Please answer quick plz be correct will give brainliest
Which data set does this stem-and-leaf plot represent?


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

{7, 0, 6, 2, 8}

{77, 7, 0, 6, 6, 0, 0, 2, 8}

{17, 27, 40, 46, 56, 60, 82, 88}
A stem-and-leaf plot with a stem value of 1 with a leaf value of 7, 7, a stem value of 2 with a leaf value of 7, a stem value of 3, a stem value of 4 with a leaf value of 0, 6, a stem value of 5 with a leaf value of 6, a stem value of 6 with a leaf value of 0, 0, a stem value of 7, and a stem value of 8 with a leaf value of 2, 8.

Key: 1|7 means 17

Answer:

Here, we have BC // ST, by applying Thales theorem:

UB/US = UC/UT

=>UB = UC x US/UT =6 x 12/(6 + 18) = 3

=> x = US - UB = 12 - 3 = 9

=> Option C is correct.

Hope this helps!

:)

Answer:

Yessirrr you are!!!

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.

For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.

x  2    5   20  40

y  40  20  5     2

Here,

[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]

So, this is neither a direct variation nor an indirect variation.

Answer:

Null hypothesis: H0 = 0.50

Alternative hypothesis: Ha > 0.50

z = 3.16

P value = P(Z>3.16) = 0.0008

Decision: we reject the null hypothesis and accept the alternative hypothesis. That is, the clerk used a method favoring Party A.

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

Given;

n = 40 represent the number of samples taken

Null hypothesis: H0 = 0.50

Alternative hypothesis: Ha > 0.50

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 40

po = Null hypothesized value = 0.50

p^ = Observed proportion = 30/40 = 0.75

Substituting the values we have

z = (0.75-0.50)/√(0.50(1-0.50)/40)

z = 3.16227766

z = 3.16

To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.

P value = P(Z>3.16) = 0.0008

Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.

Answer:

Step-by-step explanation: (2x-4)-(6x+6)

= 2x -4 - 6x - 6        [ opening brackets]

= 2x-6x -4-6                   [ bringing the same variables and numbers together]

= -4x-10

=2(2x-5)

Answer:

-4x-10

The 6x + 6 becomes negative due to the negative sign before the parenthesis. You then subtract 6x and 6 from 2x and -4 to get -4x-10

Answer:

0.45 part of the banner is painted orange.

Step-by-step explanation:

Given that the area for green = 0.75

The area of orange on green is = 0.6

So the area of orange is = 0.75*0.6 = 0.45

Learn more: https://brainly.com/question/1594198

To find the part of the banner that is painted orange, we multiply the green area by 0.6 and divide by the total area of the banner.

To find the part of the banner that is painted orange, we need to calculate the orange area compared to the total area of the banner.

Let's say the total area of the banner is 100 square units. Using the steps above:

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Answer:

(-1/2,-9/2)

Step-by-step explanation:

that is the coordinates for the vertex of the function y=2xsqaured+2x-4

Answer:

- The number of t-shirts he needs to print to obtain maximum profit = 2.79 (in thousand), that is, 2790 t-shirts.

- The maximum profit for this number of shirts is then = 12.208761 (in thousand dollars) = $12209

Step-by-step explanation:

Complete Question

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

The profit function is given as

p(x) = -x³ + 4x² + x

The maximum profit will be obtained by investigating the maximum value of the profit function

At the maximum value of the function,

(dp/dx) = 0 and (d²p/dx²) < 0

p(x) = -x³ + 4x² + x

(dp/dx) = -3x² + 8x + 1

at maximum point

(dp/dx) = -3x² + 8x + 1 = 0

Solving the quadratic equation

x = -0.12 or 2.79

(d²p/dx²) = -6x + 8

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0 (not a maximum point)

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0 (this corresponds to a maximum point!)

So, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousand).

So, the maximum profits that corresponds to this number of t-shirts is obtained from the profit function.

p(x) = -x³ + 4x² + x

p(x) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.717639 + 31.1364 + 2.79

p(x) = 12.208761 (in thousand dollars) = $12209 to the mearest whole number.

Hope this Helps!!!

Keegan should print around 2,000 shirts to maximize his profits, resulting in approximately $12,000 in earnings

To find the number of t-shirts Keegan should print to maximize his profits, we need to find the critical points of the profit function p(x) = -x^3 + 4x^2 + x.

Taking the derivative, we get p'(x) = -3x^2 + 8x + 1. Setting this equal to zero and solving for x gives:

0 = -3x^2 + 8x + 1

Using the quadratic formula, we find two potential values for x: x ≈ 2.37 and x ≈ -0.12. Since x must be a positive value representing the number of shirts, we discard the negative root.

Next, we need to determine whether this value of x corresponds to a maximum or minimum. We can do this by examining the second derivative, p''(x) = -6x + 8. Since p''(2.37) > 0, we conclude that x ≈ 2.37 corresponds to a local minimum.

However, since we're dealing with a cubic function, we need to consider behavior as x approaches infinity. As x gets very large, the -x^3 term dominates, making the function tend toward negative infinity. This means there is no global maximum, but rather a local maximum.

To find the approximate number of shirts Keegan should print, we take the nearest whole number, which is 2. The maximum profit can be found by plugging this value back into the profit function:

p(2) ≈ -2^3 + 4(2)^2 + 2 ≈ 12 (in thousands).

So, Keegan should print around 2,000 shirts to maximize his profits, which will be approximately $12,000 (rounded to the nearest whole dollar).

Complete question:

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

To learn more about profits

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Answer:

The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.

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 is:

The absolute value of the subtraction of one of the bounds by the estimate [tex]\pi[/tex]

For this problem, we have that:

[tex]n = 240, \pi = \frac{96}{240} = 0.4[/tex]

97% confidence level

So [tex]\alpha = 0.03[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.03}{2} = 0.985[/tex], so [tex]Z = 2.17[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.3314[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.4686[/tex]

0.4686 - 0.4 = 0.0686

The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.

Final answer:

To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, the proportion p is calculated from the sample data and then substituted into the formula. The margin of error is also calculated using the formula.

Explanation:

To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, we can use the formula:

CI = p ± z*(√(p(1-p)/n))

Where:

First, we calculate the proportion p = 96/240 = 0.4

Next, we find the z-value using a standard normal distribution table. For a 97% confidence level, the z-value is approximately 1.88

Finally, substituting the values into the formula:

CI = 0.4 ± 1.88*(√((0.4*(1-0.4))/240))

Calculating the margin of error:

ME = z*(√(p(1-p)/n))

ME = 1.88*(√((0.4*(1-0.4))/240))

ME ≈ 0.036

Therefore, the 97% confidence interval for the percentage of all such companies that provide on-site health club facilities is approximately 0.364 to 0.436. The margin of error for this estimate is approximately ±0.036.

Answer:

99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.

True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.

Step-by-step explanation:

For this case we need to remember that the confidence interval for the true mean is given by this formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]

And for this case the 99.7 % confidence interval for the true mean is (12.64cm , 14.44cm) we analyze one by one the possible options in order to select one:

99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.

True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.

There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.

False the confidence interval can't be interpreted as a chance

There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm.

False the confidence interval can't be interpreted as a chance

If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.

False always the confidence interval contain the mean since is the middle value.

Final answer:

The correct interpretation of a 99.7% confidence interval for mean length of frog jumps is that if we repeat the sampling many times, 99.7% of the constructed confidence intervals would contain the true population mean. This emphasizes the methodology's reliability over repeated sampling rather than assuring specifics of individual outcomes.

Explanation:

The correct interpretation of a 99.7% confidence interval, like the one provided for the mean length of frog jumps (12.64 cm, 14.44 cm), is that if we were to repeat this sampling process many times, 99.7% of the confidence intervals we construct would contain the true population mean. The other statements provided misinterpret the concept of confidence intervals by implying a probability about individual measurements or the certainty of the mean falling within a specific interval, which is not accurate.

Confidence intervals are about the process of estimation rather than specifics about single outcomes. They provide a range in which we are certain to a specified level (in this case, 99.7%) that the true population mean lies, assuming the sampling and calculations are correct. The correct interpretation underscores the reliability of the methodology over repeated sampling rather than guaranteeing specifics of individual outcomes or the exact location of the population mean.

Answer:

2

Step-by-step explanation:

y-intercept is where x = 0, and that point is (0,2), so it's 2

Answer:

its the 1st answer on edg

Step-by-step explanation:

I just took it

The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube

An equation is an expression that shows the relationship between two or more numbers and variables

The volume of the cube = h unit * h unit * h unit = h³ unit³

Volume of each pyramid = (1/6) * h³ = (1/3) * base² * height

(1/6) * h³ = (1/3) * base² * height

(1/3) * h² * (1/2)h = (1/3) * base² * height

The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube.

Find out more on equation at: https://brainly.com/question/2972832

The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

On a coordinate plane, a graph has a number of hours on the x-axis and a number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).

We know that the equation of the line passing through the two-point is given as

[tex]\rm (y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Then we have

[tex]\rm y-1 = \dfrac{2-1}{4-2} \times (x-2)\\\\y = \dfrac{1}{2}\ x - 1+1 \\\\y = \dfrac{1}{2}\ x[/tex]

The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.

More about the linear system link is given below.

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Answer:

first one is 1/2 second one is y = 1/2 x

Hope it helps!!!

Answer:

a) 11.51% probability that a random college woman has a height of 68 inches or​ more

b) This height is 70.135 inches.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

The normal distribution has two parameters, which are the mean and the standard deviation.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 65, \sigma = 2.5[/tex]

a. What is the probability that a random college woman has a height of 68 inches or​ more?

This is 1 subtracted by the pvalue of Z when X = 68. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{68 - 65}{2.5}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

1 - 0.8849 = 0.1151

11.51% probability that a random college woman has a height of 68 inches or​ more

b. To be in the Tall​ Club, a woman must have a height such that only​ 2% of women are taller. What is this​ height?

This weight is the 100-2 = 98th percentile, which is the value of X when Z has a pvalue of 0.98. So X when Z = 2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.054 = \frac{X - 65}{2.5}[/tex]

[tex]X - 65 = 2.054*2.5[/tex]

[tex]X = 70.135[/tex]

This height is 70.135 inches.

Answer: 4/10, simplified to 2/5

Step-by-step explanation:

1/10 plus 3/10 plus 2/10 is 6/10

10/10 minus 6/10 is 4/10

4/10 simplified (divide the numerator and the denominator by 2) is 2/5

Final answer:

Terry has covered 3/5 of the distance to home by running, walking, and skipping. Therefore, he still has 2/5 of the distance left to cover.

Explanation:

The question asks how much distance Terry still has to cover to reach home, given the fractions of the journey he has completed by running, walking, and skipping.

Terry ran 1/10 of the distance, walked 3/10 more, and skipped 2/10 more of the distance. To find the total distance covered, we add these fractions together:

To find the distance Terry still has to go, we subtract the fraction of the distance he has covered from the whole distance (1 or 5/5):

Therefore, Terry still has to cover 2/5 of the distance to reach home.

Answer:

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 1390

x = 514

p = 514/1390 = 0.37

q = 1 - 0.37 = 0.63

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.01 = 0.99

The z score corresponding to the area on the z table is 2.33. Thus, confidence level of 98% is 2.33

Therefore, the 98% confidence interval is

0.37 ± 2.33√(0.37)(0.63)/1390

Confidence interval = 0.37 ± 0.0302

Answer:

Positive increase of 200%

Step-by-step explanation:

Answer:

Step-by-step explanation:

percentage increase =increase /original *100

=750-250/250×100

=500/250×100

=200%

hope this helps

plzz mark me brainliest

Answer:

The minimum sample size required to create the specified confidence interval is 1804.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Minimum sample size for a margin of error of 0.06:

This sample size is n.

n is found when [tex]M = 0.06, \sigma = 1.3[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.06 = 1.96*\frac{1.3}{\sqrt{n}}[/tex]

[tex]0.06\sqrt{n} = 1.96*1.3[/tex]

[tex]\sqrt{n} = \frac{1.96*1.3}{0.06}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*1.3}{0.06})^{2}[/tex]

[tex]n = 1803.41[/tex]

Rounding up to the next integer

The minimum sample size required to create the specified confidence interval is 1804.

Answer:

0.00205%

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

n = 30, r = 24, p = 0.42, and q = 0.58.

P = ₃₀C₂₄ (0.42)²⁴ (0.58)³⁰⁻²⁴

P ≈ 0.00205%

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean. A 95% confidence interval does not mean 95% probability. It is used to express how confident we are that the true population parameter lies within the confidence interval.

With a lower limit of 10.6 and an upper limit of 29.1, and confidence interval of 95%, the correct option is

With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.

Final answer:

The 95% confidence interval represents the range within which the true mean of all widgets is likely to fall, not the individual sample mean.

Explanation:

A 95% confidence interval for widget width of 10.6 < μ < 29.1 means:

With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.

There is not a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.

Therefore, the correct interpretations are A and F.

Answer:

- 1. 15

Step-by-step explanation:

Z score is used in statistic to calculate deviation of an observed value from mean value of sample of observation.

Mathematically it is given by

[tex]z = observed \ value - mean\ value/ standard\ deviation[/tex]

using the above formula and substituting the value of of

mean = $42,800

standard deviation = $8,365

observed value =$30,000

Z = (8,365 - 42,800) / $30,000

   =  - 34,435/ 30,000 =  - 1. 14783

  = - 1. 15 ( to the nearest hundredth)

- 1. 15  Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000

Answer:

33 yd

Step-by-step explanation:

To find the area of a triangle, you can follow the formula:

(base x height) / 2

By putting this formula into context, you can substitute the values of the terms with the information provided in the problem:

(base x height) / 2

(11 yd x 6 yd) / 2

66 yd / 2

33 yd

Answer: (-2,3)

Step-by-step explanation:

Answer:

The value of test statistics is 25.

Step-by-step explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

Let [tex]\sigma[/tex] = population standard of the reading and writing section SAT score of the students in this school

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \leq[/tex] 100     {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] > 100     {means that the reading and writing section SAT score of the students in this school is higher than 100}

The test statistics that would be used here is One-sample Chi-square test statistics;

                        T.S. =  [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2} __n_-_1[/tex]

where, [tex]s^{2}[/tex] = sample variance =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]  = 13135.8

            n = sample of 11th-grade students = 20

So, the test statistics  =  [tex]\frac{(20-1)\times 13135.8^{2} }{100^{2} }[/tex]

                                     =  24.96 ≈ 25

Hence, the value of test statistics is 25.

Answer: = ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 65.3

Standard deviation r = 5.2

Number of samples n = 36

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

65.3 +/-1.645(5.2/√36)

65.3 +/-1.645(0.86667)

65.3+/- 1.4257

65.3+/- 1.4

= ( 63.9, 66.7)

Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)

Answer:

40

Step-by-step explanation:

3x^2 + 8x = 2

3x^2 + 8x - 2 = 0

D = b^2+4ac

D = 8^2+4(3)(-2)

D = 64+(-24)

D = 64-24

D = 40

Answer:

The length of rectangular photo frame is 15 cm and the breadth is 8 cm.

Step-by-step explanation:

The question is:

The diagonal of a rectangular photo frame is 2 cm more than the longest side. If the perimeter is 46 cm, how long are the sides of the frame?

Solution:

Let the length of the rectangular photo frame be denoted by x and breadth by y.

It is provided that the diagonal is 2 cm more than the length.

That is:

d = x + 2

The perimeter is 46 cm.

That is:

46 = 2 (x + y)

⇒ x + y = 23

⇒ x = 23 - y

The triangle form by the length, breadth and the diagonal of the rectangle is a right angled triangle, with the diagonal as the hypotenuse, length as perpendicular and breadth as the base.

So, according to the Pythagoras theorem,

d² = x² + y²

(x + 2)² = x² + y²

x² + 4x + 4 = y²

4x + 4 = y²

4 (23 - y) + 4 = y²

92 - 4y + 4 = y²

y² + 4y - 96= 0

Factorize the expression by splitting the middle term as follows:

y² + 4y - 96= 0

y² + 12y - 8y - 96= 0

y (y + 12) - 8 (y + 12) = 0

(y + 12)(y - 8) = 0

Either y = -12 or y = 8.

Since y represents the breadth of a rectangle, it cannot be negative.

Thus, the breadth of rectangular photo frame is 8 cm.

Compute the length as follows:

x = 23 - y

  = 23 - 8

  = 15

Thus, the length of rectangular photo frame is 15 cm.

Answer:

(x-1)(x-42) or (x-1) x (x-42)              <-----(they're basically the same thing)

Step-by-step explanation:

1. x^2-43x+42  2. x^2-x-42x+42  3. x(x-1)-42x+42  4. x(x-1)-42(x-1)  5. (x-1)(x-42)

6. answer is (x-1)(x-42)

Answer

The circumference of a circle is the length of its side, the area is the amount of space within it.

Step-by-step explanation:

The circumference of a circle represents the distance around the circle's boundary, while the area represents the surface area enclosed by the circle.

The difference between the circumference and area of a circle lies in their respective measurements and what they represent.

Circumference: The circumference of a circle is the measurement of the distance around the outer boundary of the circle. It is essentially the perimeter of the circle. The circumference is calculated using the formula:

Circumference = 2πr or πd

Where r represents the radius of the circle and d represents the diameter. It is a linear measurement and is typically expressed in units such as centimeters, inches, or meters.

Area: The area of a circle is the measurement of the region enclosed by the circle's boundary. It represents the total surface area within the circle. The area of a circle is calculated using the formula:

Area = πr²

Where r represents the radius of the circle. The area is a two-dimensional measurement and is typically expressed in square units such as square centimeters, square inches, or square meters.

To know more about distance here

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Answer:

25% probability you will roll a prime number and spin a prime number

Step-by-step explanation:

If we have two events, A and B, and they are independent, we have that:

[tex]P(A \cap B) = P(A) \times P(B)[/tex]

In this question:

Event A: Rolling a prime number.

Event B: Spinning a prime number.

Both the cube and the spinner have four values, ranging from one to four.

2 and 3 are prime values, that is, 2 of those values. Then

[tex]P(A) = P(B) = \frac{2}{4} = \frac{1}{2}[/tex]

What is the probability you will roll a prime number and spin a prime number

The cube and the spinner are independent of each other. So

[tex]P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25[/tex]

25% probability you will roll a prime number and spin a prime number

Answer:

= 1/4

Step-by-step explanation:

In a  cube , we have  numbers labeled 1 - 6

the prime numbers we have is 2 , 3 and 5

The probability of selecting a prime number is

[tex]=\frac{3}{6} \\\\=\frac{1}{2}[/tex]

Now this means the probability of rolling a prime number here is 1/2

Now we calculate the probability of spinning a prime number

Prime numbers here are just 2 and 3

The probability of spinning a prime number is thus 2/4 = 1/2

Thus, the probability of rolling a prime number and spinning a prime number also becomes; 1/2 * 1/2

= 1/4