Malia has $500 to purchase water bottles and pairs of socks for a fundraiser for her school’s cross-country team. She needs to buy a total of at least 200 items without buying too many of just one item. What graph shows the possible numbers of water bottles and pairs of socks that Malia should buy?

To find the solution of the compound inequality x − 2 > 4 or 5x ≥ 35, we need to solve each inequality separately and then combine their solutions using the OR operator.

Solving x − 2 > 4, we add 2 to both sides to get x > 6.
Solving 5x ≥ 35, we divide both sides by 5 to get x ≥ 7.

The solution of the compound inequality x − 2 > 4 or 5x ≥ 35 is the set of all values of x that satisfy at least one of the inequalities, which is x > 6 or x ≥ 7.

To graph this solution, we draw a number line and mark the points 6 and 7 with open circles (because they are not included in the solution). Then we shade the region to the right of 6 and/or to the right of 7, as shown below:

<---o---o=========>
6   7

The open circles indicate that 6 and 7 are not included in the solution, because x can be any value greater than 6 or any value greater than or equal to 7, but not both at the same time.

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the problem is x > 6 or x ≥ 7. To explain this solution, we need to solve each inequality separately and then combine the results.

First, we solve x − 2 > 4 by adding 2 to both sides to get x > 6.

Next, we solve 5x ≥ 35 by dividing both sides by 5 to get x ≥ 7.

To combine the results, we take the union of the two solutions, which gives us x > 6 or x ≥ 7. This means that any value of x that is greater than 6 or equal to 7 will satisfy the original compound inequality.

The graph that represents this solution is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

the solution to the compound inequality x − 2 > 4 or 5x ≥ 35 is x > 6 or x ≥ 7, and the graph that represents it is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

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Answer:

B.

Step-by-step explanation

714.30 was the prior balance

⟹Answer:

➧Lucas can cut the wire into 12 pieces.

Step-by-step explanation:

⟹Lets Solve!

⟹The first step is to convert \(\frac{3}{4}\) into \(\frac{}{16}\) !

      To do this we must find what number multiplied by 4 equals 16.

16 ÷ 4 = 4

⟹Now we know our multiplier is 4. So lets multiply the numerator and denominator by 4.

\(\frac{3}{4} * \frac{4}{4} = \frac{12}{16}\)

\(\frac{12}{16}\)

⟹Next we just divide  \(\frac{12}{16}\) by \(\frac{1}{16}\).

\(\frac{12}{16}\) ÷ \(\frac{1}{16}\) = 12

➧Lucas can cut the wire into 12 pieces.

Woohoo! Brainliest appreciated! Hope I helped!

Based on the original length of the wire and the length Lucas requires, he will have 12 pieces.

The wire is 3/4 feet long and each piece required will be 1/16 feet.

The number of pieces in total is:

= Length of wire / Length of pieces

Solving gives:

= 3/4 ÷ 1/16

= 3/4 × 16/1

= 48/4

= 12 pieces

In conclusion, Lucas will have 12 pieces.

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Answer: 280 calories in 3 ounces

Step-by-step explanation:

you can use a ratio to solve

840 calories per 9 ounces

\(\frac{840}{9}\)

unknown calories per 3 ounces

\(\frac{x}{3}\)

\(\frac{840}{9} =\frac{x}{3}\)

cross multiply

2520=9x

280=x

The seat in the middle of the one-way route is 34

The seats are given as:

\(First= 0\) --- the first seat behind the seat number 95

\(Last= 66\) --- my seat

The seat number half-way would be:

\(Half = \frac{Last - First}{2} + 1\)

This gives

\(Half = \frac{66- 0}{2} + 1\)

Subtract 0 from 66

\(Half = \frac{66}{2} + 1\)

Divide 66 by 2

\(Half = 33 + 1\)

Add 33 and 1

\(Half = 34\)

Hence, the seat in the middle of the one-way route is 34

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The rate at which water is being pumped into the tank is approximately 9,086 cm³/min.

Let's consider the geometry of the tank. Since the tank is an inverted cone, its volume can be calculated using the formula V = (1/3)πr²h, where r is the radius of the cone and h is the height of the water. Given that the diameter at the top is 4 m, the radius can be calculated as r = (4 m)/2 = 2 m.

Now, let's determine the rate at which the height of the water is changing with respect to time. We are given that the water level is rising at a rate of 20 cm/min when the height of the water is 2 m. Using similar triangles, we can set up the following proportion: (2 m)/(h + 2 m) = 20 cm/(h + 200 cm). Solving this proportion, we find h = 4 m.

To find the rate at which water is being pumped into the tank, we need to calculate the volume of the cone when the height is 4 m and find the derivative of the volume with respect to time. The volume of the cone at 4 m height is V = (1/3)π(2 m)²(4 m) = (16/3)π m³.

Differentiating V with respect to time, we get dV/dt = (16/3)π dh/dt. We know that dh/dt = 20 cm/min. Converting this to meters, we have dh/dt = 0.2 m/min. Substituting these values, we get dV/dt = (16/3)π (0.2 m/min) = (32/15)π m³/min.

Now, we need to convert the volume rate to cm³/min. Multiplying by 1000 to convert m³ to cm³, we have dV/dt = (32/15)π (1000 cm³/min) ≈ 6785.76 cm³/min. Finally, adding the leakage rate of 9000 cm³/min, we find that the rate at which water is being pumped into the tank is approximately 9,086 cm³/min (rounded to the nearest integer).

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Answer:

f=9

Step-by-step explanation:

f+5=323f+5=32

We move all terms to the left:

3f+5-(323f+5)=0

We get rid of parentheses

3f-323f-5+5=0

We add all the numbers together, and all the variables

-320f=0

f=0/-320

f=9

Answer:

9

Step-by-step explanation:

Answer:

Let p represent the # of pages in the book.  Then, Nora has already read 0.30p pages and has 0.70p pages left to read.

If she reads 25% pages/night, that means reading 0.25(0.70)p pages per night, or 17.5 pages/night.  If 28% p/n, that means 0.28(0.70)p pages/night, or 19.6p pages/night.

How many nights will it take Nora to finish the book if she reads 25% of 7/10 of the book per night?  Without any calculations, we can answer this by "4 nights, since she reads 1/4 of the unread portion of the book per night."

If she reads 28% of 7/10 of the book per night, that will require fewer nights:

First night:  28%

Second night:  28%  

Third night:  28%

 Total:  3(28%) = 84%

This leaves 16% to read on the final night.

This is one interpretation of what I think is a poorly worded question.

The author of this question might have meant reading 25% of the remaining unread pages per night, which leads to a different answer.

Answer: XZ = 18

Step-by-step explanation:

An Obtuse angle is an angle whose degree measure is greater than 90 and less than ... Find the measure of the angle and give the reason for knowing it. ... 2x = 26 x = 13. 18. x = ______. Alternating Exterior Angles. 8x – 4 = 160 ... What is the smallest angle? 1. ∠Q. 2. ∠P. 3. ∠R. 2. In ΔXYZ, XY = 5, YZ = 7 and XZ = 18.

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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The statement "If Events A and B are mutually exclusive, then both events cannot occur simultaneously." is true.

Therefore the answer is B.

This statement is true, but it is not a general property of probability. In probability, events are considered mutually exclusive if they cannot occur at the same time, but there is no requirement that one of the events must occur. For example, if Events A and B are the rolling of a dice resulting in an even number and rolling a dice resulting in a number greater than 4, respectively, they are mutually exclusive events but both events may not occur (if a 3 is rolled, for example).

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(a) Probability (Female) = 0.468 (b) Probability (Management job) = 0.364

(c) Probability (Female and Management job) = 0.186

(d) Probability (Management job|Female) = 0.186

(e) Probability (Female|Management job) = 0.511

(a) What is the probability that the person is a female?

Total number of employed people = 64.7 million + 74.1 million = 138.8 million

Number of female employed people = 64.7 million

The probability that a randomly chosen employed person is female = 64.7 / 138.8 = 0.468

(b) What is the probability that the person has a management job?

Total number of employed people with management jobs = 25.8 million + 24.9 million = 50.7 million

The probability that a randomly chosen employed person has a management job = 50.7 / 138.8 = 0.364

(c) What is the probability that the person is female and has a management Job?

Number of female employed people with management jobs = 25.8 million

The probability that a randomly chosen employed person is female and has a management job = 25.8 / 138.8 = 0.186

(d) Given that the person is female, what is the probability that she has a management job?

Number of female employed people with management jobs = 25.8 million

The probability that a randomly chosen employed person is female and has a management job = 25.8 / 138.8 = 0.186

(e) Given that the person has a management job, what is the probability that the person is female?

The probability that a randomly chosen employed person with a management job is female = 25.8 / 50.7 = 0.511

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b) The standard error is 0.0102.

c) The Confidence Interval is [0.0683 , 0.0109]

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given:

a) The Sample should be collected randomly.

b) The number of Failure should be larger than 15.

B) the standard error

= √p(1-p)/ n

= √64/752 (1- 64/752) / 752

= 0.0102

C) CI = p ± \(z_{\alpha /2\) (SE)

and, \(z_{0.1/2\) = 1.6449

CI = 64 / 750 ± 1.6449(0.0102)

CI = [0.0683 , 0.0109]

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Answer:

The probability of this occurring is 1/7

Step-by-step explanation:

Okay, here is a probability question.

From the question, we can identify the following;

Total number of socks = 2 + 4 + 2 = 8 socks

Since we are not given the order in which the socks was worn, we can assume any order.

Let’s say the right leg socks was worn first.

From the question, the socks on the right leg is a brown one.

So now let’s calculate the probability of selecting a brown socks out of the mix

That would be ;

number of brown socks/ total number of socks = 4/8 = 1/2

Now, for the left foot, we are having white sock here.

Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.

Now we need the probability of picking a white sock from the total 7. That would be ; 2/7

So the probability of both action occurring is simply the product of both probabilities and that is ;

1/2 * 2/7 = 1/7

Answer:

The answer is -512

Step-by-step explanation

8*8*8= 512 and the cube root of 512 is 8 and the cube root answer is negative so 512 is negative

Polly Petunia, the Chief Horticulturalist for the Southwest region, is using a method called stratified random sampling to survey amateur gardeners in her region.

Stratified random sampling involves dividing the population into distinct groups or strata based on certain characteristics that are relevant to the research objective.

In this case, Polly is dividing the population of amateur gardeners in the Southwest region into three strata based on the states: Arizona, New Mexico, and Texas.

Once the population is divided into strata, Polly selects a random sample from each stratum. She sends her survey to 150 randomly selected gardeners from each state, resulting in a total sample size of 450 gardeners (150 from each state).

By using stratified random sampling, Polly ensures that her sample is representative of the population in terms of the geographic distribution across the three states.

This method allows her to obtain insights specific to each state while still maintaining a random selection within each stratum.

Using stratified random sampling helps increase the precision and accuracy of the survey results.

It allows Polly to make more accurate inferences and draw conclusions about the water conservation practices of amateur gardeners in each state, as well as the overall Southwest region.

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The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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The concurrent validity, is being measured.

What is concurrent validity?

A sort of proof that can be gathered to support the use of a test for forecasting other outcomes is concurrent validity. It's a variable that's employed in sociology, psychology, and other behavioural or psychometric sciences.

As, a test developer asks five clinicians who are experts in depression to rank 100 depressed clients on a 1 to 5 scale from minor depression to severe depression. the rankings are then correlated with test scores on a new test of depression.

So, the concurrent validity is being measured.

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Answer:

3

Step-by-step explanation:

3

the correct answer is a. likely to be due to true differences between the groups.

If we say we have statistically significant results, it means that the results are likely to be due to true differences between the groups. Statistical significance is a term used in hypothesis testing to determine if the observed differences between groups are likely to be real and not due to chance.

When conducting a statistical analysis, researchers compare the data from different groups or samples to see if there is a significant difference between them. This involves calculating a p-value, which represents the probability of obtaining the observed results if there were no true differences between the groups.

If the p-value is less than a predetermined threshold, typically 0.05, then the results are considered statistically significant. This means that the likelihood of obtaining the observed results by chance alone is very low, and it is more likely that the differences between the groups are due to a real effect.

For example, let's say we conduct a study to compare the effectiveness of two different treatments for a medical condition. If we find that the p-value is less than 0.05, we can conclude that there is a statistically significant difference between the treatments, and the observed improvement in one group is likely to be due to the treatment itself rather than random chance.

In summary, when we say we have statistically significant results, it means that the observed differences between groups are likely to be due to true differences rather than chance. This provides evidence for the presence of a real effect or relationship between the variables being studied.

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Answer:

c.

Step-by-step explanation:

it's been a while since I've done this but I'm about 90% sure

Using it's concept, it is found that there is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these numbers of outcomes are taken from previous trials.

In this problem, in the previous trial, one out of eight students read a book, hence:

p = 1/8 = 0.125 = 12.5%.

There is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

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If the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a right triangle has side lengths of 12 feet and 5 feet

We need to find the length of the hypotenuse.

By using pythagoras theorem we find hypotenuse.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

12²+5²=x²

144+25=x²

169=x²

Take square root on both sides

x=13

Hence, if the right triangle has side lengths of 12 feet and 5 feet then the length of hypotenuse is 13 feet.

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The cake mold I would recommend to a customer that wants to  buy a cake that serves 10-12 people is the 600 cubic inches size.

Multiplication is the process of determining the product of a set of numbers by carrying out a specialised mathematical operation. The sign that denotes multiplication is x.

The cake mold to be bought can be determined by multiplying the mold per serving by the maximum number of people the customer wants to serve.

12 x 50 = 600

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The value of the integral ∫\(e^{cos(t)\) sin(2t) dt over the interval [0, π] is 0.

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To evaluate the integral ∫\(e^{cos(t) sin(2t)} dt\) over the interval [0, π], we can use integration by parts with the substitution u = sin(t) and dv = \(e^{cos(t)cos(t)}dt\). Then, du = cos(t)dt and \(v = e^{cos(t)\).

Using this substitution and the formula for integration by parts:

∫\(e^{cos(t) sin(2t)} dt\) = \(-e^{cos(t) sin(t)}\) + ∫\(e^{cos(t) cos(t)} dt\)

We can use another substitution, z = cos(t), to simplify the integral on the right-hand side:

∫\(e^{cos(t) cos(t)} dt = \int e^{z} dz = e^z + C\)

Substituting back to the original integral, we get:

∫\(e^{cos(t) sin(2t)} dt = -e^{cos(t) sin(t)} + e^{cos(t)} + C\)

Evaluating the definite integral over the interval [0, π], we get:

∫[0,π] \(e^{cos(t) sin(2t)} dt = -e^{cos(\pi ) sin(\pi )} + e^{cos(\pi )} - (-e^{cos(0) sin(0)} + e^{cos(0)})\)

Simplifying the trigonometric terms sin(π) = 0 and sin(0) = 0, and using the fact that cos(π) = -1 and cos(0) = 1, we get:

∫[0,π] \(e^{cos(t)\) sin(2t) dt = \(-e^{-1} + e^{-1} = 0\)

Therefore, the value of the integral ∫\(e^{cos(t)\) sin(2t) dt over the interval [0, π] is 0.

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Answer:

2 a ^2  +  12 a  +  18

Step-by-step explanation:

Substitute the given value into the function and evaluate.

Hope this helps!

According to the combination method, the number of elements in the sample space for this experiment is 3060

Combination method:

Basically, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter

Given,

A person eating at a cafeteria must choose 4 of the 18 vegetables on offer.

Here we have to calculate the number of elements in the sample space for this experiment.

While we looking into the given question, we have identified the following things,

They are

Total number of available vegetables = 18

Number of choices we have made = 4

Therefore, here the value of n = 18 and the value of x = 4,

Therefore, according to the ncx formula, it can be written as,

=> ¹⁸n₄ = 18! / 4! (18 - 4)!

=> ¹⁸n₄ = 18! / 4! (14)!

=> ¹⁸n₄ = 3060.

Therefore, there are 3060 number of elements in the sample space for this experiment.

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Thus, a basis for s⊥ is the set {(-2, 2, 0)}.

What is a basis for s ⊥?

The question involving the terms "subspace," "containing," and "spanned."

If s is the subspace of R³ containing only the zero vector, s⊥ (the orthogonal complement of s) is the entire R³ space. This is because all vectors in R³ are orthogonal to the zero vector.

If s is spanned by (1, 1, 1), to find s⊥, we need a vector that is orthogonal to (1, 1, 1). We can use the dot product to determine orthogonality. For a vector (x, y, z), the dot product with (1, 1, 1) should be zero:

(1, 1, 1) · (x, y, z) = 0
x + y + z = 0

One possible vector that satisfies this equation is (-1, 1, 0). So, s⊥ is the subspace spanned by (-1, 1, 0).

If s is spanned by (1, 1, 1) and (1, 1, -1), to find a basis for s⊥, we need a vector orthogonal to both given vectors. We can use the cross product of the given vectors to find the orthogonal vector:

(1, 1, 1) × (1, 1, -1) = (-2, 2, 0)

Thus, a basis for s⊥ is the set {(-2, 2, 0)}.

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Answer: 60%

Step-by-step explanation:

if you calculate it. It would give you 40% as pastrami and 60% as not pastrami

Answer: 36/90

Step-by-step explanation: