The difference of a number and
its reciprocal is 15/13. What is the
number.

The expression has 3 terms and 3 factors

The terms are the constant, the r term and the t term

The factors that are in the equation are 1500, 1 and 12

An exponential equation is an equation that involves an exponential function, which has the form f(x) = a^x, where "a" is a constant base and "x" is the exponent. Exponential equations are used to model phenomena that grow or decay at a constant relative rate. The solutions to exponential equations can be found by manipulating the equation algebraically to isolate the variable in the exponent, taking logarithms of both sides, or by using exponential rules such as the power rule or the product rule.

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In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.

To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:

Future value = Present value * (1 + inflation rate)^n

where:

Present value = $897.20/month

Inflation rate = 4% per year

n = number of years

When we substitute the specified values, we get:

Future value = $897.20 * [tex](1 + 0.04)^9[/tex]

= $897.20 * 1.3981

= $1254.77 (to two decimal places in rounding)

Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

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The two plants would have the same height in 7 weeks and the height would be 31 inches.

The form of the expression that represents the length of the plant on the window sill is:

initial length + (length of growth per week x number of weeks)

3 + (4 x w)

3 + 4w

The form of the expression that represents the length of the plant on the coffee table is:

initial length + (length of growth per week x number of weeks)

17 + (2 x w)

17 + 2w

When the two plants have the same height, the two expressions would be equal:

17 + 2w = 3 + 4w

17 - 3 = 4w - 2w

14 = 2w

w = 14/2

w = 7 weeks

Height of the plant = 3 + 4(7)

3 + 28 = 31 inches

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The answer to the given fill in the blanks is "Residual". in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the Residual come from a normal distribution.

In linear regression, we make several assumptions about the relationship between the predictor variable and the response variable. One of these assumptions is that the residuals (the differences between the predicted values and the actual values) follow a normal distribution with a mean of zero and constant variance. To check this assumption, we can create a normal quantile plot of the residuals. A normal quantile plot is a graphical method that compares the distribution of the residuals to a normal distribution. If the residuals are normally distributed, the plot should follow a straight line. If the plot deviates from a straight line, it suggests that the residuals are not normally distributed. A non-normal distribution of residuals can have several implications, such as indicating the presence of outliers or influencing the accuracy of the model’s prediction. Therefore, checking for normality of residuals is a crucial step in evaluating the model's assumptions and determining whether the model is appropriate for the data.

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If the scale factor of figure A to figure B is 3:8, the value of x is 9.

We are given Figure A and Figure B, along with their respective scale factors. To solve the problem, we must utilize the proportion rule. The ratio of the two figures is 3:8, so we can write the equation for proportion as follows -

3/8 = x/24

Applying the cross-multiplication rule, we get,

3 * 24 = 8 * x

Further solving for the value of x, we get,

x = (3 * 24) / 8

x = 9

Hence, the value of x is 9.

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The complete question is -

If the scale factor of figure A to figure B is 3:8 find the value of x.

The correct interpretation of the 90% confidence interval is given as follows:

There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).

It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

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Answer:

bro do u have a pic i will give u your points back but i need a pic to help

Step-by-step explanation:

The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

[tex]\sigma = 61.1\\[/tex]

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

[tex]Z = \frac{(x-u)}{\sigma}[/tex]

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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The following statements are true about the function f(x) = -( x-4) ² -1

1. The y intercept is (0,-17)

2. The axis of symmetry x = 4

3. The x intercept is (3,0)

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

The equation f(x) = -(x-4)² -1 can be expanded as

f(x) = -x²+8x-16-1 = -x²+8x-17

therefore when x = 0

the y-intercept = -17

therefore the y intercept = (0,-17)

The x intercept of the function,

when y = f(x) and y = 0

-(x-4)² = 1

-(x-4) = 1

-x+4 = 1

-x = -3

x = 3

the x intercept of the function is (3,0)

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The area of the figure is given as follows:

100.56 mm².

The figure in this problem is composed as follows:

The areas for each region are given as follows:

Hence the total area is of:

48 + 14 + 20 + 6 + 12.56 = 100.56 mm².

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The area of the composite figure is equal to 254 m² square metres.

The composite figure can be observed to be a vertical rectangle, a square and an horizontal rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the vertical rectangle = 19 m × 7 m

area of the vertical rectangle = 133 m²

area of the square = 5 m × 5 m

area of the square = 25 m²

area of the horizontal rectangle = 16 m × 6 m

area of the horizontal rectangle = 96 m²

total area of the composite figure = 133 m² + 25 m² + 96 m²

total area of the composite figure = 254 m²

Therefore, the area of the composite figure is equal to 254 m² square metres.

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The probability that at least one pair of people have the same birthday, with 30 people in a classroom is approximately 0.7063.

To solve this problem, we can use the concept of the complement of an event. The complement of the event "at least one pair of people have the same birthday" is the event "no pair of people have the same birthday." So, we can find the probability of this complement event and subtract it from 1 to get the probability of the original event.

The probability that the first person has a unique birthday is 1, since there are no other people in the room yet. The probability that the second person also has a unique birthday is (364/365), since there are 364 remaining days in the year that they could be born on.

Similarly, the probability that the third person has a unique birthday is (363/365), and so on, down to the 30th person, whose probability of having a unique birthday is (336/365).

To find the probability that no pair of people have the same birthday, we can multiply these probabilities together:

P(no pair share a birthday) = 1 * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

Therefore, the probability that at least one pair of people have the same birthday is:

P(at least one pair share a birthday) = 1 - P(no pair share a birthday) ≈ 1 - 0.2937 = 0.7063

So the probability that at least one pair of people have the same birthday is approximately 0.7063, which is quite high. This is known as the birthday problem or birthday paradox.

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The amount of money that is take home pay would be = $3,491.91

The amount of money that is your fix expenses would be = $1,257.09

The amount of money that you make each month = $3,764.82.

The percentage of deduction made for FICA = 7.25%

That is;

= 7.25/100 × 3,764.82/1

= 27294.945/100

= $272.91

Therefore, the take home pay ;

= $3,764.82-$272.91

= $3,491.91

The percentage of the fixed expenses = 36% of the realised income.

That is, 36/100 × 3,491.91/1

= 125708.76/100

= $1,257.09.

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Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

The sides of the right triangle are as follows:

x = 18 units

y = 15.6 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the sides of the right triangle using trigonometric ratios

tan 30° = opposite / adjacent

tan 30° = 9 / y

cross multiply

y = 9 / tan 30

y = 15.5884645362

y = 15.6 units

Let's find x

sin 30 = opposite / hypotenuse

sin 30° = 9 / x

x = 9 / 0.5

x = 18 units

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Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.

The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.

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The measure of angle DBC is 60 degrees

Any triangle's three angles always sum to 180 degrees. Therefore, if you only have two angles available, add them up, and then take 180 away from the result.

The computation of the measure of angle ABC is shown below:

Given that

Angle ABC is 120 degrees

And, the measure of angle BAC is 60 degrees

So based on the above information

The  measure of angle  is

= Angle ABC - Angle ABD

= 120 degrees - 60 degrees

= 60 degrees

hence, the measure of angle DBC is 60 degrees

Q - Angle ABC is equal to 120 degrees. The measure of angle ABD is 60 degrees. What is the measure of angle DBC?

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Answer: Look below :)

Step-by-step explanation:

Hello again Sarah!

a. the dashed line indicated our answer will use > or <

furthermore, we can see two points, (0,2) and (1,6) on the graph.

So the slope is: 4/1 = 4

and the y intercept can be visually seen as 2

Since the shaded part is to the right, we will use <

The final equation is: y < 4x + 2

I wont show working for the others, but its pretty similar:

b. [tex]y \geq 0.5x - 3[/tex]

c. y < 0.75x - 2

The function [tex]f(x) = 4x^3 - 4[/tex] is a polynomial function. It takes an input value x and returns an output value f(x) based on the expression [tex]4x^3 - 4.[/tex]So the value of f(-1/2) is -4.5.

When we evaluate f(-1/2), we substitute -1/2 for x in the expression for f(x). This gives us:

[tex]f(-1/2) = 4(-1/2)^3 - 4[/tex]

The expression inside the parentheses, [tex](-1/2)^3,\\[/tex] is the cube of -1/2. To simplify this expression, we need to first raise -1/2 to the power of 3:

[tex](-1/2)^3 = (-1/2) * (-1/2) * (-1/2) = -1/8[/tex]

Next, we substitute this value back into the expression for f(-1/2):

f(-1/2) = 4(-1/8) - 4

Now we can simplify the expression by multiplying 4 and -1/8:

f(-1/2) = -1/2 - 4

Finally, we subtract 4 from -1/2 to get the final answer:

f(-1/2) = -4.5

So the value of f(-1/2) is -4.5.

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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)?

The vector equation for a line segment that joins two points P and Q can be found by subtracting the position vectors of P and Q and representing the result as a vector from P.

The position vector of point P is given by [0, -4, 4] and the position vector of point Q is given by [1/2, 1/3, 1/4]. So, the direction vector of the line segment is found by subtracting the position vectors:

d = Q - P = [1/2, 1/3, 1/4] - [0, -4, 4] = [1/2, 5/3, -3/4]

The vector equation of the line segment can be written as:

r(t) = P + t * d = [0, -4, 4] + t * [1/2, 5/3, -3/4] = [t/2, -4 + 5t/3, 4 - 3t/4]

where t is a scalar parameter that varies from 0 to 1 to give the points on the line segment between P and Q.

The parametric equations of the line segment are:

x(t) = t/2

y(t) = -4 + 5t/3

z(t) = 4 - 3t/4

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Find a vector equation and parametric equations for the line segment that joins P to Q?

P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )

vector equation r(t)

parametric equations x(t), y(t), z(t)

Answer:

In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:

SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm

[tex]above \: the \: line[/tex]

The length of the unknown side is 11.2ft

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

From the image shown,we have the parameters as;

Now, substitute the values, we have;

x² = 10² + 5²

Find the squares

x² = 100 + 25

Add the values

x ² = 125

Find the square root

x = 11.2 ft

Hence, the value is 11.2ft

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Answer: To determine the amount in Heidi's 401(k) account after 15 years, we need to calculate her total contribution each month and the interest earned on that contribution over the 15-year period.

First, let's calculate Heidi's contribution each month:

11% of $3,250 = $357.50

Next, let's calculate her employer's contribution each month:

6% of $3,250 = $195

Since Heidi's contribution is $357.50, and her employer matches her contribution up to 6% of her salary, her employer will contribute $195 each month.

So, Heidi's total contribution each month is $357.50 + $195 = $552.50

Next, we can use the formula for compound interest to calculate the balance in her 401(k) account after 15 years:

A = P * (1 + r/n)^(nt)

where:

A is the balance in the account after t years

P is the principal (initial deposit)

r is the interest rate

n is the number of times the interest is compounded in a year

t is the number of years

In this case, n = 12 (because interest is compounded monthly) and t = 15 (because the calculation is for 15 years). The principal P is $552.50 (Heidi's total contribution each month). The interest rate r is 6.25%.

Plugging in the values, we get:

A = $552.50 * (1 + 0.0625/12)^(12 * 15) = $552.50 * (1.00520833)^180

Using a calculator or spreadsheet software, we can calculate this value to be approximately $27,973.81.

So, the amount in Heidi's 401(k) account after 15 years, rounded to the nearest cent, is $27,973.81.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6(x + 4)/5(x - 7) * 9(x - 7)/7(x + 4) =

Cancel the x + 4 and x - 7

54/35

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

According to graph, the value of p(x) = 8, when x = -2, as this point lies on the curve ~

Now, put the value of x in each of the choices provided to check if its equal to 8.

[tex]\qquad \sf  \dashrightarrow \: p( x) = (0.35) {}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = (0.35) {}^{ - 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = \dfrac{1}{(0.35 ){}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = \dfrac{1}{0.1225} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = 8.1632[/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) \approx 8[/tex]

Since the value satisfy the first equation, the correct choice will be (A)

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

19. The area is given as,

A = (x + 5)(3x)

A = 3x² + 15x

19. The area is given as,

A = (x + 4)(x + 2)

A = x² + 6x + 8

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

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Answer:

Not equal and Congruent should be your answers