Which is the more reasonable temperature for a snowy day: 30° C or 30° F?

Answer:

-2

Step-by-step explanation:

The slope of a line is

m = (y2-y1)/(x2-x1)

   = (-2 -4)/(-1 - -4)

   = -6/ ( -1 +4)

   = -6 /3

    =-2

Answer:

[tex]= - 2 \\ [/tex]

Step-by-step explanation:

[tex]( - 4 \: \: \: \: \: \: \: \: \: \: \: 4) = > (x1 \: \: \: \: \: \: y1) \\ ( - 1 \: \: \: \: - 2) = > (x2 \: \: \: \: \: \: y2)[/tex]

Now let's find the slope

[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - ( - 2)}{ - 4 - ( - 1)} \\ = \frac{4 + 2}{ - 4 + 1} \\ = \frac{6}{ - 3} \\ = - 2[/tex]

hope this helps you.

brainliest appreciated

good luck! have a nice day!

Answer:

2400

Step-by-step explanation:

You have to follow PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction).  Based off of this, you have to do the multiplication first, and then add.

263 × 24 - 164 × 24 + 24

6312 - 3936 + 24

2376 + 24

2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The expression is given below.

⇒ 263 · 24 − 164 · 24 + 24

Simplify the expression, then the value of the expression is given as,

⇒ 263 · 24 − 164 · 24 + 24

⇒ 6312 − 3936 + 24

⇒ 6336 − 3936

⇒ 2400

The value of the expression 263 · 24 − 164 · 24 + 24 will be 2400.

More about the value of the expression link is given below.

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Answer:

The sample mean is 6.1

Step-by-step explanation:

Margin of Error (E) = (upper limit - lower limit)/2 = (6.8 - 5.4)/2 = 1.4/2 = 0.7

Sample mean = lower limit + E = 5.4 + 0.7 = 6.1

Answer:

-3

Step-by-step explanation:

I'm not sure what the 0s are all about, but I can help with the equation;

To do this, we can do substitution. By equaling x-4 to 3x+2, we get

x-4=3x+2

By isolating the x, we get

-2x=6

x=-3

Hope this helped!

Answer:

b. not all the children can be above average

d. half the children must be below average

Step-by-step explanation:

In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.

Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.

Therefore, the correct answers are:

b. not all the children can be above average

d. half the children must be below average

Answer:

Second and last options are correct choices.

Step-by-step explanation:

If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.

Best Regards!

Answer:

The height and the radius of the cylinder are 3.67 centimeters and 5.19 centimeters, respectively.

Step-by-step explanation:

The volume ([tex]V[/tex]) and the surface area ([tex]A_{s}[/tex]) of the cone, measured in cubic centimeters and square centimeters, respectively, are modelled after these formulas:

Volume

[tex]V = \frac{h\cdot r^{2}}{3}[/tex]

Surface area

[tex]A_{s} = \pi\cdot r \cdot \sqrt{r^{2}+h^{2}}[/tex]

Where:

[tex]h[/tex] - Height of the cylinder, measured in centimeters.

[tex]r[/tex] - Radius of the base of the cylinder, measured in centimeters.

The volume of the paper drinking cup is known and first and second derivatives of the surface area functions must be found to determine the critical values such that surface area is an absolute minimum. The height as a function of volume and radius of the cylinder is:

[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]

Now, the surface area function is expanded and simplified:

[tex]A_{s} = \pi\cdot \sqrt{\frac{3\cdot V}{h} }\cdot \sqrt{\frac{3\cdot V}{h}+ h^{2}}[/tex]

[tex]A_{s} = \pi\cdot \sqrt{\frac{9\cdot V^{2}}{h^{2}} + 3\cdot V\cdot h }[/tex]

[tex]A_{s} = \pi\cdot \sqrt{3\cdot V} \cdot\sqrt{\frac{3\cdot V+ h^{3}}{h^{2}} }[/tex]

[tex]A_{s} = \pi\cdot \sqrt{3\cdot V}\cdot \left(\frac{\sqrt{3\cdot V + h^{3}}}{h}\right)[/tex]

If [tex]V = 33\,cm^{3}[/tex], then:

[tex]A_{s} = 31.258\cdot \left(\frac{\sqrt{99+h^{3}}}{h} \right)[/tex]

The first and second derivatives of this function are require to determine the critical values that follow to a minimum amount of paper:

First derivative

[tex]A'_{s} = 31.258\cdot \left[\frac{\left(\frac{3\cdot h^{2}}{\sqrt{99+h^{2}}}\right)\cdot h - \sqrt{99+h^{3}} }{h^{2}}\right][/tex]

[tex]A'_{s} = 31.258\cdot \left(\frac{3\cdot h^{3}-99-h^{3}}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]

[tex]A'_{s} = 31.258\cdot \left(\frac{2\cdot h^{3}-99}{h^{2}\cdot \sqrt{99+h^{2}}} \right)[/tex]

[tex]A'_{s} = 31.258\cdot \left[2\cdot h\cdot (99+h^{2}})^{-0.5} -99\cdot h^{-2}\cdot (99+h^{2})^{-0.5}\right][/tex]

[tex]A'_{s} = 31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5}[/tex]

Second derivative

[tex]A''_{s} = 31.258\cdot \left[(2+198\cdot h^{-3})\cdot (99+h)^{-0.5}-0.5\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-1.5}\right][/tex]

Let equalize the first derivative to zero and solve the resultant expression:

[tex]31.258\cdot (2\cdot h - 99\cdot h^{-2})\cdot (99+h)^{-0.5} = 0[/tex]

[tex]2\cdot h - 99 \cdot h^{-2} = 0[/tex]

[tex]2\cdot h^{3} - 99 = 0[/tex]

[tex]h= \sqrt[3]{\frac{99}{2} }[/tex]

[tex]h \approx 3.672\,cm[/tex]

Now, the second derivative is evaluated at the critical point:

[tex]A''_{s} = 31.258\cdot \{[2+198\cdot (3.672)^{-3}]\cdot (99+3.672)^{-0.5}-0.5\cdot [2\cdot (3.672) - 99\cdot (3.672)^{-2}]\cdot (99+3.672)^{-1.5}\}[/tex]

[tex]A''_{s} = 18.506[/tex]

According to the Second Derivative Test, this critical value leads to an absolute since its second derivative is positive.

The radius of the cylinder is: ([tex]V = 33\,cm^{3}[/tex] and [tex]h \approx 3.672\,cm[/tex])

[tex]r = \sqrt{\frac{3\cdot V}{h} }[/tex]

[tex]r = \sqrt{\frac{3\cdot (33\,cm^{3})}{3.672\,cm} }[/tex]

[tex]r \approx 5.192\,cm[/tex]

The height and the radius of the cylinder are 3.672 centimeters and 5.192 centimeters, respectively.

Answer:

B. A shirt costs $15, and a pair of shoes costs $20.

Step-by-step explanation:

Let s = price of 1 shirt.

Let p = price of 1 pair of shoes.

Adam:

5s + 4p = 155

Friend:

3s + 2p = 85

We have a system of simultaneous equations.

5s + 4p = 155

3s + 2p = 85

Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Add the equations.

      5s + 4p = 155

(+)  -6s - 4p = -170

--------------------------

      -s          = -15

s = 15

A shirt costs $15.

Now we replace s with 15 in the first original equation and solve for p.

5s + 4p = 155

5(15) + 4p = 155

75 + 4p = 155

4p = 80

p = 20

A pair of shoes costs $20.

Answer:

a) This t-value obtained (2.92) is in the rejection region (t > 1.69), hence, the sample does not support the cofdee industry's claim.

b) p-value for this test = 0.006266

c) The p-value obtained for this test is lesser than the significance level at which the test was performed, hence, we can reject the nuĺl hypothesis and say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Step-by-step explanation:

a) Degree of freedom = n - 1 = 34 - 1 = 33

The critical value of t for a significance level of 0.10 and degree of freedom of 33 = 1.69

Since we are testing in both directions whether the the average U.S. adult drinks 1.7 cups of coffee per day using our sample,

The rejection region is t < -1.69 and t > 1.69

So, we compute the t-statistic for this sample data to test the claim.

t = (x - μ)/σₓ

x = sample mean = 1.95 cups of coffee per day

μ₀ = The standard we are comparing against = 1.7 cups of coffee per day

σₓ = standard error = (σ/√n)

σ = standard deviation = 0.5 cups

n = Sample size = 34

σₓ = (0.5/√34) = 0.0857492926 = 0.08575

t = (1.95 - 1.70) ÷ 0.08575

t = 2.9154759464 = 2.92

This t-value obtained is in the rejection region, hence, the sample does not support the cofdee industry's claim.

b) Checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 34 - 1 = 33

Significance level = 0.10

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.92, at 0.10 significance level, df = 33, with a two tailed condition) = 0.006266

c) To use PHStat, the claim that the average U.S. adult drinks 1.7 cups of coffee per day is the null hypothesis.

The alternative hypothesis is that the real number of cups of coffee that the average U.S. adult drinks as obtained from the sample data, is significantly different from the 1.7 in the coffee industry's claim.

The p-value obtained from PHstat = 0.0063

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.10

p-value = 0.0063

0.0063 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to suggest that the coffee industry's claim isn't true based in results obtained from the sample data.

Hope this Helps!!!

Answer:pete

Step-by-step explanation:

If the integral as written in my comment is accurate, then we have

[tex]I=\displaystyle\int_{3/2}^2\sqrt{(x-1)(3-x)}\,\mathrm dx[/tex]

Expand the polynomial, then complete the square within the square root:

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

[tex]I=\displaystyle\int_{3/2}^2\sqrt{1-(x-2)^2}\,\mathrm dx[/tex]

Let [tex]x=2-\cos\theta[/tex] and [tex]\mathrm dx=\sin\theta\,\mathrm d\theta[/tex]:

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{1-(2-\cos\theta-2)^2}\sin\theta\,\mathrm d\theta[/tex]

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{1-\cos^2\theta}\sin\theta\,\mathrm d\theta[/tex]

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{\sin^2\theta}\sin\theta\,\mathrm d\theta[/tex]

Recall that [tex]\sqrt{x^2}=|x|[/tex] for all [tex]x[/tex], but for all [tex]\theta[/tex] in the integration interval we have [tex]\sin\theta>0[/tex]. So [tex]\sqrt{\sin^2\theta}=\sin\theta[/tex]:

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sin^2\theta\,\mathrm d\theta[/tex]

Recall the double angle identity,

[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]

[tex]I=\displaystyle\frac12\int_{\pi/3}^{\pi/2}(1-\cos(2\theta))\,\mathrm d\theta[/tex]

[tex]I=\dfrac\theta2-\dfrac{\sin(2\theta)}4\bigg|_{\pi/3}^{\pi/2}[/tex]

[tex]I=\dfrac\pi4-\left(\dfrac\pi6-\dfrac{\sqrt3}8\right)=\boxed{\dfrac\pi{12}+\dfrac{\sqrt3}8}[/tex]

You can determine the more general result in the same way.

[tex]I=\displaystyle\int_p^q\sqrt{(x-a)(b-x)}\,\mathrm dx[/tex]

Complete the square to get

[tex](x-a)(b-x)=-(x-a)(x-b)=-x^2+(a+b)x-ab=\dfrac{(a+b)^2}4-ab-\left(x-\dfrac{a+b}2\right)^2[/tex]

and let [tex]c=\frac{(a+b)^2}4-ab[/tex] for brevity. Note that

[tex]c=\dfrac{(a+b)^2}4-ab=\dfrac{a^2-2ab+b^2}4=\dfrac{(a-b)^2}4[/tex]

[tex]I=\displaystyle\int_p^q\sqrt{c-\left(x-\dfrac{a+b}2\right)^2}\,\mathrm dx[/tex]

Make the following substitution,

[tex]x=\dfrac{a+b}2-\sqrt c\,\cos\theta[/tex]

[tex]\mathrm dx=\sqrt c\,\sin\theta\,\mathrm d\theta[/tex]

and the integral reduces like before to

[tex]I=\displaystyle\int_P^Q\sqrt{c-c\cos^2\theta}\,\sin\theta\,\mathrm d\theta[/tex]

where

[tex]p=\dfrac{a+b}2-\sqrt c\,\cos P\implies P=\cos^{-1}\dfrac{\frac{a+b}2-p}{\sqrt c}[/tex]

[tex]q=\dfrac{a+b}2-\sqrt c\,\cos Q\implies Q=\cos^{-1}\dfrac{\frac{a+b}2-q}{\sqrt c}[/tex]

[tex]I=\displaystyle\frac{\sqrt c}2\int_P^Q(1-\cos(2\theta))\,\mathrm d\theta[/tex]

(Depending on the interval [p, q] and thus [P, Q], the square root of cosine squared may not always reduce to sine.)

Resolving the integral and replacing c, with

[tex]c=\dfrac{(a-b)^2}4\implies\sqrt c=\dfrac{|a-b|}2=\dfrac{b-a}2[/tex]

because [tex]a<b[/tex], gives

[tex]I=\dfrac{b-a}2(\cos(2P)-\cos(2Q)-(P-Q))[/tex]

Without knowing p and q explicitly, there's not much more to say.

Answer:

1) We have to multiply both sides by  1/(de)

2) c=ab/(cd)

Step-by-step explanation:

We have to achieve the right side expression be c only.  To do that we have to multiply cde by   1/(de) .  However we have to multiply the left side by

1/(de) as well.

So the resulting left side expression is:

ab *1/(de)=ab/(de)

So c= ab/(de)

Given equation in the question is,

ab = cde

To solve the given equation for the value of c, follow the algebraic rules,

1). Multiply both the sides of the equation with [tex]\frac{1}{de}[/tex],

   [tex]ab\times \frac{1}{de} = \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}= \frac{cde}{de}[/tex]

   [tex]\frac{ab}{de}=c[/tex]

Therefore, resulting equation for c will be,

[tex]c=\frac{ab}{de}[/tex]

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Answer:

-5°C < 5°C

The temperature was higher on Wednesday than on Tuesday.

Answer:

75%

Step-by-step explanation:

There are 3 numbers that fit this rule, 3, 5, and 6. There is a 3/4 chance spinning one or a 75% chance.

Answer:

75%

Step-by-step explanation:

The numbers 6 or odd are 3, 5, and 6.

3 numbers out of a total of 4 numbers.

3/4 = 0.75

Convert to percentage.

0.75 × 100 = 75

P(6 or odd) = 75%

4. 12 cent

5. $2.06

6. $1.56

7. $1.30

8. 86 cent

Answer:

150/250 or 3/5 or a 60% chance

Step-by-step explanation:

Why?

because you need to calculate the number of balls that are a three-digit number and they will not be a three-digit number up until you get to 100 so what is 250-100? its 150  so your fraction is  150/250 or 3/5 if you need it simplified. To get a percent you need to divide 150 by 250 to get 0.6 and then you multiply by 100.

Answer:

The Matlab code along with the plot of slope field for the given differential equation is provided below.

Step-by-step explanation:

Matlab quiver function:

The Matlab's quiver function may be used to plot the slope field lines for any differential equation.

The syntax of the function is given by

quiver(x, y, u, v)

Where matrices x, y, u, and v must all be the same size and contain corresponding position and velocity components.

Matlab Code:

[t,y] = meshgrid(0:0.2:2, 0:0.2:2);

v = sin(y) + sin(t);

u = ones(size(v));

quiver(t,y,u,v)

xlabel('t')

ylabel('y(t)')

xlim([0 2])

ylim([0 2])

Output:

The plot of the given differential equation is attached.

Answer:

a. 0.48

b. 0.14

c. 0.47

Step-by-step explanation:

Data provided in the question

0 - 2        0.48

3 - 5        0.26

6 - 8        0.12

9- 11        0.09

12- 14       0.05

Based on the above information

a. The probability for fewer than three phobias is

= P( x < 3)

= 0.48

b.  The probability for more than eight phobias is

= P( x >8)

= 0.09 + 0.05  

= 0.14

c. Probability between 3 and 11 phobias is  

= P(3 < x < 11)

= 0.26 + 0.12  + 0.09

= 0.47

Answer:

[tex] {9}^{1} = 9 \\ {3}^{1} = 3 \\ {1}^{3} = 1[/tex]

Answer:

4.9 hours = 4 hours 54 minutes

Step-by-step explanation:

speed = distance/time

time * speed = distance

time = distance/speed

time = (284 miles)/(58 mph) = 4.9 hours

4.9 hours - 4 hours = 0.9 hours

0.9 hours * (60 minutes)/(1 hour) = 54 minutes

4.9 hours = 4 hours 54 minutes

Answer:

40 deg

-320 deg

Step-by-step explanation:

400 deg - 360 deg = 40 deg

400 deg - 360 deg = 40 deg; 40 deg  360 deg = -320 deg

Answer:

  m less-than-or-equal-to 28

Step-by-step explanation:

Xander's charge for m miles will be (3 +1.50m). He wants this to be no more than $45, so ...

  3 +1.50m ≤ 45

  1.50m ≤ 42 . . . . . . subtract 3

  m ≤ 28 . . . . . . . . . .divide by 1.5

Answer: M is less than or equal to 28 or C

Step-by-step explanation:

GOT RIGHT ON E D G

Step-by-step explanation:

Q1. 1,075÷12.5 =8

So Therefore 1g of medicine cost 8 naira

Q2.645÷42=15.3

so therefore 1 hour cost 15.3 naira

The cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours  is 27090 naira.

A division is a process of splitting a specific amount into equal parts.

Given that 12.5g of medicine cost 1,075 naira.

We have to find the cost of 1g of medicine.

12.5g=1075 naira

1g=1075/12.5

1g=86 naira.

the total pay for someone who works 42 hours and gets 645 naira per hour

The cost for 42 hours

42×645

27090 naira

Hence,  the cost of 1g of medicine is 86 naira and the total pay for someone who works 42 hours  is 27090 naira.

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Answer:

21564 ÷ 2 = 10782

40565 ÷ 5 = 8113

6365 ÷ 8 = 795.625

1436 ÷ 7 = 205.142857143

Answer:

(-1, 6)

(0, 7)

Step-by-step explanation:

Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.

Answer:

60

Step-by-step explanation:

We are using sigma notation to solve for a sum of arithmetic sequences:

The 5 stands for stop at i = 5 (inclusive)

The i = 1 stands for start at i = 1

The 12 stands for expression of each term in the sum

Answer:

x=½

y=5

Step-by-step explanation:

(8x+7y=39)2

16x+14y=78

4x-14y=-68 add the two equations

20x=10.

divide both sides by 20

x=½

8x+7y=39

4+7y=39

7y=39-4

7y=35

y=5

The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.

8x + 7y = 39

4x – 14y = –68

Multiply by 2

16x + 14y = 78

-14y + 14y = 0

4x + 16x = 20x

-68 + 78 = 10

20x = 10

x = 1 / 2

8(1 / 2) + 7y = 39

4 + 7y = 39

7y  = 35

y = 35 / 7

y = 5

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Answer:

a) Check Explanation

b) Probability that 11 out of the 17 randomly selected flights are on time = P(X = 11) = 0.0680

c) Probability that fewer than 11 out of the 17 randomly selected flights are on time

= P(X < 11) = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

= P(X ≥ 11) = 0.9623

e) Probability that between 9 and 11 flights, inclusive, out of the randomly selected 17 are on time = P(9 ≤ X ≤ 11) = 0.1031

Step-by-step explanation:

a) How to know a binomial experiment

1) A binomial experiment is one in which the probability of success doesn't change with every run or number of trials. (Probability of each flight being on time is 80%)

2) It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (It's either the flights are on time or not).

3) The outcome of each trial/run of a binomial experiment is independent of one another.

All true for this experiment.

b) Probability that exactly 11 flights are on time.

Let X be the random variable that represents the number of flights that are on time out of the randomly selected 17.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 17 randomly selected flights

x = Number of successes required = number of flights required to be on time

p = probability of success = Probability of a flight being on time = 80% = 0.80

q = probability of failure = Probability of a flight NOT being on time = 1 - p = 1 - 0.80 = 0.20

P(X = 11) = ¹⁷C₁₁ (0.80)¹¹ (0.20)¹⁷⁻¹¹ = 0.06803777953 = 0.0680

c) Probability that fewer than 11 flights are on time

This is also computed using binomial formula

It is the probability that the number of flights on time are less than 11

P(X < 11) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0376634429 = 0.0377

d) Probability that at least 11 out of the 17 randomly selected flights are on time

This is the probability of the number of flights on time being 11 or more.

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17)

= 1 - P(X < 11)

= 1 - 0.0376634429

= 0.9623365571 = 0.9623

e) Probability that between 9 and 11 flights, inclusive, are on time = P(9 ≤ X ≤ 11)

This is the probability that exactly 9, 10 or 11 flights are on time.

P(9 ≤ X ≤ 11) = P(X = 9) + P(X = 10) + P(X = 11)

= 0.0083528524 + 0.02672912767 + 0.06803777953

= 0.1031197592 = 0.1031

Hope this Helps!!!

Answer:

22 more days

Step-by-step explanation:

so basically you have to find out the LCM of 2 and 11. which is 22. And that means they go hiking AND swimming in the same day the next 22 days. (basically what the other person said lol)

AND that is basically your answer :D

Answer:

6 Inches

Step-by-step explanation:

First Photograph

Length:Width = 24:18

Second Photograph

Let the unknown width =x

Length:Width = 8:x

Since the proportions of the two photographs are the same

[tex]8:x=24:18\\\\\dfrac{8}{x}= \dfrac{24}{18}\\\\24x=8 \times 18\\\\x=(8 \times 18) \div 24\\\\x=6$ inches[/tex]

The width of the photograph is 6 inches.

Answer:

A repeating decimal is not a rational number and The product of two irrational numbers is always rational

Step-by-step explanation:

One statement that is not true is "The product of two irrational numbers is always rational". Take for example the irrational numbers √2 and √3. Their product is √6 which is also irrational.

The other false statement is "A repeating decimal is not a rational number". Take for example the repeating decimal 0.33333..... It can be written as 1/3 which is a rational number.