"7 less than a number t" written as an algebraic expression is:

Answer:

Amount required is [tex]x=\frac{3}{8}[/tex]

Step-by-step explanation:

Given : Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid in one experiment. She used [tex]2\frac{1}{8}[/tex] ounces of the acid in a second experiment.

To find : How much more acid did Cameron use in the second experiment?

Solution :

In one experiment,

Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid

i.e [tex]1\frac{3}{4}=\frac{7}{4}[/tex]

In second experiment,

She used [tex]2\frac{1}{8}[/tex] ounces of the acid.

i.e. [tex]2\frac{1}{8}=\frac{17}{8}[/tex]

Let x amount more she used then experiment 1 in experiment 2.

So, the equation became

[tex]\frac{7}{4}+x=\frac{17}{8}[/tex]

[tex]x=\frac{17}{8}-\frac{7}{4}[/tex]

[tex]x=\frac{17-14}{8}[/tex]

[tex]x=\frac{3}{8}[/tex]

Therefore, Amount required is [tex]x=\frac{3}{8}[/tex]

Answer:

4x + 15y = 12

Step-by-step explanation:

The standard form of a linear equation is Ax + By = C where A and B cannot be fractions and A is not negative. To write in standard form, move -5/2y to the other side of the equal sign. Then clear the denominators by multiplying the equation by 6.

2/3x=-5/2y+2

2/3x + 5/2y = 2

6(2/3x + 5/2y = 2)

4x + 15y = 12

Answer:

1.  The scatter plot does not show a linear model.2. Since the plotted data are all around the temperature of 10, the slope would be a horizontal line at 10. A horizontal line does not have any slope, this tell me that the average temperature stays an average of 10 no matter what the humidity level is.3. There is no vertical intercept shown.2nd page:1. yes, because there were 2 small clusters separated by a little bit of space.2. I think the location of the area the data came from may change the relationship between the variables.3. I think by switching the axis's the data may be grouped closer together since most of the data points are along a vertical line.

Step-by-step explanation:

Option B is the right answer.

Step-by-step explanation:

An accountant was struck by lightening three times in his lifetime. This event is Possible, but very unlikely.

We know that a probability near 0 means an unlikely event. Probability around 1/2 indicates an event that is neither unlikely nor likely. Similarly, probability near 1 indicates a likely event.

Here, in a lifetime the accountant was struck 3 times. If the average lifetime is 70 years, so probability becomes [tex]\frac{3}{70}= 0.04[/tex]. This is close to zero, indicating that the event is very unlikely.

And people are struck by lightening so it is a possible event.

Combining both, we get option B as the final answer.

Answer:

font size of top line will be 1.067

Step-by-step explanation:

Scale factor between 4th line text size to the 3rd line text will be

= [tex]\frac{0.937}{0.878}=1.067[/tex]

Scale factor between 3rd line and second line will be = [tex]\frac{1}{0.937}=1.067[/tex]

Therefore, scale factor between 2nd and 1st text size will be = [tex]\frac{x}{1}=1.067[/tex]

x = 1.067

It reveals that the font size of top line will be 1.067

Answer:

Step-by-step explanation:

[tex]\\\to\:\:\to\:\:\rm\red{40z - 20}[/tex]

[tex]\\\to\:\:\to\:\:\rm\green{20(2z-1)} \\ [/tex]

(Refer the attachment for graph representation)

[tex]\bigstar\:\:\bf\purple{y = 40z-20} \\ [/tex]

The correct equation used to create the function table provided is Option D: y = 2x, which indicates a linear relationship where y is twice the value of x.

The function table given in the question indicates the relationship between values of x and their corresponding y values. To determine which equation was used to create this table, you can compare the differences between these values. In the given pairs (1, 2), (3, 6), (4, 8), (5, 10), and (10, 20), it is observed that the y values are exactly twice the x values. Therefore, the equation representing this relationship must be y = 2x, which is a linear function with a slope of 2.

Looking at the options provided, Option D: y = 2x is the correct one, as it fits the pattern shown in the function table: for every unit increase in x, y increases by 2 units, implying a line with a slope of 2.

Answer:

7(5 sqrt x^2y) or C

Step-by-step explanation:

Answer:

Step-by-step explanation:

C) f(4)=5

Final answer:

Ordered pairs with opposite signs for their coordinates are located in the second or fourth quadrants of a Cartesian plane, depending on the signs of the x and y-coordinates.

Explanation:

The coordinates of an ordered pair with opposite signs indicate its position in the coordinate plane. When the x-coordinate and y-coordinate have opposite signs, the ordered pair lies either in the second or fourth quadrant. This is because the sign of the x-coordinate is positive on the right side of the y-axis (first and fourth quadrants) and negative on the left side (second and third quadrants), and similarly, the sign of the y-coordinate is positive above the x-axis (first and second quadrants) and negative below it (third and fourth quadrants). Thus, if an ordered pair has coordinates with opposite signs, it lies in the quadrant where one axis is positive and the other is negative. For example, if the x-coordinate is positive and the y-coordinate is negative, the ordered pair will be in the fourth quadrant. Conversely, if the x-coordinate is negative and the y-coordinate is positive, it will lie in the second quadrant.

The correct statement that describes a method that will help the group accurately estimate this percentage is;

⇒ Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."

Random sampling is defined as a sampling method that utilizes randomization of sample selection.

In random sampling, each sample has the same probability of being selected as that of other samples to be selected to serve as a representation of an entire population.

Now, in this question, since the group would like to estimate the percentage of town residents who would support a teen curfew, then the sampling method they should use is random sampling which is in option C.

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There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be 2 by 1, 2by 3, and 2 by 4.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Mrs. Wilton is planning a rectangular flower box for her front window.

She wants the flower box to hold exactly 16 cubic feet of soil.

Let the height of the flower boxes will be 1 foot.

Then the number of the flower boxes with the whole dimensions and different-size base will be

Volume = Area × 1

Area = 16 square ft.

There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be

Area = 16

Area = 2 + 6 + 8

Area = 2 × 1 + 3 × 2 + 2 × 4

Then the dimensions are 2 by 1, 2by 3, and 2 by 4.

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Final answer:

The original basket contained 72 mangoes, determined by working backward from the known remainder of 3 after the sequential distribution between the king, queen, and princes.

Explanation:

From a basket of mangoes, the distribution among the royal family leads to a classic fractional subtraction problem. The solution involves working backward from the known remainder. The youngest child took the remaining 3 mangoes, which indicates that this was what was left after the king, the queen, and the three chief princes took their respective shares.

Let's denote the original number of mangoes as x. The king took 1/6 of x, leaving 5/6x. The queen then took 1/5 of the remainder (5/6x), leaving 4/5 * 5/6x = 4/6x or 2/3x. Successively, the three chief princes took 1/4, 1/3, and 1/2 of their respective remainders, each action further reducing the quantity of mangoes. The problem states that after these distributions, 3 mangoes were left, which were taken by the youngest child.

To find the original number of mangoes, we begin by denoting the final 3 mangoes as the remaining half after the last prince's share, work through the inverse operations for each prior transaction, and solve for x. Through this back calculation, we find that the original number of mangoes was 72.

The directional derivative of f(x, y, z) = xy + yz + zx at p(1, -1, 7) towards q(2, 4, 5) is found by first calculating the unit vector in the direction from p to q, then the gradient of f at p, and calculating the dot product of the two vectors. The directional derivative comes out to be 16/ √30.

The directional derivative of the function f(x, y, z) = xy + yz + zx at a point p(1, -1, 7) towards the point q(2, 4, 5) can be found by first getting the unit vector in the direction from p to q, then calculating the gradient of the function at p, and finally calculating the dot product of these two vectors (the unit vector and the gradient of the function).

First, calculate the unit vector u = (q - p) / |q - p|. That gives u = (1, 5, -2), and normalize it to get u = 1/ √30 (1, 5, -2).

Next, get the gradient of the function at p(1, -1, 7), which is the vector of first order derivatives. The partial derivatives of f(x, y, z) with respect to x, y, z are y+z, x+z, and x+y respectively. This gives the gradient vector at p as (-8, 8, 0).

Finally, the directional derivative is the dot product of the unit vector and the gradient, which comes out to be 1/ √30 * ((1*-8) + (5*8) + ((-2)*0)) = 16/ √30.

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Answer:

it will take 2 minutes for 200 nurses to measure the blood pressure of 200 patients .

Step-by-step explanation:

We know that the work-time and number of labor and efficiency formula is given by:

[tex]Efficiency=\dfrac{Number\ of\ labor\times Time}{Work\ done}[/tex]formula is given by:

Here Number of labor=Number of nurses.

Work=Number of patients whose blood pressure were noted.

As the efficiency will be same this means that:

[tex]\dfrac{2\times 2}{2}=\dfrac{200\times x}{200}[/tex]

where x denotes the number of time taken by 200 nurses.

Hence,

[tex]x=2[/tex]

          Hence, the answer is:

                    2 minutes.

Answer:

B. there is only one solution, and it is viable

Step-by-step explanation:

To find the weight of an object on Mars, we can use a direct variation equation. By finding the constant ratio from the given values, we can then solve for the weight on Mars when the weight on Earth is known. In this case, the object would weigh 40 pounds on Mars if it weighs 120 pounds on Earth.

To solve this problem, we will use the concept of direct variation. The weight of an object on Mars varies directly with its weight on Earth. This means that the weight on Mars can be found by multiplying the weight on Earth by a constant ratio. Let's represent the weight on Mars as WM and the weight on Earth as WE. According to the problem, an object that weighs 50 pounds on Mars weighs 150 pounds on Earth. This gives us the following direct variation equation:

WM = k * WE

where k is the constant ratio.

We can now substitute the given values: 50 pounds for WM and 150 pounds for WE.

50 = k * 150

To solve for k, divide both sides of the equation by 150:

k = 50 / 150

k = 1 / 3

Now that we have the value of the constant ratio, we can find the weight of an object on Mars when it weighs 120 pounds on Earth. Let's represent the weight on Mars as x and the weight on Earth as 120:

x = (1 / 3) * 120

x = 40

Therefore, the object would weigh 40 pounds on Mars.

Answer:

D)5

Step-by-step explanation:

The initial value of the linear relationship is the value that exists in the "Y" axis when the "x" value is 0, as you can see in the graph, when the X value is 0, the Y value is 5, so the inital value of the linear relationship is 5.

If you wish to calculate this on an inequality, you just have to insert in the inequality 0 as the value for x, and you will get as a result the initial value.

The Euclidean Algorithm is used to find the greatest common divisor (GCD) of two numbers, this method has been applied to find the GCDs of multiple pairs of numbers.

The Euclidean Algorithm is basically a method to find the greatest common divisor (GCD) of two numbers. It is based on the principle that the GCD of two numbers is the same as the GCD of the remainder when the larger number is divided by the smaller one.

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