1. (a) Show that the polynomial x⁴+ 4x³ + 6x² - 8 is divisible by x+2​

Answer:

[tex] 25.75 = z_{\alpha/2} \frac{100}{\sqrt{100}}[/tex]

And solving for the critical value we got:

[tex] z_{\alpha/2}= \frac{25.75*10}{100} = 2.575[/tex]

Now we need to find the confidence level and for this case we can use find this probability:

[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)[/tex]

And using the normal standard distribution or excel we got:

[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)= 0.9950-0.0050= 0.99[/tex]

So then the confidence interval for this case is 99%

Step-by-step explanation:

For this case the random variable X is the scores for the SAT math scores and we know that the distribution for X is normal:

[tex] X\sim N(\mu , \sigma =100)[/tex]

They select a random sample of n =100 and they construc a confidence interval for the true population mean of interest and they got:

[tex]512.00 \pm 25.75[/tex]

for this problem we need know that the confidence interval for the true mean when the deviation is known is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is given by:

[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

And the margin of error for this interval is [tex] ME = 25.75[/tex] then we can solve for the critical value in order to find the confidence level:

[tex] 25.75 = z_{\alpha/2} \frac{100}{\sqrt{100}}[/tex]

And solving for the critical value we got:

[tex] z_{\alpha/2}= \frac{25.75*10}{100} = 2.575[/tex]

Now we need to find the confidence level and for this case we can use find this probability:

[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)[/tex]

And using the normal standard distribution or excel we got:

[tex] P(-2.575< Z<2.575)= P(Z<2.575) -P(Z<-2.575)= 0.9950-0.0050= 0.99[/tex]

So then the confidence interval for this case is 99%

Answer:

1.5b (kg)

Step-by-step explanation:

Let's begin by listing out the variables we were given:

weight of the watermelon = b (kg),

weight of watermelon = (2/5) * weight of candies

weight of candies = 1 ÷ (2/5) = 1 ÷ 0.4

weight of candies = 2.5b (kg)

How much is the weight of the box of candies greater than the weight of the watermelon is given by:

weight of the box of candies - weight of watermelon= 2.5b - b = 1.5b (kg)

Therefore, the weight of the box of candies is greater than the weight of the watermelon by 1.5b (kg)

Answer: 1.5b

Step-by-step explanation:

b kg is the weight of the watermelon

(5/2)b kg is the weight of the box of candies

(5/2)b - b = (5/2 - 1)b = 1.5b

The weight of the box of candies is 1.5b kg greater than the weight of the watermelon.

Answer: The required probability is 0.79

Step-by-step explanation:

Given: P(A) = 0.14

P(B) = 0.24

P(A and B) = 0.19

To find:  P(A given B)

The conditional probability of an event A is the probability that the event will occur given the knowledge of an already occurred event B and is denoted by

[tex]P(A/B)[/tex] or [tex]P(A \text { given } B)[/tex] where the value of [tex]P(A/B)= \dfrac{P(A \text { and } B)}{P(B)}[/tex]

So we have

[tex]P(A/B) = \dfrac{0.19}{0.24} \approx 0.79[/tex]

Hence ,the required probability is 0.79

Answer:

thee answer is 22.22 hopes this helps

To multiply fractions 16, 5/9, and 2 1/2 and reduce to lowest terms, convert mixed numbers to improper fractions, multiply the numerators and denominators, and then simplify by common factors. The reduced answer is 200/9.

To multiply the fractions and reduce to lowest terms of the expression 16 x 5/9 x 2 1/2, we first convert the mixed number to an improper fraction. The number 2 1/2 can be written as 5/2 because 2 x 2 + 1 = 5.

Now, we have the multiplication of three numbers, which is 16 x 5/9 x 5/2. Multiplying the numerators together and the denominators together, we get 16 x 5 x 5 in the numerator and 1 x 9 x 2 in the denominator, simplifying to 400/18.

To reduce this fraction to the lowest terms, we divide the numerator and the denominator by the greatest common divisor, which is 2. This gives us 200/9. The final answer cannot be reduced further, so the reduced fraction is 200/9.

Answer:

c.systematic random sampling.

Step-by-step explanation:

Using sampling concepts, it is found that this type of sample is called systematic random sampling, which means that option c is correct.

Samples may be classified as:

In this problem, after the 1st person is surveyed, every kth person, with k = 5 is surveyed, hence it is a systematic random sampling and option c is correct.

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The exact value of cot(3π/4) is 1.

Cotangent (cot) is defined as the ratio of the adjacent side to the opposite side of a right triangle. In the case of 3π/4, which is a 45-degree angle in the third quadrant, we can use the reference angle of π/4 (45 degrees in the first quadrant) to find the corresponding values.

In the first quadrant, the tangent of π/4 is 1, meaning the opposite side is equal to the adjacent side. In the third quadrant the values are negated, so the opposite side becomes -1, and the adjacent side becomes -1.

Therefore, cot(3π/4) can be calculated as the ratio of the adjacent side (-1) to the opposite side (-1), resulting in:

cot(3π/4) = -1/-1 = 1.

So, the exact value of cot(3π/4) is 1.

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Maria's test score is calculated by dividing the number of correct answers (22) by the total number of questions (25) and then multiplying by 100, resulting in a score of 88%.

Maria took a history test with 25 questions and correctly answered 22 questions. To find her test score as a percent, you divide the number of correct answers by the total number of questions and then multiply the result by 100. So, Maria's score would be (22 correct answers / 25 total questions) × 100 = 88%.

This is how it calculates:

First, write the number of correct answers over the total number of questions as a fraction: 22/25.

Then, convert this fraction to a decimal by dividing 22 by 25, which equals 0.88.

Finally, multiply the decimal by 100 to get the percentage. So, 0.88 × 100 equals 88%.

Maria's test score expressed as a percent is 88%.

Answer:

The answer would be 332

Step-by-step explanation:

You take how many birds were there when he woke up and subtract it by how many birds there was when he went to bed. Hope this helps :)

Answer:

wrong ^ its 269 on ixl

Step-by-step explanation:

Answer:

2 pizza's

Step-by-step explanation:

15x2=30

30 divided by 2 equals 15

the amount of pizza required is 30

there are a group of 15 people

each of these person gets 2 slices of pizza

each pizza has 15 slices

therefore the number of pizza needed is

= 2 × 15

= 30

Hence 30 pizzas are needed for the group of 15 people

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Answer:

Answer 2 is right, you welcome :)

Step-by-step explanation:

The stem-and-leaf plot corresponds to the data set {17, 27, 40, 46, 56, 60, 82, 88}.

In this plot, the first digit is 'stem' and the last digit is a 'leaf'.

And this plot is used to describe the quantitative data.

The stem-and-leaf plot shows the first digit (the stem) of each data point followed by the second digit (the leaf) of each data point. For example, the first row of the plot shows a stem of 1 and two leaves of 7, which corresponds to the number 17 in the data set. Similarly, the second row shows a stem of 2 and a leaf of 7, which corresponds to the number 27 in the data set.

Therefore, the correct option is:

{17, 27, 40, 46, 56, 60, 82, 88}.

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Answer:

3

Step-by-step explanation:

2 ÷ 2/3

Make the whole number a fraction

2/1 ÷ 2/3

Copy dot flip

2/1 * 3/2

The 2 in the numerator and denominator cancel

1/1 * 3/1

3

Answer:

I think you mentioned the problem “Five is the quotient of 120 divided by some number. What is the number?” In that case the answer is 24. Option b

Step-by-step explanation:

I got a 100 on the test!

Answer:

:C it not 24 it 20

Step-by-step explanation:

Final answer:

To determine if the mean rating assigned to the wine when the cost is described as $90 is greater than the mean rating assigned to the wine when the cost is described as $10, a hypothesis test is conducted.

Explanation:

To determine whether the mean rating assigned to the wine when the cost is described as $90 is greater than the mean rating assigned to the wine when the cost is described as $10, a hypothesis test is conducted. The null hypothesis assumes that the mean rating difference is not greater than zero, while the alternative hypothesis assumes that the mean rating difference is greater than zero.

A one-sample t-test is used, and the test statistic is calculated by dividing the mean difference of the ratings by the standard error. The degrees of freedom are determined by the sample size minus 1.

The resulting test statistic is compared to the critical value from the t-distribution with the given alpha level. If the test statistic is greater than the critical value, the null hypothesis is rejected, indicating that there is sufficient evidence to conclude that the mean rating assigned to the $90 wine is greater than the mean rating assigned to the $10 wine.

Answer:

x=5

Step-by-step explanation:

3/5(x-10)=18-4x-1

3/5x-30/5=18-4x-1

3/5x-6=18-4x-1

+6 +6

3/5x=23-4x

+4x +4x

4 3/5x=23

23/5x=23

23/5 divide , so you actually multiply both sides by the reciprocal 5/23

x=5

The solution of equation will be : x=5

Given,

3/5(x-10)=18-4x-1

Here,

Multiply 3/5 inside the bracket,

3/5(x-10)=18-4x-1

3/5x-30/5=18-4x-1

3/5x-6=18-4x-1

Now solve like terms individually.

3/5x=23-4x

4x +  3/5x=23

23/5x=23

x=5

Thus the value of x is 5 .

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Answer:

- 4 new classrooms can be built on the newly acquired plot.

- The number of classrooms on the first floor of the school's land = 8

- The amount of extra space on the new land needed to add just 2 more rooms and a soccer field 3/4 of the original land = 375 m²

Step-by-step explanation:

The current rectangular plot for the school has dimensions 50 m length and 12 m width.

The current school plot has an area of (50×12) that is, 600 m².

The newly acquired rectangular plot, is said to be (1/4) of the current plot.

Area of the newly acquired rectangular plot

= (1/4) × 600 = 150 m²

Each classroom on the current school's plot occupies (1/16) of the the current rectangular plot, area of a classroom on the current plot.

= (1/16) × 600 = 37.5 m²

So, how many classrooms can be obtained from the newly acquired rectangular plot?

Area of the newly acquired rectangular plot = 150 m²

Area of one classroom = 37.5 m²

Number of classrooms obtainable from the newly acquired rectangular plot = (150/37.5)

= 4 classrooms

b) The schoolyard is equal to 3/5 of the land. How many classrooms on the first floor does the school have?

Total area of school land now = 600 m² + 150 m² = 750 m²

Schoolyard occupies (3/5) of the space.

Then, the classrooms on the first floor will occupy (2/5) of the space.

Area occupied by classrooms = (2/5) × 750

= 300 m²

Recall, each classroom occupies 37.5 m² of space,

Hence, the number of classrooms on the first floor = (300/37.5) = 8 classrooms to the nearest whole number.

c) If you wanted to add just 2 more rooms and a soccer field 3/4 of the original land, so much more space would be needed in the new field?

2 more classrooms will occupy = 2 × 37.5 = 75 m²

(3/4) of the original land = (3/4) × 600 = 450 m²

Total new space required = 75 + 450 = 525 m²

The newly acquired rectangular plot has an area of 150 m², So, to achieve those two projects (add just 2 more rooms and a soccer field 3/4 of the original land) that would require 525 m².

The amount of extra space that will be required = 525 - 150 = 375 m²

Hope this Helps!!!

Answer:

the answer is D

Step-by-step explanation:

67 x e is MPH

The probability of not spinning a 5 and flipping heads in a coin toss, assuming a spinner with 10 numbers and a fair coin, is 0.45 or 45%. This is calculated by multiplying the individual probabilities of each independent event.

The question asked is related to the concept of probability, which refers to the likelihood of an event occurring. Specifically, it involves two independent events: spinning a number (other than 5) on a spinner, and flipping a coin to get heads. In this case, the two events do not affect the outcomes of each other.

Let's assume the spinner has 10 numbers (1 to 10) and the coin is fair (meaning the probabilities of getting heads and tails are equal). The probability of not getting a 5 on the spinner is 9/10 (because 9 out of the 10 possible outcomes meet this criterion), and the probability of getting heads on a coin flip is 1/2 (because 1 out of the 2 possible outcomes meets this criterion)

Since these are independent events, we can use the rule of product in probability to calculate the combined probability by multiplying the individual probabilities: (9/10) * (1/2) = 9/20, or 0.45. So, the probability of both not spinning a 5 and flipping heads is 0.45, or 45%.

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The student's question involves calculating the combined probability of independent events in a high school Mathematics context. It also touches on the law of large numbers, which predicts the long-term outcomes of random events. Additionally, the principles of entropy and orderliness in potential outcomes are discussed.

The question at hand deals with the concept of probability, specifically the likelihood of spinning a number other than 5 on a device, such as a spinner or die, and flipping a coin to get heads. When we assess the chance of getting either of these outcomes, if we presume each event to be independent, the combined probability is the product of their individual probabilities.

The statistical underpinning of this concept lies in the law of large numbers, which articulates that as the number of trials in a probability experiment increases, the observed or empirical frequency approaches the theoretical probability. This law reinforces why the outcomes of coin tosses and die rolls often do not match expected results exactly in small sample sizes but do over many repetitions.

Furthermore, when analyzing the microstate probabilities of coin tosses, we assume each result has an equal likelihood of occurring, which allows us to predict the macrostate frequencies. When tossing coins, we consider symmetrical outcomes such as 5 heads or 5 tails to be orderly and less likely than the more disorderly and common 3 heads with 2 tails.

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Answer:

We need a sample size of at least 1161.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error for the interval is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, we have that:

[tex]\pi = 0.22[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

How large a sample should she take?

We need a sample size of at least n.

n is found when [tex]M = 0.02[/tex]

So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.645\sqrt{\frac{0.22*0.78}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.645\sqrt{0.22*0.78}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.22*0.78}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.645\sqrt{0.22*0.78}}{0.02})^{2}[/tex]

[tex]n = 1160.88[/tex]

Rounding up

We need a sample size of at least 1161.

To estimate the proportion of defective parts with 90% confidence and 0.02 margin of error, the manager needs to use the formula for sample size, resulting in at least 1532 parts needed to be sampled.

This question involves the calculation of sample size in statistical inference. To estimate the proportion of defective parts with a 90% confidence interval, the production manager will need to use the formula for estimating sample size, which is n = Z² * P(1-P) / E².

In this formula, Z is the z-score associated with the desired confidence level (for a 90% confidence level, the Z value is 1.645), P is the estimated proportion of the population (in this case, 0.22), and E is the margin of error (in this case, 0.02).

By substituting these values into the formula, we get: n = 1.645² * 0.22(1 - 0.22) / 0.02² = 1531.025

Since we can't have a fraction of a sample, we round this up to the nearest whole number and the manager should sample at least 1532 parts.

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Answer:

12.7

Step-by-step explanation:

If this is a right triangle then you just have to use pythagorean theorem. If fifteen is the hypotenuse then fifteen squared minus eight squared will give you x squared. Fifteen squared is 225 and eight squared is 64 so you subtract 64 from 225 to acquire the number 161. The square root of 161 is not exact but when rounded it is 12.7

Answer:

Explanation:

The function f(x) = √x has been translated 3 units to the left and 1 unit down to make g(x). That means translating g(x) 3 units right and 1 unit up will make f(x). (matches choices A and E)

__

The range of the function is the vertical extent, all y-values ≥ -1. (matches choice C)

__

The translated function is ...

  g(x) = f(x+3) -1 = √(x +3) -1 . . . . . does not match choice D

__

The domain of the function is the horizontal extent, all x-values ≥ -3. (does not match choice B)

Answer: A, C, E

Step-by-step explanation:

Had to do this Q on test

Answer:

0.20 or 20%

Step-by-step explanation:

Brown shoes = 3

Black shoes = 2

Total shoes = 5

Brown pants = 1

Black shoes = 3

Total pants = 4

Brown socks =4

Black socks = 6

Red socks = 2

Total socks = 12

In order to choose shoes, pants and socks of the same color, Teddy can go either all black or all brown. For all black, there is a 2 in 5 chance he gets the right shoes, 3 in 4 chance for pants and 6 in 12 for socks. For all brown, there is a 3 in 5 chance he gets the right shoes, 1 in 4 chance for pants and 4 in 12 for socks.

[tex]P=P(All\ black)+P(All\ brown)\\P=\frac{2}{5}*\frac{3}{4}*\frac{6}{12}+ \frac{3}{5}*\frac{1}{4}*\frac{4}{12}\\P=0.20[/tex]

The probability that he chooses shoes, pants, and socks of the same color is 0.20 or 20%.

Answer:

5 Cars

Step-by-step explanation:

Let the number of cars to be sold to make the total pay equal be x.

The first company pays a salary of $12,500 plus commission of $1500 for each car sold.

The second company pays a salary of $17,500 plus a commission of $500 per car sold.

Equating both sides

12500+1500x=17500+500x

Collect like terms

1500x-500x=17500-12500

1000x=5000

Divide both sides by 1000

x=5

Therefore, when 5 cars are sold, the total pay would be the same.

To simplify the expression 18 + 12x, combine the constant term 18 and the variable term 12x.

To simplify the expression 18 + 12x, we combine like terms. The term 18 is a constant term and does not have any variables. The term 12x is a product of the coefficient 12 and the variable x.

Here, 18 is a constant term (a term with no variable), and 12x is a term with the variable x. Since the constant term and the x term are not like terms, they can't be combined.

So, the simplified expression is 18 + 12x.

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Answer:

see below

Step-by-step explanation:

This problem could have 2 solutions

We could be given two legs

a^2 + b^2 = c^2

5^2 +13^2 = c^2

25+169 = c^2

194 = c^2

Taking the square root on each side

sqrt(194) = c

Or the 13 could be the hypotenuse

a^2 + 5^2 = 13^2

a^2 +25 = 169

a^2+25-25 = 169-25

a^2 = 144

Taking the square root of each side

a = 12

Answer:

Step 2

Step-by-step explanation:

Answer:28.5

Step-by-step explanation:

Answer:

(0, -1)

Step-by-step explanation:

((4 + (-4))/2, (2 + (-4))/2) =

(0/2, -2/2) =

(0, -1)

Answer:

220

Step-by-step explanation:

Initial number of brainliest = 200

Additional given by me = 20

So,

Total number of brainliest = 200 + 20 = 220

Answer: 4) 157

Step-by-step explanation:

We know that there is no association between the grade level and the andedness, then we should find that the ratio between left handeds and right handed is the same for both grades.

In 7-th grade we have:

Left handed : 11

Right handed: 72

The ratio is 11/72 = 0.14

Then, the ratio for the 8-th graders must be about the same:

Left handed: 24

Right handed: X

Ratio: 24/X

Let's start with the bigger option, X = 157.

24/157 = 0.15

Ok, we now see that with the bigger option we obtained almost the same ratio (if we use the smaller values for X, we will get a ratio bigger than 0.15, so 0.15 is the better aproximation that we can find to the 0.14 of the 7-th graders)

Then the correct option is 4) 157

The number of right-handed graders should be option 4.

Since in 7th grade

We have

Left-handed: 11

Right-handed: 72

So, The ratio is = 11: 72 = 0.14

Now the ratio for the 8th grade should be the same

So,

Left-handed: 24

Right-handed: X

so,

Ratio: 24/X

Now

if we can do

[tex]24\div 157 = 0.15[/tex]

0.15 = 0.15

Therefore, the option 4 is correct.

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