Translate story problems into equations. Solve equations. Translate story problems into inequalities.

The given data is used to obtain the equation as y = x - 2 and the table and graph has been drawn clearly.

A straight line can be written in the slope-intercept form as, y = mx + c.

In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.

The data is given as below,

slope = 1 and y-intercept = -2.

The equation, graph and table for the given data can be formed as follows,

(a) The slope-intercept equation is y = mx + c, where m is the slope and c is the y-intercept.

Substitute the corresponding values to obtain,

y = 1 × x + (-2)

  = x - 2

(b) The graph for the given equation is plotted below as,

(c) The table for the given equation can be formed with different values of x and y as below,

y = x - 2

Substitute x = 0 to get y = -2, x = 1, y = -1 and x = 2, y= 0.

Now, the table can be formed as below,

Hence, the equation is given as y = x - 2 and the graph and table for the equation is drawn properly.

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The table that represents exponential growth is the second table.. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows.

What is exponential growth?

Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.

In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.

One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.

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Step-by-step explanation:

In order for measuring devices to produce correct findings, they must have zero error. Zero error also makes it possible to determine if an instrument is functioning properly or not.

Instruments used by researchers and practitioners to assist in the assessment or evaluation of subjects, clients, or patients are known as measurement tools. From physical functioning to psychosocial welfare, the tools are used to assess or gather data on a number of aspects.

Electrical instruments are one of three categories for measuring devices. Instrument for electronics. a mechanical instrument.

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Answer:

5^-4

1/-625

Step-by-step explanation:

5^3 x 5^-7

They have the same base is 5, which means we just need to add the root, so 3 + (-7) = -4, so the answer is 5^-4

5^ -4

5 times 5 times 5 times 5 = -625

Because it is a negative exponent, means it is a fraction. So, the answer is

1/ -625

The height of the wall where the ladder reaches will be 6.33 feet.

It communicates that the area of the square whose side is the hypotenuse is identical to how much the locale of the squares on the other various sides.

The Pythagoras theorem formula is given as

H² = P² + B²

A 12-foot ladder is set against a vertical mass of construction, with the lower portion of the ladder staying on level ground 10 feet from the underpinning of the design.

The height of the wall where the ladder reaches will be calculated as,

12² = P² + 10²

144 = P² + 100

P² = 44

P =6.33 feet

The level of the wall where the stepping stool arrives freely will be 6.33 feet.

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Answer: [tex]\frac{3}{6}[/tex]

Step-by-step explanation:

[tex]Three\ divided\ by\ 6\ is\ \ \frac{3}{6} \ or\ simplified\ to\ \frac{1}{2}[/tex]

Answer: 3/6  = 0.5

Step-by-step explanation: Divide 3 divided by 6 as a fraction and that should give you 0.5 if your teacher tells you the answer cannot be a decimal then the answer will be 12 or if he tells u to simplify then the answer wil be 1/2

Answer:

$16.50

Step-by-step explanation:

y=mx+b

y is total cost, m is the miles, x is the cost per mile driven, and b is the pickup charge.

y=(7 miles x $2) + $2.50

y= $16.50

Answer:

Step-by-step explanation:

y=(7 miles x $2) + $2.50

y= $16.50

In the inequality 3x + 1 ≤ 4 at x = {1, 0, -1, -2, -3} all the values are satisfied therefore, the graph matches with this inequality.

What is Linear Inequality?

A linear inequality is a mathematical inequality that incorporates a linear function. A linear inequality contains one of the inequality symbols. It displays data that is not equal in graph form.

Solution:

To find the answer we need to put the values of x in options

3x + 1 ≤ 4

Putting x = {1, 0, -1, -2, -3}

At x =  1

3*1 + 1 ≤ 4

At x = 0

3*0 + 1 ≤ 4

At x = -1

3*-1 + 1 ≤ 4

At x = -2

3 * -2 + 1 ≤ 4

At x = -3

3*-3 + 1 ≤ 4

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The base in math formula is the sum that is multiplied when an exponent is used.

In mathematics, a base is a group of digits that are used to represent numbers. Different number systems employ various digit combinations as their base.

Depending on the situation, the word "base" can signify many things. The word "base" typically refers to the first component, core component, or base layer of a supporting structure.

The total number of digits a number system uses to express numbers is known as base in mathematics. The term "radix" is sometimes used to describe a number system's base.

Examples: In the expression 62, the base is 6, and the answer is 6 × 6 = 36.

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The Discriminant of the quadratic equation "2x + 5x² = 1" is 24  .

The Discriminant(D) of the Quadratic Equation ax² + bx + c can be calculated using the formula ; D = b² - 4ac .

the quadratic equation is given as 2x + 5x² = 1 ;

after rearranging the terms ,

the equation can be written as :

⇒ 5x² [tex]+[/tex] 2x - 1 = 0  ;

Substituting the values in the discriminant formula ,

we get ;

D = (2)² - 4×5×(-1)

Simplifying further ,

we get ;

D = 4 + 20

D = 24 .

Therefore , the value of the Discriminant is 24 .

The given question is incomplete , the complete question is  

What is the discriminant of the quadratic equation 2x + 5x² = 1  ?

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Answer:

Step-by-step explanation:

Yes, the residual plot supports the appropriateness of a linear model because it displays a clear pattern and has roughly equal amounts of positive and negative residuals.

Is the residual plot relatively symmetrical around the centerline?

Yes, if the residual plot is relatively symmetrical around the centerline, it suggests that the linear model is appropriate because it is capturing the variance in the data evenly. If the residual plot is skewed or has outliers, it may indicate that the linear model is not accurately representing the data and a different model may be needed.

A residual plot is a graph that plots the residuals (the differences between the observed values and the predicted values) on the y-axis and the independent variable on the x-axis. The residual plot is used to assess the appropriateness of a linear model. If the residual plot displays a clear pattern and has roughly equal amounts of positive and negative residuals, it suggests that the linear model is appropriate. On the other hand, if the residual plot is scattered randomly or displays a clear pattern, it suggests that the linear model is not appropriate. In this case, the residual plot supports the appropriateness of a linear model because it displays a clear pattern and has roughly equal amounts of positive and negative residuals. This suggests that the linear model is able to accurately predict the dependent variable based on the independent variable.

Therefore, the residual plot supports the appropriateness of a linear model.

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Yes, because it displays a clear pattern and has roughly equal amounts of positive and negative residuals.

What is a residual plot and how does it support the appropriateness of a linear model?

A residual plot is a graphical representation of the residuals (prediction errors) of a regression model. It can be used to assess the appropriateness of a linear model by examining the pattern of the residuals and the presence of any unusual points or trends.

If the residual plot shows a clear pattern, such as a trend or curvature, it suggests that the linear model may not be appropriate for the data. On the other hand, if the residual plot appears random and shows roughly equal amounts of positive and negative residuals, it supports the appropriateness of a linear model.

The residual plot is used to judge whether a linear model is suitable. The linear model may be useful if the residual plot exhibits a distinct pattern and contains nearly equal numbers of positive and negative residuals. On the other hand, it indicates that the linear model is inappropriate if the residual plot is dispersed randomly or exhibits a distinct pattern. The residual plot shows a distinct pattern and about equal numbers of positive and negative residuals, which in this instance confirms the suitability of a linear model. This suggests that the dependent variable may be accurately predicted by the linear model utilising the independent variable.
Therefore, the residual plot confirms that a linear model is adequate.

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The vertical asymptote of a function can be determined by setting its denominator equal to zero (0) and solving for x.

The horizontal asymptote of a function can be found by determining the degrees of the numerator and denominator.

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).

In order to graph any rational function, you should determine the values for which it is undefined. This ultimately implies that, a function is considered as undefined when the value of the denominator is equal to zero, which represents vertical asymptote lines.

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Answer:

B

Step-by-step explanation:

16 = 2⁴

9 = 3²

(2⁴)¹¹¹ × (3²)²²² = 2⁴⁴⁴ × 3⁴⁴⁴ = (2×3)⁴⁴⁴ = 6⁴⁴⁴

you can only combine the exponents of the same bases, or the bases of the same exponent.

in our case here the latter is used.

and indeed

6⁴⁴⁴ = (6²)²²² = 36²²²

so, essentially you were right. but you still needed to transform this into the form of the given answer option.

Answer:

Step-by-step explanation:

The weight of Y = 108 pound and weight of P is 27 pound

What does the math ratio mean?

Definitions: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Given that :

A = 36 pound

A:P =4:3

so when A is 36 = 4*9

then P is 3*9 = 27

Hence the weight of P is 27 pound

Now we have Y:A = 9:3

when A = 36 = 3*12

Then Y is 9*12 = 108

Hence weight of Y is 108 pound

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Answer:

x = 27

Step-by-step explanation:

[tex] \frac{1}{3}x - 3 + 4 = 10[/tex]

[tex] \frac{1}{3}x + 1 = 10 [/tex]

multiply both sides by (3)

[tex]3 \times \frac{1}{3}x + 3 \times 1 = 3 \times 10[/tex]

x + 3 =30

x = 30–3

x = 27

i hope i helped

A line is positive negative or undefined as per its slope is positive negative or undefined.

The slope is the ratio of change of the dependent variable with respect to the change in the independent variable.

It is calculated for both straight lines as well as curves.

for example, let us say , we have a straight line y = mx +c , then the coefficient of the dependent variable 'm' is the slope of the line. It is also calculated by (y2-y1)/ (x2-x1) where y2, x2 are the final positions and y1,x1 are the initial positions.

So, we can say that if the slope is positive, i.e. the line extends up to right , its a positive line ;  if the slope is negative, i.e. the line extends down to right , its a negative line and if the slope is undefined i.e. the change in the independent variable is zero like for a vertical line, then its an undefined line.

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The required real-world situation has been written in the solution part which could be modeled by the expression Y equals 1/20 XP.

A real-world situation that could be modeled by the expression Y = 1/20XP is the relationship between the distance a person runs and the number of calories they burn.

In this situation, Y represents the number of calories burned and X represents the distance run in miles. The constant 1/20 represents the rate at which calories are burned per mile.

For example, if a person runs 5 miles, we can substitute 5 for X in the expression to find the number of calories they burn:

Y = 1/20 × 5X

Y = 1/4

Thus, the person burns 1/4 calorie for every mile they run.

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Negative infinity is obtained by taking the limit of a decreasing sequence of negative real numbers as they approach negative infinity.

Negative infinity is an abstract concept that is used to represent a value that is less than the lowest possible number.  To get negative infinity, one must take the limit of a decreasing sequence of negative real numbers. This means that the sequence of numbers must get closer and closer to negative infinity as it continues to decrease. For example, if you take the sequence of numbers -1, -2, -3, -4, -5, -6, and so on, the limit of this sequence is -∞. As the sequence continues to decrease, it eventually reaches a point where the numbers become so small that they cannot be measured. At this point, the limit of the sequence is -∞.

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2 × 3 × 2 can be written as 2 × 6, so the answer is 6/1, which is an equivalent fraction to 6.

We can solve this problem by converting the expression into a fraction. First, we need to multiply 2 and 3 together, which gives us 6. Then, we need to multiply this result by 2, so we get 12. Finally, we need to express this result as a fraction. To do this, we put the numerator (12) over the denominator (1). So, the answer is 12/1, which simplifies to 4/32 × 3 × 2 can be written as 2 × 6, so the answer is 6/1, which is an equivalent fraction to 6

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The process to verify SSS number is to submit your printed records together with the required documentary requirements

The term documentary is referred as document reality, primarily for the purposes of instruction, education or maintaining a historical record

Here we need to find the process to verify the SSS number.

In order to find that we  must know the definition of SSS,

The term SSS refers an independent federal agency that administers compulsory military service.

In order to verify the SSS number, you must have the following documentaries,

Last name

Social Security Number

Date of Birth

Now, we have to do the following steps to verify the SSS number,  now you have to submit these to the appropriate department to do the verification.

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Answer: yes

Step-by-step explanation: it is a 2 dimensional shape if it was 3d it would end up being a prism

8 students like only tennis and​ football. When, In a survey of students about favorite​ sports, the results include 34 who like​ tennis, 37 who like​ football, 17 who like tennis and​ football, 21 who like tennis and​ baseball, 25 who like football and​ baseball, 9 who like all three​ sports, and 7 who like none of the sports.

One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols. The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.

Given

Number of student who only likes tennis and football

= number of student likes only tennis and football - who like all three sports

= 17 - 9

= 8

8 students like only tennis and​ football. When, In a survey of students about favorite​ sports, the results include 34 who like​ tennis, 37 who like​ football, 17 who like tennis and​ football, 21 who like tennis and​ baseball, 25 who like football and​ baseball, 9 who like all three​ sports, and 7 who like none of the sports.

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When the null hypothesis is rejected, the F-ratio and probability of rejection both rise.

The F-ratio is calculated using the formula F = variance between treatments/variety within treatments. An increase in the numerator will raise the F-ratio, while a reduction in the denominator will raise it even further. The probability of rejecting the null hypothesis rises with increasing F.When the null hypothesis is rejected, the F-ratio and probability of rejection both rise.

The null hypothesis for an ANOVA test is that the means of the different groups are equal. If the F-ratio is high enough (i.e., if it is significantly different from 1), then it is likely that the means of the different groups are indeed different. Therefore, if the variance between treatments increases and the variance within treatments decreases, then the F-ratio will be higher, and the likelihood of rejecting the null hypothesis will be greater.

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A removable discontinuity is when a function has an isolated point where it is not defined, and the function can be made continuous by removing that point. A hole is an example of a removable discontinuity.

In mathematics, a discontinuity is a point or set of points where a function does not behave as expected or fails to exist. There are three types of discontinuities: removable discontinuities, jump discontinuities, and infinite discontinuities. A removable discontinuity is when a function has an isolated point where it is not defined, and the function can be made continuous by removing that point. In other words, the function can be made continuous by “filling in” the discontinuity. An example of a removable discontinuity is a hole, where the graph has a gap that can be filled in. Jump discontinuities occur when the left-hand and right-hand limits of the function do not agree at a point, and the function “jumps” from one value to another at that point. An example of a jump discontinuity is a cusp, where the graph has a sharp point. Finally, an infinite discontinuity is when the function does not exist at a point, such as a vertical asymptote. In all three cases, the discontinuity can be easily identified by looking at the graph of the function.

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Using trigonometric identities, If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is; 1

We are told that sinA + sin² A = 1.

Now, we want to find (cos²A + cos⁴A).

From trigonometric identities, we know that;

cos²A = 1 -  sin² A

Thus;

cos²A + cos⁴A = 1 -  sin² A + cos⁴A

Similarly, using trig identities on the given expression;

From sinA + sin² A = 1, we can say that;

sinA = 1 - sin² A

Since cos²A = 1 -  sin² A, then we can say that;

sinA = cos²A

Thus;

sin²A = cos⁴A

Thus;

cos²A + cos⁴A = 1 -  sin² A +  sin²A

= sinA +  sin²A= 1

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Correct question is;

If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is

Answer:

Length of the base = 15 cm

Volume = 1125√2 cm³ = 1590.99 cm³ (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.6cm}\underline{Lateral Surface Area of a square pyramid}\\\\$LSA=a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{6.6cm}\underline{Base Area of a square pyramid}\\\\$BA=a^2$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\end{minipage}}[/tex]

If the lateral surface area (LSA) of the pyramid is three times the base area (BA):

[tex]\implies a \sqrt{a^2+4h^2}=3a^2[/tex]

Rearrange the equation to isolate h²:

[tex]\implies \sqrt{a^2+4h^2}=3a[/tex]

[tex]\implies (\sqrt{a^2+4h^2})^2=(3a)^2[/tex]

[tex]\implies a^2+4h^2=9a^2[/tex]

[tex]\implies 4h^2=8a^2[/tex]

[tex]\implies h^2=2a^2[/tex]

[tex]\boxed{\begin{minipage}{6.6cm}\underline{Total Surface Area of a square pyramid}\\\\$SA=a^2+a \sqrt{a^2+4h^2}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]

Given:

Substitute these values into the formula for the total surface area and solve for a:

[tex]\implies a^2+a\sqrt{a^2+4(2a^2)}=900[/tex]

[tex]\implies a^2+a\sqrt{a^2+8a^2}=900[/tex]

[tex]\implies a^2+a\sqrt{9a^2}=900[/tex]

[tex]\implies a^2+a(3a)=900[/tex]

[tex]\implies a^2+3a^2=900[/tex]

[tex]\implies 4a^2=900[/tex]

[tex]\implies a^2=225[/tex]

[tex]\implies a=15[/tex]

Therefore, the length of the base of the square based pyramid is:

To find the height (h), substitute the found value of a into the formula for h² and solve for h:

[tex]\implies h^2=2(15)^2[/tex]

[tex]\implies \sqrt{h^2}=\sqrt{2(15)^2}[/tex]

[tex]\implies h=\sqrt{2}\sqrt{(15)^2}[/tex]

[tex]\implies h=15\sqrt{2}[/tex]

Therefore, the height of the square based pyramid is:

[tex]\boxed{\begin{minipage}{5cm}\underline{Volume of a square pyramid}\\\\$V=\dfrac{1}{3}a^2h$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the base edge \\\phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]

Given:

Substitute the values into the formula and solve for volume:

[tex]\implies V=\dfrac{1}{3}(15)^2 \cdot 15\sqrt{2}[/tex]

[tex]\implies V=\dfrac{225}{3} \cdot 15\sqrt{2}[/tex]

[tex]\implies V=75\cdot 15\sqrt{2}[/tex]

[tex]\implies V=1125\sqrt{2}[/tex]

[tex]\implies V=1590.99[/tex]

Therefore, the volume of the square based pyramid is: