2)^3(b^2)^3(b)(c^3)^3}\)

                 \(=(4a^2b^2c^3)\sqrt[3]{b}\)

Option (1)

\(2abc^2\sqrt[3]{4a^2b^3c}\) = \(2ab^2c^2\sqrt[3]{a^2c}\)

Option (2)

\(4a^2b^2c^3(\sqrt[3]{b})\) [Fully simplified form]

Option (3)

\(8a^3b^3c^4(\sqrt[3]{bc} )\) [Fully simplified form]

Option (4)

\(8a^2b^2c^3(\sqrt[3]{b})\)

Expression given in Option (2) is equivalent to the given expression.

Option (2) will be the answer.

Answer:

Scale factor = 1/2

Explanation:

The purple shape is a dilation of the black shape.

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

Now findd the scale factor.

If given two shapes and need to find the scale factor, We must know which one was the original and which one is the image or the new shape. Then we need to know the length of corresponding sides and set them up in a ratio

Answer:Scale factor = 1/2

The purple shape is a dilation of the black shape.

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

Now findd the scale factor.

If given two shapes and need to find the scale factor, We must know which one was the original and which one is the image or the new shape. Then we need to know the length of corresponding sides and set them up in a ratio like so: Scale Factor = purple/black

Scale factor = 10/20 = 1/2

Answer:

A. 6x^2-17x+12

The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.

Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.

Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.

The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.

The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.

The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.

The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.

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Answer:

3:1

Step-by-step explanation:

brown:black

15:5

Divide both sides by five;

15/5 :5/5

= 3:1

Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

The equation of the circle in this problem is given as follows:

x² + y² = 90000

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The center for this problem is given as follows:

(0,0).

The radius is given as follows:

300 ft.

Hence the equation is of:

x² + y² = 90000

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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total number​of bento boxes in the container.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = LWH

Where:

Part a.

Therefore, the manager can use the following formula;

Volume of container = LWH

Volume of container = 7/2 × 3/2 × 3/2

Volume of container = 63/8 cm³.

Part b.

For the number of bento boxes that can fill the container, we have:

Number of bento boxes = Volume of container/Volume of bento boxes

Number of bento boxes = 63/8/(1/2)³

Number of bento boxes = 63/8/1/8

Number of bento boxes = 63/8 × 8

Number of bento boxes = 63 bento boxes = 3 layers × 21.

Part d.

Volume of container = Volume of bento boxes

63/8 cm³ = 63 × 1/8 cm³

63/8 cm³ = 63/8 cm³ (equal).

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Answer:

\(k=35\)°

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.

\(130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95\)

The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;

\((unknown_1)+(unknown_2)+(k)=180\)

Substitute,

\(50+95+k=180\)

Simplify,

\(50+95+k=180\\\\145+k=180\\\\k=35\)

\(\sf \bf {\boxed {\mathbb {TO\:FIND :}}}\)

The measure of angle \(k\).

\(\sf \bf {\boxed {\mathbb {SOLUTION:}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}\)

\(\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}\)

➪ \(x\) + 85° = 180°

➪ \(x\) = 180° - 85°

➪ \(x\) = 95°

Also,

Exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

➪ 130° = \(k\) + \(x\)

➪ \(k\) + 95° = 130°

➪ \(k\) = 130°- 95°

➪ \(k\) = 35°

Therefore, the value of \(k\) is 35°.

\(\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}\)

\(\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ 50° + 35° + 95° = 180°

( where 50° = 180° - 130°)

➪ 180° = 180°

➪ L. H. S. = R. H. S.

Hence verified.

(Note: Kindly refer to the attached file.)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}\)

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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Answer:

Step-by-step explanation:

D is the answer. You shift the function to the left 5 units, hence the term |x+5|, and move it down 1, hence the term -1.

a) In April, the number of students who had not passed their driving test decreased by 5%.

b) The equation is 1.2x + 0.95(1000 - x) = 1000.

c) 200 students passed their driving test in January.

a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).

In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

b)

The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).

The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.

c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.

Expanding the equation, we get:

1.2x + 950 - 0.95x = 1000

0.25x = 50

x = 200

Therefore, 200 students passed their driving test in January.

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Answer:

225

Step-by-step explanation:

9514 1404 393

Answer:

 15/7 < x < 13

Step-by-step explanation:

The triangle inequality requires that side lengths a, b, c satisfy ...

  a + b > c

  a + c > b

  b + c > a

These can let us write three inequalities for the side lengths given:

  6x -11 +3x -1 > 2x +3   ⇒   7x > 15

  6x -11 +2x +3 > 3x -1   ⇒   5x > 7

  3x -1 +2x +3 > 6x -11   ⇒   x < 13

The first two resolve to ...

  x > 15/7 ≈ 2.143

  x > 7/5 = 1.4

So, the final requirement is that ...

 15/7 < x < 13

The value of x is 6

A line segment can be defined as the partition formed by end points of a line.

From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L

This can be represented as;

JK + KL = JL

Where;

Substitute the values into the formula, we have;

5x -8 + 7x - 12 = 52

Now, collect like terms

12x = 52 + 20

Add like terms

12x = 72

Make 'x' the subject of formula

x = 72/12

x = 6

Thus, the value of x is 6

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