Sally had some marbles. After buying 12 more marbles, she had 25 marbles. How many marbles did Sally have before she bought more?

(a) The statement "The sum of 4 and 6 is prime if and only if either 4 or 6 is prime" is false.

(b) The statement "If 3 divides 20, then 6 divides 20" is true.

(a) The sum of 4 and 6 is prime if and only if either 4 or 6 is prime.

To determine the truth value of this statement, we need to evaluate both directions separately.

Direction 1: If the sum of 4 and 6 is prime, then either 4 or 6 is prime.

This direction is true because the sum of 4 and 6 is 10, which is not a prime number. Therefore, the statement is true.

Direction 2: If either 4 or 6 is prime, then the sum of 4 and 6 is prime.

This direction is false because neither 4 nor 6 is a prime number, but their sum is 10, which is not a prime number. Therefore, the statement is false.

Since the statement is not true in both directions, the overall statement is false.

(b) If 3 divides 20, then 6 divides 20.

To determine the truth value of this statement, we need to evaluate the implication.

If 3 divides 20, then 6 divides 20.

This statement is true because 3 divides 20 (3 is a factor of 20), and 6 also divides 20 (6 is a factor of 20). Therefore, the statement is true.

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Answer: the amount of socks they will collect in four days is less than the amount of socks they plant to collect, in other words 915<1500 socks.

Step-by-step explanation:

If they collect 183 pairs of socks in one day, and there are four days left, then 183 x 5 = 915 (pairs of socks) in five days. They need to collect 1,500 pairs.

Let's denote the lengths of the legs of the right triangle as a and b, and the length of the hypotenuse as c. We are given that the altitude perpendicular to the hypotenuse is 12 cm.

Using the Pythagorean theorem, we have:

[tex]a^2 + b^2 = c^2[/tex]

The perimeter of the right triangle is given by:

Perimeter = a + b + c

We want to express the length of the hypotenuse (c) as a function of the perimeter.

Rearranging the equation for the perimeter, we have:

c = Perimeter - (a + b)

Substituting the equation for c into the Pythagorean theorem equation, we get:

[tex]a^2 + b^2[/tex] = (Perimeter - [tex](a + b))^2[/tex]

Expanding and simplifying, we have:

[tex]a^2 + b^2[/tex]= [tex]Perimeter^2[/tex] - 2Perimeter(a + b) +[tex](a + b)^2[/tex]

Simplifying further:

[tex]a^2 + b^2[/tex]= [tex]Perimeter^2[/tex]- 2Perimeter(a + b) + a^2 + 2ab + b^2

The terms with [tex]a^2[/tex] and [tex]b^2[/tex]cancel out, giving:

[tex]2ab = Perimeter^2 - 2Perimeter(a + b)[/tex]

Dividing both sides by 2, we have:

[tex]ab = (Perimeter^2 - 2Perimeter(a + b))/2[/tex]

[tex]ab = (Perimeter^2 - 2Perimeter(a + b))/2[/tex]

Now, since we are given that the altitude perpendicular to the hypotenuse is 12 cm, we know that:

ab = [tex]12^2 = 144[/tex]

We can solve this equation for either a or b, and then substitute the value into the expression for the hypotenuse (c):

For example, let's solve for a:

a = 144/b

Substituting this into the expression for c

c = Perimeter - (a + b)

c = Perimeter - (144/b + b)

Therefore, the length of the hypotenuse (c) can be expressed as a function of the perimeter.

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Answer:

It is really hard to see the picture

Step-by-step explanation:

Could you also give the choices to the answers that are possible? It would help out a lot. Just lmk in the comments and then I will revise my answer :)

Answer:

Part A: The appropriate measure of center to describe the distribution of the data would be, median.

Part B: The appropriate measure of spread to describe the distribution of data would be, interquartile range.

Part C: The box plot represents the data. Calculate the appropriate measure of spread, IQR = 13

Got it right on math nation. Hope this helps!

Answer:

B

Step-by-step explanation:

It is what it is

Answer:

37 degrees

Step-by-step explanation:

Cos x = 48/60

Cos x = 0.8

x = cos^-1 0.8

x = 36.8699

Answer:

6.25

Step-by-step explanation:

Answer:

46 + W = 231

Step-by-step explanation:

Answer:

My guess: 231 = 46 + b

Step-by-step explanation: Because they didn't mention how many were colored brown, we would use a variable to represent them, in this case I use b. But we do know 46 of them were white. so the equation would simply be 231 = 46 + b. After you add 46 and b you will get the total to 231. You can find b from subtracting 231 to 46. Then add b to 46 and get the total of 231

Answer:

5

Step-by-step explanation:

Answer:  5

Step-by-step explanation:

We rerange the number in 1,2,3,4,9,12,13

The median is 4, and a number x between 4 and 9.

We have 4.5 for median, which is the average of 4 and x.

(4 + x) /2 = 4.5

4 + x = 9

x = 5

20-10=10

10-3=7

7cm

Then the volume is 7cm

Step-by-step explanation:

Answer:

D?

Step-by-step explanation:

Im not exactly sure

Answer:

i believe the answer you're looking for is A/ 15

Step-by-step explanation:

hi there!

so its been a quick minutes since i have done a stem and left plot but the question is asking how many quarters had less then 20 points scored

here is a stem and leaf plot that i had made to make it easier for me to explain this problem it you!

_stem__|__leaf_____________________________________

         0   |  0, 2, 3, 7, 7, 8, 9

         1    |  0, 1, 4, 4, 4, 7, 7, 7

         2   |  0, 1, 7, 8, 9

         3   |

         4   | 2, 3, 6, 8

as you can see, i bolded each number that was less then the number 20, if we counted how many of the numbers that were bold in that stem and leaf plot the number would be 15!

sorry this was such a short answer! but i do hope i helped you with this :)

Answer:

30.5

Step-by-step explanation:

Step-by-step explanation:

the the height should be 16 cm I used the Pythagoras theory thank you.

Answer: 11

Explanation: You did everything right in terms of the steps you took. It looks like you accidentally wrote "1" instead of "-4" as the answer to "2(-2)".

The margin of error for the 97% confidence interval is approximately 0.021

The margin of error for the 97% confidence interval used to estimate the population proportion can be calculated using the formula: margin of error = z * √((p * (1 - p)) / n), where z is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.

To calculate the margin of error, we need to determine the sample proportion, which is the ratio of the number of adults who said they had tried alternative medicine to the total sample size: p = 744/1485 = 0.5017.

The z-score for a 97% confidence level is approximately 1.8808 (obtained from the standard normal distribution table).

Plugging in the values:

margin of error = 1.8808 * √((0.5017 * (1 - 0.5017)) / 1485) ≈ 0.021

Therefore, the margin of error for the 97% confidence interval is approximately 0.021, rounded to three decimal places.

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For a small change in x (dx), the corresponding change in y (dy) is given by the equation dy = (6x² - 4)dx.

To find the relationship between a small change in x (dx) and the corresponding change in y (dy) for the function f(x) = 2x³ - 4x, we can differentiate the function with respect to x.

f(x) = 2x³ - 4x

Differentiating both sides with respect to x:

f'(x) = d/dx (2x³ - 4x)

f'(x) = 6x² - 4

Now, we can express the relationship between dx and dy in the form of dy = f'(x)dx:

dy = (6x² - 4)dx

Therefore, for a small change in x (dx), the corresponding change in y (dy) is given by the equation dy = (6x² - 4)dx.

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Answer: 81.2

Step-by-step explanation:

The Volterra integral equation:

x(t) - xo = ∫[to, t] y(s) ds

y(t) - x₁ = ∫[to, t] f(s, x(s)) ds

(a) To write the initial value problem dx = f(t, x), x(to) = xo dt as an integral equation, we can use the integral representation of the solution.

Let's consider the integral equation:

x(t) = xo + ∫[to, t] f(s, x(s)) ds

This integral equation is of the Volterra type, as it involves a definite integral and depends on the function x(s) evaluated over the interval [to, t].

(b) To transform the second-order initial value problem d²x/dt² = f(t, x), x(to) = xo, x'(to) = x₁ into a Volterra integral equation, we can introduce a new variable, y(t), defined as the derivative of x(t):

y(t) = dx/dt

Now, we can rewrite the second-order differential equation as a system of first-order differential equations:

dx/dt = y(t)

dy/dt = f(t, x)

To represent this system as an integral equation, we'll integrate both equations from to to t.

This yields:

x(t) - xo = ∫[to, t] y(s) ds

y(t) - x₁ = ∫[to, t] f(s, x(s)) ds

Combining these two equations, we obtain the Volterra integral equation:

x(t) - xo = ∫[to, t] y(s) ds

y(t) - x₁ = ∫[to, t] f(s, x(s)) ds

This integral equation is also of the Volterra type, involving definite integrals and depending on the functions x(s) and y(s) evaluated over the interval [to, t].

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Answer:

11:00 AM+ 50 minutes= 11:50

11:50 AM+30 minutes= 12:20

Step-by-step explanation:

Gloria went to the mall and spent 50 minutes shopping. Then she had lunch for 30 minutes. If Gloria arrived at the mall at 11:00 A.M., at what time did she finish lunch?

Answer: 20°  &  70°

Step-by-step explanation:

We know complementary angles will add up to 90° and we also know we can divide the total by 9 parts because our ratio is 2 parts to every 7 parts.

To find each individual part size...

9x=90

x=10

so use our ratio...

2x10=20  for first angle

7x10=70 for second angle

a. To determine if the two populations of crawfish from Devon and Cornwall have the same mean carapace length, we can use the two-sample t-test.

This test compares the means of two independent samples to assess whether they are significantly different.

We can calculate the sample means and sample standard deviations for both groups:

Next, we calculate the t-value using the formula:

To determine if this t-value is statistically significant, we need to compare it to the critical value from the t-distribution for the given degrees of freedom

If the calculated t-value falls outside the critical region, we can reject the null hypothesis and conclude that the two populations have different mean carapace lengths. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean carapace length between the two populations.

b. To answer the question using the Wilcoxon rank sum test, we need to combine the observations from both samples, assign ranks based on their relative positions, and calculate the sum of ranks for one of the samples (either Devon or Cornwall). The null hypothesis for this test is that the two distributions are the same.

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Answer:

htgjyk

Step-by-step explanation:

Answer:

4 hours and a half. 4 hours and 30 minutes

Step-by-step explanation:

Answer:

4hrs 30 minutes

Step-by-step explanation:

6hrs = 372miles

372 ÷ 6 = 62

1hr = 62 miles

62 x 4hrs = 248 miles

You need to 279 miles. 0.5 = 30 minutes.

Answer/Step-by-step explanation:

a. Given that 32° is the reference angle, thus:

Hypotenuse is the side opposite to the right angle

Opposite side is opposite to the defence angle = x

Adjacent side is adjacent to defence angle = 15 m

b. Recall SOHCAHTOA.

We know the length of the adjacent side. We are asked to find x, which is the opposite side. So, we are dealing with Opposite side and Adjacent side.

The trigonometric function we will use to find x would be TOA:

That is,

Tan θ = Opp/Adj

c. Applying TOA:

Tan θ = Opp/Adj

θ = 32°

Opp = x

Adj = 15 m

Plug in the values

Tan 32 = x/15

15 × Tan 32 = x

9.37304028 = x

x = 9.4 (nearest tenth)

Answer:

432 each.

Step-by-step explanation:

You make 20% .2%

A. P(62 or over and has a loan)= 4.05%

B. P(has a loan)=48.6%

C.  P(62 or over and has a loan)=0.486

15% of the population are 62 or over

27% of those 62 or over have loans

54% of those under 62 have loans

To find the probabilities that a person fits into the following categories:

a) 62 or over and has a loan:

P(62 or over) = 15% = 0.15

P(62 or over and has a loan) = P(62 or over) * P(have a loan|62 or over)

= 0.15 * 0.27

= 0.0405 or 4.05%

b) Has a loan:

P(has a loan) = P(62 or over) * P(have a loan|62 or over) + P(under 62) * P(have a loan|under 62)

= 0.15 * 0.27 + 0.85 * 0.54

= 0.486 or 48.6%

c) P(62 or over and has a loan) = P(62 or over) * P(have a loan|62 or over)

= 0.15 * 0.27

= 0.0405 or 4.05%

P(62 or over) = 0.15 and P(have a loan) = 0.486

So, P(62 or over and has a loan) ≠ P(62 or over) * P(have a loan)

Hence, the events that a person is 62 or over and that the person has a loan are not independent.

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Answer:

[tex]\{x: 0 \le x \le 40 \}[/tex]

Step-by-step explanation:

Given

See attachment for graph

Required

The domain of the graph

To do this, we simply write out the range of value of the x-coordinate.

From the attached graph, the x values are:

[tex]x = [0,40][/tex] i.e. from 0 to 40 (both inclusive)

So, the domain is:

[tex]\{x: 0 \le x \le 40 \}[/tex]

Answer:

I think C or D

Step-by-step explanation:

Answer:

1,300 centameters

Answer: 1,300 centimeter meters is bigger

Step-by-step explanation: