Rosa is making a game board that is
16 inches by 24 inches. She wants to
use square tiles. What is the largest
tile she can use?

Please show working

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

0.9

Step-by-step explanation:

Answer:

top dot is (5,7) lower dot is (-3.5,-3)

Step-by-step explanation:

The minimum value of a - b is around 2.2 with a = 8.4 rounded to one decimal place and b = 6.19 rounded to two decimal places.

We must first subtract b (lower bound) from a (upper bound) to determine the least value of a - b, which is equal to 8.4 - 6.19 = 2.21. 2.21 is the difference between a and b. However, the question requests that we round off this number to the nearest tenth.

We remove the first decimal point because 1 is

less than 5, giving us 2.2. Hence the minimum value of a -b to the nearest decimal is found to be 2.2.

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The complete question is:

Given a = 8.4 rounded to 1 decimal place and b = 6.19 rounded to 2 decimal places, find the minimum value of a - b rounded to 1 decimal place.

The missing side of the right angled triangle is √202.

Given is a right angled triangle as shown in the image attached.

We can write -

(hypotenuse)² = (base)² + (perpendicular)².

x² = 11² + 9²

x² = 121 + 81

x² = 202

x = √202

Therefore, the missing side of the right angled triangle is √202.

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With Square Payments, you can easily and safely accept all forms of payment. You can collaborate with customers rather than competing with them when it comes to how they want to pay for goods and services when you use Square Payments.

Through Square, you can accept credit cards, Apple Pay, Android Pay, and a lot of other payment options. A client is an individual or company who purchases goods or services from another company. Customers are essential because they produce income. Without them, companies would cease to exist. A customer is the recipient of a good, service, product, or idea in sales, commerce, or economics that they have purchased from a seller, vendor, or supplier in exchange for money or another useful consideration. When a customer buys something and uses it themselves, they are considered a consumer. Although they might not be the final users, customers always buy goods or services. Although they might not have paid for it, consumers are always the ones who use a good or service in the end.

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By cancelative property, the roots of quadratic equation x² + 4 · x - 20 are: Exact: - 2 + 2√6, - 2 - 2√6, Approximate: 2.899, -6.899.

In this problem we must factorize a quadratic equation and use an algebraic property known as cancelative property, defined as:

If a · b = 0, then a = 0 or b = 0.

In addition, we can apply the following factorization rule:

x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)

First, factorize the quadratic equation:

x² - (- 2 + 2√6 - 2 - 2√6) · x + (- 2 + 2√6) · (- 2 - 2√6)

(x + 2 - 2√6) · (x + 2 + 2√6)

Second, apply cancelative property:

x + 2 - 2√6 = 0

x = - 2 + 2√6

x + 2 + 2√6 = 0

x = - 2 - 2√6

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A gallon of milk at Wegmans is $0.99 more expensive compared to Smart Shop.

To compare the price of a gallon of milk at Wegmans and Smart Shop, we need to use the z-scores and convert them back to the actual prices using the mean and standard deviation.

Mean (μ) = $2.89

Standard Deviation (σ) = $0.2

For Smart Shop, with a z-score of -1.3, we can use the formula:

z = (x - μ) / σ

Rearranging the formula, we can solve for x (price at Smart Shop):

x = z \(\times\) σ + μ

Substituting the values:

x = -1.3 \(\times\) $0.2 + $2.89

x ≈ $2.57

Therefore, the price of a gallon of milk at Smart Shop is approximately $2.57.

For Wegmans, with a z-score of 0.6, we can use the same formula:

x = z \(\times\) σ + μ

Substituting the values:

x = 0.6 \(\times\) $0.2 + $2.89

x ≈ $3.01

Therefore, the price of a gallon of milk at Wegmans is approximately $3.01.

To find the difference in prices between Wegmans and Smart Shop:

Difference = Wegmans price - Smart Shop price

Difference = $3.01 - $2.57

Difference ≈ $0.44

Therefore, a gallon of milk is approximately $0.44 more expensive at Wegmans compared to Smart Shop.

In summary, based on the given z-scores and the mean and standard deviation of milk prices, a gallon of milk is approximately $0.44 more expensive at Wegmans compared to Smart Shop.

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Answer:

The bag contains $2.39

Explanation 40% of 50 coins is 20 dimes which equals 2 dollars

8 percent is 4 pennies

2.00+ .04 is 2.04

Plus 7 nickels because there are 3 more nickels than pennies 7*5= 35

2.04+.35= 2.39

To find the perimeter of triangle formed by the tangents to the circles, find radii of circles and side lengths of triangle. The perimeter of triangle formed by the tangents to the circles is 12 times the radius of each circle.

Let's denote the radius of each circle as r. Since the circles are externally tangent to each other, the distance between their centers is equal to the sum of their radii, which is 2r.

When a triangle is formed by connecting the points of tangency on each circle, it creates three isosceles triangles. Each of these isosceles triangles has two congruent sides, which are the radii of the circles.By drawing the triangle, we can observe that the base of each isosceles triangle is equal to 2r, which corresponds to the diameter of one of the circles. The height of each isosceles triangle is equal to r, which is the radius of the circle.

Therefore, each side of the triangle formed by the tangents has a length of 4r.Since the triangle has three equal sides, its perimeter is given by 3 times the length of one side, which is 3 * 4r = 12r.The perimeter of the triangle formed by the tangents to the circles is 12 times the radius of each circle.

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The gallons of gas required by Ryan to travel 286 miles is 13.2 gallons.

As the stated question;

Total gallon of gas used to drive the 260 miles = 12 gallons

Let 'x' be the gallon of gas used to drive the 286 miles.

Then, bu using the proportion

12 / 260 = x / 286

Thus,

x = 286 x 12 / 260

x = 13.2 gallons

Thus, the amount of gas required by Ryan to travel 286 miles is 13.2 gallons.

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The given function is y = (x - 1)^(1/3). The domain of the function y = (x - 1)^(1/3) is [1, ∞).        

Explanation:Given function is y = (x - 1)^(1/3).Let's write down the definition of cube root: Cube root of a number y is a number x such that x^3 = y or x = y^(1/3)Let x be the input or independent variable of the function. To define the function we take cube root of x - 1. The cube root is defined only for non-negative numbers. Thus, x - 1 ≥ 0x ≥ 1The domain of the function is the set of all permissible values of x which satisfies the given condition.x belongs to [1, ∞)

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\(\large\bf{\underline{Given:}}\)

__________________________________________

\(\large\bf{\underline{Using\: formula:}}\)

\(\boxed{\bf\underline\pink{⟹\frac{h}{3} \times (b_1 + b_{2} + \sqrt{b_{1} } \times b_{2})}}\)

__________________________________________

\(\large\bf{\underline{Therefore}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = \frac{12}{3} \times (16 + 6 + \sqrt{16 \times 6)} \)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = 4 \times (16 + 6 + 9.7979)\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = 4 \times 31.7979\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = 127.1917\)

__________________________________________

\(\large\bf{\underline{Hence}}\)

\(\large\bf{⟹Volume=127.19{cm}^{2}(approx)}\)

Answer:

Step-by-step explanation:

-11+?=15

?=15+11

15+11= 26

So, -11+26=15.

?-(-3)= 5

?+3=5

?=5-3

?=2

So, 2-(-3)=5.

?+(-4)=7

?-4=7

?=7+4

?=11

So, 11+(-4)=7.

?+-8=3

?=3+8

?=11

So, 11+-8=3.

-2+?=1

?=1+2

?=3

So, -2+3=1.

?-12=-4

?=-4+12

?=8

So, 8-12=-4.

The expression a/b * c/d is an illustration of number types

The expression is given as:

a/b * c/d

Next, we test the given numbers

(a) 8.96

Express 8.96 as a fraction

8.96 = 896/100

Express the numerator and the denominator as products

8.96 = (224 * 4)/(50* 2)

Split the fraction

8.96 = 224/50 * 4/2

The above equation shows that 8.96 can be written in the form a/b * c/d.

Hence, the truth value of 8.96 is yes

(b) 5√6

Express 5√6 as a product expression

5√6 = 5 * √6

Evaluate the product

5√6 = 12.2474.....

The result of 5√6 is a non-terminating decimal

Hence, the truth value of 5√6 is no

(c) 15

Express 15 as a fraction

15 = 90/6

Express the numerator and the denominator as products

15 = (9 * 10)/(3 * 2)

Split the fraction

15 = 9/3 * 10/2

The above equation shows that 15 can be written in the form a/b * c/d.

Hence, the truth value of 15 is yes

(d) π/4

Express π as 22/7

π/4 = 22/7/4

Rewrite the expression as products

π/4 = 22/7 * 1/4

The above equation shows that π/4 can be written in the form a/b * c/d.

Hence, the truth value of π/4 is yes

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Answer:

I think the answer is option C

Option C is the correct answer. The 95% confidence interval is (22.12,27.48)

A confidence interval is defined as the mean of the estimation of the plus and minus is the variation in estimation, and if the confidence interval does not include the value of zero effect, then it can be determined as the significant result.

It also embraces the value of no difference between treatments that are indicating to the treatment under investigation that is not significantly different from the control.

The given data is:

Significance level:

\(α=1-0.95=0.05\)

Sample size  n= 8, so we use a t-test.

Critical values using t-distribution:

\( \frac{t_{n} - 1 \alpha }{2} = t_{7} .0.025 = 2.365\)

Sample mean,

\(x=24.8\)

Standard deviation,

\(σ=3.2 hours\)

The confidence interval for population means is given by:-

\(x±tₙ₋₁,α/₂σ/√n\\

24.8±(2.365)32/√8 \\

24.8±2.6756 \\

24.8±2.68 \\

24.8-2.68, 24.8+2.68 =22.12,27.48\)

Hence, the 95% confidence interval, is normally distributed in the interval of (22.12, 27.48)

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a. the probability that the sample mean exceeds the population mean by two hours is 0.3085.

b. the probability that the sample mean is more than 3 three hours below the population mean is 0.2266.

c. the probability that the sample man differs from the population mean by more than 4 hours is 0.3174.

d. independent random sample of 10 students is taken. With the increase in the number of observations the sample standard deviation decreases. Therefore the probabilities of (a), (b), and (c) will be lower for the second sample.

What is probability?

Probability is a method of determining how likely something is to happen. Many things can't be known for sure in advance.

What is a normal distribution with a standard deviation?

A probability distribution known as a "normal distribution" is symmetric about the mean and indicates that data that are close to the mean are more likely to occur than data that are far from the mean.

Here we have,

Suppose that the random variable is denoted by x

X∼N(μ,σ)

X∼N(μ,8)

The sample mean will follow a normal distribution with parameters.

x∼N(μ,8/√4)

x∼N(μ,4)

The standard normal variable Z is given by

Z∼N(0,1)

Z = (x−μ)/ (σ/√n)

= (x−μ) / 4

a.

P [(x−μ) > 2] = P [x−μ / (σ /√n)>2/ (σ /√n)]

= P (Z>2/4) = P(Z>0.5)

= 1 − P(Z<0.5) = 0.3085

Now using the standard normal table to calculate the probability

P (Z < 0.5) = 0.6914

1 − P(Z<0.5) = 0.3085

Hence, the probability that the sample mean exceeds the population mean by two hours is 0.3085.

b.

P [(x−μ) < -3] = P [x−μ / (σ /√n)>-3/ (σ /√n)]

= P (Z< -3/4) = P (Z< -0.75)

=  P(Z< -0.75) = 0.2266

Now using the standard normal table to calculate the probability

P (Z< -0.75) = 0.2266

Hence, the probability that the sample mean exceeds the population mean by 3 hours is 0.2266.

c.

P [|x−μ)| > 4] = P ((x−μ) > 4) + P ((x−μ) < −4)

= 1 − P (−4 < (x−μ) < 4)

= 1 − P [−4/ (σ/√n) < (x−μ) / (σ/√n) < 4/ (σ/√n)]

= 1 − P (−1 < Z < 1)

= 1 − [P (Z < 1) − P (Z < −1)]

= 1 − ((0.8413)-(0.1587))

= 0.3174

Now using the standard normal table to calculate the probability

P (Z < 1) = 0.8413

1 − P (Z < -1) = 0.1587

Hence, the probability that the sample mean exceeds the population mean by 4 hours is 0.3174.

d. The independent random sample of 10 students is taken. With the increase in the number of observations the sample standard deviation decreases. Therefore the probabilities of (a), (b), and (c) will be lower for the second sample.

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Answer:

B. 13/5

A. 0

Explanation:

Part 1

Given the expression:

We begin by evaluating the absolute value.

We simplify further to obtain:

The correct choice is B.

Part 2

Given the expression:

We begin by evaluating the absolute value.

We simplify further to obtain:

The correct choice is A.

The probability is 0.421 that the mean time spent commuting from home to work by a sample of 12 employees.

Empirical states that if most of the values or observations of a data set fall within the 3-population standard deviation, then the distribution of the data said to be a normal otherwise non-normal. It is also known by the name of the three-sigma rule.

We have the following information from the question is:

Sample size (N) = 12,

standard deviation (σ) = 8.1

and  mean (μ) = 42.7

The probability mean time spent commuting from home to work by a sample of 12 employees will be between 43.26 and 49.35 minutes is:

\(p[43.26 < x(bar) < 49.35]\)

\(p[\frac{43.26-43.7}{\frac{8.1}{\sqrt{12} } } < z < \frac{49.35-43.7}{\frac{8.1}{\sqrt{12} } }]\)

=> -0.18 < z < 2.41

=> p[z ≤ 2.41] - p[z ≤ 0.18] = 0.992 - 0.571

                                         = 0.421

Therefore, the probability 0.421 (rounded to three decimal places)  

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The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.

The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.

To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.

However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.

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The wall can be built in 22 days by 6 workers in first 6 days and 9 workers in the rest of time.

In this question we must use the definition of inverse proportionality, in which the number of workers (\(n\)), no unit, is inversely proportional to the building time (\(t\)), in days.

According to the statement, 6 workers spent 6 days building a wall and there are 24 days left for completion, but 3 more workers entered to reduce building time, which can be represented by the following expression:

\(x = 24\,days \times \frac{6}{9}\)

\(x = 16\,days\)

In this scenario, the wall can be built in 22 days. \(\blacksquare\)

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The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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Answer: 4cos(pi/6x)+3

Step-by-step explanation:

Answer:

y= 1\6x -5

Step-by-step explanation:

lmk if that is correct.

also that should be in slope int. form

Answer:

y=1/6x-5

Step-by-step explanation:

x-6y=30

move the x

-6y=30-x

divide all by -6

-6/-6y=30/-6 -x/-6

y=-5+1/6x

rearrange

y=1/6x-5

your answer is the second one

\(\\ \tt\hookrightarrow m<6+m<8=180\)

\(\\ \tt\hookrightarrow 21+m<8=180\)

\(\\ \tt\hookrightarrow m<8=180-21\)

\(\\ \tt\hookrightarrow m<8=159\)

Now

\(m< 6+ m< 8 = 180\)

\(21+ m < 8 = 180\)

\(m<8 = 180- 21\)

\(m<8 = 159\)

So,

\(m<4\) and \(m < 8\) [corresponding angles]

\(m<4=m<8=159°\)

Answer:

m= -1/2

this is the answer

Answer:

C) y=3/2x+3

Step-by-step explanation:

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

m=(6-3)/(2-0)

m=3/2

y-y1=m(x-x1)

y-3=3/2(x-0)

y=3/2(x)+3

y=3/2x+3

Answer:

C) y=3/2x+3

Step-by-step explanation:

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

m=(6-3)/(2-0)

m=3/2

y-y1=m(x-x1)

y-3=3/2(x-0)

y=3/2(x)+3

y=3/2x+3

Answer:

w=18

Step-by-step explanation:

So, lets go over what we know:

A line is 180 degrees.

5w+36 is the first part of the line.

3w is the other part of the line.

So 5w+36 and 3w is 180 degrees.

We can write this as:

5w+36+3w=180

Combine the 5w and 3w:

8w+36=180

Subtract 36 from both sides:

8w=144

Divide 8 from both sides to get w alone:

w=144/8

=

w=18

Hope this helps!