let $d$ be any positive integer not equal to $2, 5$ or $13$. show that one can find distinct $a,b$ in the set $\{2,5,13,d\}$ such that $ab-1$ is not a perfect square.

We have to make sure that we are taking square roots of non-negative values to stay within the real number system.

You have to make sure x^2-16 ≥ 0 for the inner square root to stay in the real numbers.

You also have to make sure sqrt(x^2-16)-3 ≥ 0 for the outer square root to stay in the real numbers.

Solving x^2-16 ≥ 0 we have that x^2 ≥ 16, so either x≥4 or x≤-4.

Solving sqrt(x^2-16)-3 ≥ 0, we have

     sqrt(x^2-16) ≥ 3

              x^2-16 ≥ 9

                   x^2 ≥ 25

    either x ≥ 5 or x ≤ -5.

Since that second condition is more restrictive that x ≥ 4 or x ≤ -4, we can default to just using

   { x | x ≥ 5 or x ≤ -5 }

   (-infty, -5) U (5, infty)

Answer: I think that y =18

Step-by-step explanation: I thought this bc the one across from it is also 18 and they look equal. I hope I helped

The solution set of the compound inequality is written as:

(-∞, -4] U (6,  ∞)

First, we need to simplify the two given inequalities, the first one is:

7x + 6 > 4x + 24

Grouping like terms we will get:

7x - 4x > 24 - 6

3x > 18

x > 18/3

x > 6

The other inequality gives:

2*(-13x - 1) - 8 ≥ -10x + 54

-26x - 2 - 8 ≥ -10x + 54

-26x - 10  ≥ -10x + 54

-10 - 54 ≥ -10x + 26x

-64 ≥ 16x

-64/16 ≥ x

-4 ≥ x

So the compound inequality is:

-4 ≥ x

x > 6

Then the solution set written as an interval is:

(-∞, -4] U (6,  ∞)

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The graph of the equation y=-3/5+3 will be a straight line

The graph of a straight line is always straight.  The equation is written in slope intercept for where -3/5 is the

The form of an equation in slope intercept form is y=mx+c

Here, m=-3/5

c=3

To draw the line, from the point 3 on the x-axis, rise negative 3 and run 5

The draw the line for form a straight line

Note that the formula for slope is

S=rise/run

In conclusion, the equation forms a straight line.

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Answer:

22years old

Step-by-step explanation:

Let Fiona's age = x

Darwin age

2x+6 = 50

2x = 50 -6

2x = 44

x= 44/2

x = 22years old

Answer:

f(-4)=16

Step-by-step explanation:

since f(x)=8-2x and we are asked to find f(-4),

we plug -4 in for x and we get

[tex]f(-4)=8-2(-4)[/tex]

[tex]2*-4=-8[/tex]

[tex]8-(-8)=8+8[/tex]

[tex]8+8=16[/tex]

[tex]f(-4)=16[/tex]

8/3X = 1 + 5/3X

8/3X - 5/3 = 1 + 5/3X - 5/3X

3/3X = 1

X = 1

first box = 8

second box = 8

third box = 5/3x

fourth box = 3

fifth box = 1

sixth box = 1

Answer:

s= 2

Step-by-step explanation:

4s - 14 = -6  Add 14 to both sides

4s - 14 + 14 = -6 + 14  Simplify

4s = 8  Divide both sides by 4

s = 2

Check

4x - 14 = -6

4(2) - 14 = -6

8 - 14 = -6

-6 = -6

First, we should the leave the variable [tex]s[/tex] on the left side of the equation.

Divide both sides by [tex]4.[/tex]

Conclusion:

   Consequently, the element [tex]2[/tex] in the given set is the only real solution of this equation. What we need to do in such questions is to leave the unknown alone. Since the power of the variable [tex]s[/tex] of our unknown is [tex]1[/tex] we can only find [tex]1[/tex] root, respectively.

Answer: C. 2x+3y=7.20  4x+2y=8.80

Step-by-step explanation: 2x and 4x = grapefruit,  3y and 2y = oranges

Answer:

To solve the equation |2x - 5| = 7, you can set up two equations, one for the positive solution and one for the negative solution.

For the positive solution, you can start by isolating the absolute value expression on the left-hand side of the equation: |2x - 5| = 7 can be rewritten as 2x - 5 = 7. Then, you can solve this equation by adding 5 to both sides to get 2x = 12, and then dividing both sides by 2 to get x = 6.

For the negative solution, you can start by noting that the absolute value of a number is equal to its opposite if it is negative, so |2x - 5| = 7 can be rewritten as -(2x - 5) = 7. This equation can be solved by multiplying both sides by -1 to get 2x - 5 = -7, and then adding 5 to both sides to get 2x = -2. Then, dividing both sides by 2 to get x = -1.

Therefore, the two equations to solve the equation |2x - 5| = 7 are 2x - 5 = 7 and 2x - 5 = -7.

Answer:

C

Step-by-step explanation:

To solve the equation |2x - 5| = 7, we need to set up two equations, one for the case where the absolute value is equal to the positive value of the expression inside the absolute value bars, and one for the case where the absolute value is equal to the negative value of the expression inside the absolute value bars.

The first equation we need to set up is 2x - 5 = 7. In this case, the absolute value is equal to the positive value of 2x - 5, so we can simply set the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:

2x - 5 = 7

The second equation we need to set up is -(2x - 5) = 7. In this case, the absolute value is equal to the negative value of 2x - 5, so we need to set the negative of the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:

-2x+5 = 7

We can use these two equations to solve for the value of x. To solve the first equation, we can simply add 5 to both sides to get 2x = 12, and then divide both sides by 2 to get x = 6. To solve the second equation, we can first distribute the negative sign to get -2x + 5 = 7, and then add 5 to both sides to get -2x = 2. Finally, we can divide both sides by -2 to get x = -1.

Therefore, the two solutions to the equation |2x - 5| = 7 are x = 6 and x = -1.

Alternative:

2x-5 = 7

2x-5 = -7

Answer: To make 7 servings of the recipe, you will need:

Sauce: 7 servings * 15 cups/5 servings = <<7*15/5=21>>21 cups

Oregano: 7 servings * (2.5 tsp/5 servings) = <<7*(2.5/5)=1.75>>1.75 tsp

So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

Step-by-step explanation:

They will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, To make 7 servings of the recipe, you will need:

Sauce:

⇒ 7 × 15 /5

⇒ 21 cups

Oregano: \

⇒ 7 × (2.5 /5 )

⇒ 1.75 tsp

So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

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The probability that the student lived in the Gold dorm and was an underclassmen is of:

0.035 = 3.5%.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

The parameters for this problem are given as follows:

Hence the probability that the student lived in the Gold dorm and was an underclassmen is calculated as follows:

p = 0.7 x 0.05 = 0.035 = 3.5%.

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The rule that describes the transformation that Triangle ABC is rotated to create the image A'B'C' is; (x, y) → (-x, -y)

In transformation in mathematics, there are different types such as rotation, translation, dilation, reflection e.t.c

Now, from the diagram attached showing the given transformation, we see that the coordinates of the original triangle are;

A'(-1, -1)

B(1, -1)

C(0. -4)

We now see the coordinates of the transformed triangle are;

A'(1, 1)

B'(-1, 1)

C'(0, 4)

We can see that in the transformation both x and y are negative of each other. Thus, the transformation rule is; (x, y) → (-x, -y)

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Answer:

Solutions: (0,2) and (3,1)

Not a solution (6,4)                                                                                            

Step-by-step explanation:

x + 3y = 6

0 + 3y = 6

3y = 6

y = 2

(0,2)

x + 3y = 6

3 + 3y = 6

3y = 3

y = 1

(3,1)  

x + 3y = 6

6 + 3(4) = 6

6 + 12 = 12

18≠12

(6,4)

The standard deviation of the income that the insurer will receive can be determined which is 9708 using the distribution and mean.

Given in the question that the high probability would gain  in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.

According to the information, the gain around is 1250

Amount would lost in case of death is 100000.The expected value with its probability is:

E(X) = ∑x ×P(x)

=(-99750) × 0.00183 + ...+ (1250) × 0.99058

= 303.35

The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is

The standard deviation of Y can be determined as

α = under root {∑x2 × P(x) - (∑x × P(x) }

= 9708

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3/5 of 595 students are 7th graders:

5/8 of them participated in the competition:

2/5 of the 595 students are 8th graders:

7/8 of them participated in the competition:

About how many total students participated?

Find the sum of participated students from parts A and B:

The inequality statement that same as x ≥ -3 or x > 2 is option (A) x ≥ -3

The inequality statement is

x ≥ -3 or x > 2

The inequality is the mathematical statement that shows the relationship between two expression with inequality sign. The inequality signs are less than, less than or equal to, greater than, greater than or equal to etc.

The compound inequality is

x ≥ -3 or x > 2

The value of x is greater than or equal to -3 also value of x is greater than 2

Here x ≥ -3 express then values of the compound inequality

Therefore, the same inequality statement is option (A) x ≥ -3

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Answer:

Infinite number of integers that satisfy the inequality |x|<4.

Step-by-step explanation:

The absolute value of a number indicates its distance from 0 on the number line. Therefore, the inequality |x|<4 indicates that x is less than 4 units away from 0 on the number line. Because there are an infinite number of integers on the number line, there are an infinite number of integers that satisfy the inequality |x|<4.

Answer:

128/25

Step-by-step explanation:

(3 1/5) / (5/8) =

(3 + 1/5) / (5/8) =

(15/5 + 1/5) / (5/8) =

(15+1)/5 / (5/8) =

16/5 / (5/8) =

16/5 * 8/5 =   ==> dividing by a number is equaled to multiplying by its

                           reciprocal: the reciprocal of 5/8 is 8/5.

(16 * 8) / (5*5) = 128/25

The function f such that F = ∇f does not exist, and the answer is DNE (does not exist).

Generally, To determine whether or not the vector field is conservative, we need to check if its curl is zero. The curl of the given vector field is:

curl(F) = ∇ x F

          = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k

Substituting in the values of the components of F, we get:

curl(F) = (-cos(z))i + (0)j + (-y sin(z))k

Since the curl of the vector field is nonzero, the vector field is not conservative.

Therefore, the solution is DNE, and the function f such that F = f does not exist (does not exist).

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On analyzing the data given in question we get to know that the sensitivity is negative.

Our function is 40 + 24 x 2.4 /1 + 4x  to the point.

For the time being, our first task is to determine the sensitivity, which is the derivative of our discovery. The quotient rule, whose derivative we shall be utilizing, says that the derivative of F org equals G f prime minus f g prime all over g squared.

The bottom function is one plus four times the top function's derivative, or 40.4 times. 40 has a derivative of zero.

When a light source is x cm away from a light probe, the light's intensity is measured as y microwatts per square cm. The outcomes are displayed as ordered pairs( x , y).

So we just need to multiply 24 x240.4.

Using the power rule, we can reduce the 0.4 point to 9.6 x to the minus 0.6.

We subtract one from the initial exponents minus the top function 40 + 24 x to the point for times the bottom function's derivative 10 So we have the derivative of four additional 40.4 by the power rule,

we bring down the 0.4 multiplied by four against 1.6 next to the minus 0.6, and we divide all of that by one plus four x to the 40.4 squared.

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The probability that exactly one other guest has the same birthday as you is 0.3483.

The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event by the probability that it won't.

The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We express P(heads) = 12.

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The value of the missing sides assuming both triangles are similar will be 18 inches.

Similar figures are those figures which are identical in shape, but not necessarily in size.

Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.

As per the given two triangle,

Suppose the length of missing side is x inches.

Suppoes both triangles are similar by AAA rule.

The ratio of corresponding sides will be same thus,

x/6 = 12/4

x = 3 x 6 = 18 inches

Hence "If both triangles are comparable, the value of the missing sides will be 18 inches".

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Answer:

No (not a proportional relationship)

Step-by-step explanation:

The cost of fountain drinks at Hot Dog Hut:

[tex]\begin{array}{|c|c|}\cline{1-2} \sf Volume & \sf Cost \\\sf \sf (fluid\;ounces) & \sf(\$) \\\cline{1-2} \vphantom{\dfrac12}16& 1.49\\\cline{1-2} \vphantom{\dfrac12}20&1.59 \\\cline{1-2} \vphantom{\dfrac12}30& 1.89\\\cline{1-2} \end{array}[/tex]

A proportional relationship is one in which two quantities vary directly with each other.

Calculate the rate of change of the ordered pairs.

Rate of change between (30, 1.89) and (20, 1.59):

[tex]\implies \dfrac{1.89-1.59}{30-20}=\dfrac{0.3}{10}=0.03[/tex]

Rate of change between (20, 1.59) and (16, 1.49):

[tex]\implies \dfrac{1.59-1.49}{20-16}=\dfrac{0.1}{4}=0.025[/tex]

As the rates of change are different (not constant), the relationship is not proportional.

Note:  The graph of a proportional linear relationship is a line that passes through the origin (0, 0).

Answer:64

Step-by-step explanation:

just trust trust

The statement that best reflects the grade is "The variances of anxiety scores were roughly the same in the different groups of musicians."

The term variances refers the mean squared difference between each data point and the center of the distribution measured by the mean

Here we have given that a music teacher had noticed that some students went to pieces during exams and he wanted to test whether this performance anxiety was different for people playing different instruments. While he took groups of guitarists. drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. Here he also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8 ).

Now, we need to find the statements best reflects what the effect of GRADE in the table tells us.

While we looking into he given question we have identified that this performance anxiety was different for people playing different instruments.

So, based on this concept the correct statement id option (c).

Because, here the variances of anxiety scores were roughly the same in the different groups of musicians where if Levine's test of equality of error variances is non-significant (sig > .05) then there is equality of variances.

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We are 95% confident that the interval 29.7215 to 30.5029 includes the population mean age of all respondents.

What does a 95% confidence interval indicate?

With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

According to the given question:

Conclusions about statistical significance are possible with the help of the confidence interval. If the confidence interval does not include the value of zero effect, it can be assumed that there is a statistically significant result.

±2828.6, ±3370.3, and ±4429.6

a. A larger sample size would cause the interval to narrow.

b. Near certainty; 50.1% (a majority) is far below the 95% confidence interval for the population proportion.

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The continuous function f is defined on the closed interval −6 ≤ x ≤ 5. The figure above shows a portion of the graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3). It is known that the point (3, 3 −√5 ) is on the graph of f. 4.

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.

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The value of (a) x is 3 and (b) the length RT is= 14 units

The corrected question form a triangle. and the lengths of the triangle are give as

rs=9x-13

st=10x-3

rt=4x+2

Using the supporting values to find the lengths we have

s=t and rs=rt

This implies that

rs=9x-13=rt=4x+2

Equating the two equations we have

9x-13=4x+2

Collecting like terms

9x-4x=2+13

⇒5x=15

Making x the subject of the formula

x=15/5=3 units

In the same way, rs=9x-13=9(3)-13

=27-13=14 units

Also, st=10x-3

Substitute x=3 in the equation we have

10(3)-3

=30-3

=27

Recall that rt=4x+2

by substitution we have

4(3)+2

=12+2

=14 units

In conclusion, the value of (a) x is 3 units and (b) the length RT is= 14 units

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Corrected question:

in rst, if s=t, rs=9x-13, st=10x-3, and rt=4x+2, find x and the measurement of the side rt.

There is sufficient warrant to rejection of the claim that 64% of the readers of the publisher own a personal computer at a = 0.01 level of significance.

What is the null hypothesis?

Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.

Here, we have

P = population proportion of readers, who own personal computers.

The claim of the publisher: 64% of their readers own a personal computer.

Since the claim indicates a specific value about P, it should be treated as the null hypothesis and thus the required null and alternative hypothesis would be -

H₀ : p = 0.64

H₁  : p ≠ 0.64

Now, at a = 0.01, it is decided to reject the null hypothesis.

Hence, there is sufficient warrant to rejection of the claim that 64% of the readers of the publisher own a personal computer at a = 0.01 level of significance.

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