eight more than the sum of a number and 7 is 90. write the equation and define a variable.

Answer:

Let's assume that the length of the athletics track is "L" units, and let "x" be the speed (in units per minute) at which you run the first lap.

Since you're running two laps, the total distance covered is 2L. The time it takes to complete the first lap is L/x, since time = distance ÷ speed. For the second lap, you want your average speed to be twice the speed of the first lap, so your total time for the second lap must be half the time of the first lap:

Total time for second lap = 0.5 * (L/x) = L/2x

The total time for the two laps is the sum of the time for each lap:

Total time = L/x + L/2x = (2L + L)/(2x) = 3L/(2x)

The average speed for the two laps is the total distance (2L) divided by the total time (3L/2x):

Average speed = (2L) / (3L/2x) = 4x/3

Since you want your average speed for the second lap to be twice the speed of the first lap, you can set up the following equation:

2x = (4x/3) - x

Solving for x, we get:

2x = 4x/3 - x

5x/3 = 0

x = 0

This means that you would have to run the first lap at a speed of 0 units per minute, which is impossible. Therefore, it's not possible to run two laps of an athletics track such that the average speed of the second lap is twice the speed of the first lap.

Step-by-step explanation:

Answer:

12 lbs of food per bag

Step-by-step explanation:

To distribute cat food equally into a certain number of bags, we can divide the amount of cat food by the number of bags to get how much food should go in each bag.

60 lbs of food ÷ 5 bags = 12 lbs of food per bag

Answer: I believe the answer would be 53.85%

Step-by-step explanation:

6+8=14

14+7+5=26

14/26=.53846

Move decimal and round up.

The product of any two terms in the sequence is also a term in the sequence has been proved.

What is a sequence?

A series is an ordered collection of numbers (or other things like geometric objects), and it typically has a particular structure or function. Sequences can be A series is an ordered collection of numbers (or other things like geometric objects), and it typically has a particular structure or function. Sequences can be either infinite or illimitable in length.either infinite or illimitable in length.

Suppose there is a sequence 3, 9, 27, 81.

Taking product of first two numbers, we get

3 × 9 = 27

We can see that the term 27 is present in the sequence.

This represents that in a sequence, the product of two numbers will be the term in the sequence.

Hence, the product of any two terms in the sequence is also a term in the sequence.

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Answer:

Step-by-step explanation:

To solve this problem, we need to standardize the IQ score using the formula:

z = (x - μ) / σ

where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

So, for x = 98, we have:

z = (98 - 100) / 15 = -0.1333

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -0.1333 is approximately 0.4483.

Therefore, the probability of a random person on the street having an IQ score of less than 98 is 0.4483 (or 44.83% rounded to four decimal places).

The factoring of the polynomial expression is presented as follows;

Part A; The greatest common factor is; 5

Part B; 15·x² + 25·x - 10 = 5·(3·x - 1)·(x + 2)

Part C; 5 × (3·x - 1) × (x + 2) = 15·x² + 25·x - 10

A polynomial is an expression containing algebraic terms that consists of variables and coefficients, joined together by operators.

The expression is 15·x² + 25·x - 10

Part A; The greatest common factor of the polynomial is the value that divides each of the terms of the polynomial, therefore;

The greatest common factor of 15·x² + 25·x - 10 is obtained as follows;

The largest number that divides each term of he polynomial expression is 5

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2)

Part B; The expression, 15·x² + 25·x - 10, can be factored as follows;

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2)

3·x² + 5·x - 2 = 3·x² + 6·x - x - 2

3·x² + 6·x - x - 2 = 3·x·(x + 2) - 1·(x + 2) = (3·x - 1)·(x + 2)

3·x² + 5·x - 2  = (3·x - 1)·(x + 2)

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2) = 5·(3·x - 1)·(x + 2)

Factoring the expression completely, we get;

15·x² + 25·x - 10 = 5·(3·x - 1)·(x + 2)

Part C: The factoring of the expression, 15·x² + 25·x - 10, can be checked as follows;

The factored expression is; 5·(3·x - 1)·(x + 2)

5 × (3·x - 1) × (x + 2) = 5 × (3·x² + 6·x - x - 2) = 5 × (3·x² + 5·x - 2)

5 × (3·x² + 5·x - 2) = 15·x² + 25·x - 10, which is the original expression

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Answer:  28/9  (choice D)

Explanation:

You don't need a calculator for this.

Each fraction involves 9 in the denominator. The numerators are the only thing that change. Let x be the numerator.

x/9 = 3.1 can be estimated to x/9 = 3 and that solves to x = 27

The numerator is around 27.

Choices A,B,C are ruled out since the numerators are smaller than 28. The only thing left is choice D.

You can use a calculator or long division to confirm that 28/9 = 3.1111... where the '1's go on forever.

The roots of the function y = 2x^3+ 8x^2 - 32x - 128, considering it's graph, are given as follows:

The roots of a function can be obtained from the graph of the function, as they also represent the x-intercepts of the function.

The x-intercepts of a function are given by the values of x at which the graph of the function crosses the x-axis, which is the horizontal axis.

The multiplicities of each root are given as follows:

From the graph given by the image presented at the end of the answer, the roots of the function are given as follows:

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Answer:

Rounding 395,621 to the nearest ten thousand is 400,000.

Step-by-step explanation:

Answer:

the nearest 10 thousand is 400,000.

Step-by-step explanation:

hope this helps!

It sure looks like a linear function to me.

You can confirm this by finding the slope of "down 10/right 2" to give you a slope of -5.

Answer:

If Input is 150, then Output is 25.

Step-by-step explanation:

The rule is to divide 6.

IF: You input 72 & the output is 12:

72/6 = 12

IF: You input 54 & the output is 9:

54/6 = 9

IF: You input 120 & the output is 20:

120/6 = 20

etc.

Therefore, you are dividing 6 each time. The given input is 150. Divide 150 with 6 to find your output:

150/6 = 25

25 would be your output.

~

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As a result, the variable x is 9 which is the correct answer.

By combining two expressions, the equation generates a mathematical expression, similar to an expression. A typical equation would have been 3x - 5 = 16. The solution to this equation reveals that the value assigned to the variable x is 7.

We'll refer to the number we're looking for as "x" for the time being.

The problem states that the result of "x" and -6.5 is -58.5:

-6.5x = -58.5

We can divide all of the equation's components by -6.5 to find the answer to "x":

x = -58.5 ÷ -6.5

x = 9

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Answer:

Step-by-step explanation:

A standard deck of cards has 52 cards, including 4 queens. If you are certain to get a queen when selecting 49 cards from a shuffled deck, it means that one of those 49 cards must be a queen, and the remaining 48 cards can be any of the remaining 48 cards in the deck.

So, the probability of selecting a queen from a shuffled deck of cards is:

probability = number of favorable outcomes / total number of possible outcomes

Since we are certain to get a queen, the number of favorable outcomes is 4 (the number of queens in the deck), and the total number of possible outcomes is 49 (the number of cards selected from the deck).

Therefore, the probability of selecting a queen is:

probability = 4/49

This fraction cannot be simplified any further. Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.0816.

Answer:

6

Step-by-step explanation:

radius is 1/2 the diamiter

Answer:

Step-by-step explanation:

Answer: 6 inches.

Explanation:

Since the radius is 3 inches, the diameter will be twice the size of the radius. The radius is half the width of a circular object. The diameter is the full width. Therefore Omar's lollipop has a diameter of 6 inches.

Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

Data are pieces of information that have undergone modifications to make them transferable or computer-processable. For usage with modern computers and communication networks, data is information that has been converted into binary digital form. The topic of the data is admissible in both its singular and plural variants.

To find the z-score of a data value x, we use the formula:

z = (x - μ) / σ

where:

x is the data value

μ is the mean

σ is the standard deviation

In this case, we are given the mean μ = 21 and the standard deviation σ = 1.2. The data value x is also equal to 21.

Substituting the values into the formula, we get:

z = (21 - 21) / 1.2 = 0 / 1.2 = 0

Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

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The answer of imaginary expression is option a. The value is -3i[tex]\sqrt2[/tex] .

Imaginary expression is a specific type of algebraic expression which involves the square root of a negative number. For example 2+3i is an Imaginary expression.

Given that,

          -1[tex]\sqrt{-1[/tex] [tex]\sqrt9[/tex] [tex]\sqrt{2[/tex]

      =-1×i×3×√2 [since [tex]\sqrt-1[/tex]= i and [tex]\sqrt{9[/tex] =3]

[Here [tex]\sqrt-1[/tex] is an imaginary number]

      = -3i√2

Hence the answer is -3i√2 .

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The requried it cannot conclude whether the variable is normally distributed or skewed based on the given data. None of the options are correct.

The statistic is the study of mathematics that deals with relations between comprehensive data.

It is not possible to determine if the variable "footprint" is normally distributed or skewed based on the given data.

The data represents the measurements of shoe prints for 5 males, but it is not enough to determine the distribution of the variable without additional information such as a larger sample size, the mean and standard deviation of the variable, or a histogram or frequency plot of the data.

Therefore, we cannot conclude whether the variable is normally distributed or skewed based on the given data.

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the answer is 42 will be 42 because i answer that before

The eighth term of the sequence is 256.

To find the eighth term in the sequence 4, 16, 36, 64, 100, ...., we need to first determine the pattern that generates the sequence.

Looking at the sequence, we notice that;

Therefore, we can see that the nth term of the sequence is equal to n^2 * 2^0, 2^2, 2^2, 2^2, 2^2, 2^2, ...

So, the eighth term of the sequence would be:

8^2 * 2^2 = 64 * 4 = 256

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Answer:

h'(1) = 19

Step-by-step explanation:

if h(x) = f(x) + g(x), and f(x) = x³ and g(x) = 4x⁴,

then h(x) = (x³) + (4x⁴)

h(x) = x³ + 4x⁴

h'(x) is the derivative of h(x), which = 3x² + 16x³. Thus, h'(1) = 3(1)² + 16(1)³ = 19

The first term in this sequence is 7 and the common ratio is -3, so the formula for the 7th term, a7, can be written as a7 = 7(-3)6.7 multiplied by -18 is equal to -126, so the 7th term in this geometric sequence is -126.

Geometric sequences are used to represent growth and decay. The common ratio determines whether the sequence is increasing (if r > 1) or decreasing (if 0 < r < 1). When the common ratio is a whole number, such as 2 or 3, the terms in the sequence are whole numbers as well.

Geometric sequences are sequences where each term is found by multiplying the previous term by a fixed number, called the common ratio. In this case, the first term is 7 and the common ratio is -3, so each term is found by multiplying the previous term by -3. This means that the second term is 7(-3) = -21, the third term is -21(-3) = 63, the fourth term is -63(-3) = -189, and so on. By using the formula a7 = ar6 and substituting in the first term and common ratio, the 7th term can be calculated as -126.

The 7th term of a geometric sequence is calculated by using the formula a7 = ar6, where a is the first term and r is the common ratio. The first term in this sequence is 7 and the common ratio is -3, so the formula for the 7th term, a7, can be written as a7 = 7(-3)6. To calculate this, the exponent 6 must be multiplied by -3, giving -18. 7 multiplied by -18 is equal to -126, so the 7th term in this geometric sequence is -126.

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The length of the line of sight from the ship to Nicole is approximately 2046.1 feet, rounded to the nearest tenth.

Trigonometry is a branch of mathematics that studies the relationships between triangle sides and angles.

The term trigonometry is derived from the Latin derivative of the Greek words for triangle (trigonon) and measurement (measur) (metron).

Trigonometry is a branch of mathematics concerned with angle relationships and length ratios.

Let's assume that the distance between Nicole's window and Nick's position is "x" feet. Then, we can use trigonometry to set up the following equation:

tan(5) = (175 + 10) / x

Simplifying and solving for "x", we get:

x = (185) / tan(5)

x ≈ 2046.1 feet

Therefore, the length of the line of sight from the ship to Nicole is approximately 2046.1 feet, rounded to the nearest tenth.

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Answer:

Step-by-step explanation:

The statement "65% of 150 students" could represent the estimate that 100 students attended the school's play.

To see this, we can calculate 65% of 150:

0.65 x 150 = 97.5

Since 97.5 is close to 100, it is possible that the estimate was based on 65% of 150 students.

The other statements do not come close to 100, so they are not likely to represent the estimate that 100 students attended the school's play.

The probability that a son will inherit the​ disease would be

P{E} = 1/4.

Given is that men have XY​ (or YX) chromosomes and women have XX chromosomes.​ X-linked recessive genetic diseases​ (such as juvenile​ retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase​ x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

The probability that a son will inherit the​ disease if a father has the

defective {x} chromosome and the mother has good {XX}​ chromosomes

as -

P{E} = 4/16

P{E} = 1/4

Therefore, the probability that a son will inherit the​ disease would be

P{E} = 1/4.

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The point after 30, 000 km will they first have to change the oil, rotate the tires and replace the wiper blades all at once.

Arithmetic Progression (AP) is a numerical series in which the difference between any two consecutive numbers is a constant value. Arithmetic Sequence is another name for it.

The First term is an "oil change" with a step d = 3000 km;

and, the second term is tire rotation = 10, 000 Km

and, the third term is replacement of wiper blades = 15, 000 Km

Now, we know from the formula of Arithmetic Progression is

= + d(n-1)

So, 15,000 = 10,000 + 10,000 (n-1)

15, 000 = 10,000 + 10, 000n- 10,000

150000 = 10000n

n = 1.5

This means that at the point 15 000 km and all three progressions will not intersect.

Now, We take the second term of the progression as  = 30,000 km

So, 30,000 = 10,000 + 10,000 (n-1)

20,000 = 10,000n - 10,000

30, 000 = 10,000n

n= 3

Similarly, check this intersection point for the first progression with a step of d = 3 000 km we get n =9.

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The complete question is :-

Peter's parents follow a regular schedule for taking care of the car. They change the plugs every 30 000km, rotate the tyres every 10 000km and replace the brake pads blades every 15 000km. After how many kilometers will they have to change the plugs, rotate the tyres and replace the brake pads all at once for the first time?

The area of the circle is 78.5m² And when the radius is doubled, the area will be 314m².

The ratio of the larger circle to the smaller circle is 4 : 1

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area is measured in squared units.

The area of a circle is expressed as :

A = πr²

A = 3.14 × 5²

A = 3.14 × 25

A = 78.5m²

When the radius is doubled, i.e

r = 5×2 = 10m

A = πr²

A = 3.14 × 100

A = 314m²

Therefore the area of the new circle is 314m²

The ratio of the area of the larger circle to the area of the smaller circle is ;

314/78.5 = 4/1 = 4 : 1

therefore the ratio of the larger circle to the smaller circle is 4 : 1

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(I) Break even sales: S = 40,000

(ii) Sales needed to earn a profit  Rs 6000 per period: S = Rs. 45,000.

The formula for the Break even sales is:

(S‐v) /S= F + P  

s x P/V Ratio = Contribution

First calculate P/V Ratio:

P/V Ratio = Contribution/sales x 100

P/V Ratio = (40‐24)/40 x 100

P/V Ratio= 16/40 x 100

P/V Ratio = 40%

(I) Break even sales  

S x P/V Ratio = Fixed Cost

For break even sales, deposition equals fixed cost.

Thus,

Put the values:

S x 40/100 = 16,000

S = 16,000 x 100 / 40

S = 40,000

S = 1000 units

(II) Sales to gain a profit of Rs. 6,000

S x P/V Ratio = F + P

Put the values:

S x 40/100 = 16000 + 2000

S = 18,000 x 100/40  

S = Rs. 45,000

S =  1125 units

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The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.

Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

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