Select the correct answer.
Simplify the following expression.

Answer:

Step-by-step explanation:

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

That is what Slope is.

Answer:

Step-by-step explanation:

Slope :( 1,1)

You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)

Answer:

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Find the prime factors of 1352:

We need another factor of 2 as a minimum added in order to have even number of same factors:

Hence we need to multiply the given number by 2.

Example of samples of 100 people for two-sided p-value of less than 0.001 represents that the new drug is indeed effective.

Example of a scenario that could lead to a two-sided p-value of less than 0.001 is ,

To investigate whether a new drug reduces blood pressure in patients.

Randomly select 100 patients with hypertension and divide them into two groups.

One group receives the new drug, while the other group receives a placebo.

After a month of treatment, you measure the blood pressure of each patient .

And compute the difference between the pre- and post-treatment measurements.

Assuming that the blood pressure measurements are normally distributed.

Perform a two-sample t-test to compare the mean difference in blood pressure between the two groups.

If the difference is statistically significant at the 0.001 level.

It means that the probability of obtaining such a large difference by chance is less than 0.001.

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This means that in order for the profits in 2022 to match those in 2020, the profits in 2021 would also need to match those in 2020.

 [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

Profits for mesne. According to Section 2(12) C.P.C., the term “mesne profit” refers to any earnings that the person who is in wrongful possession of a piece of property has actually received or may obtain in the future. High Court of Telangana.

The earnings in 2022 must match the profits in 2020, hence we must choose the value of r such that:

[tex]P \times(1-r/100)^² = P[/tex]

By simplifying and dividing both sides by P, we obtain:

[tex](1-r/100)^² = 1[/tex]

Taking the square root of both sides, we get:

1-r/100 = ±1

Each time we solve for r, we obtain:

[tex]1-r/100 = 1[/tex] , which implies [tex]r = 0[/tex]

and

 [tex]1-r/100 = -1,[/tex] which implies [tex]r = 200[/tex]

We reject the [tex]r = 200[/tex] Option because a percentage drop cannot be larger than 100%.

Therefore,  [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

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Answer:b

Step-by-step explanation:

The given statement " when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests. " is false. Because in distribution of sample means, population variance is unknown.

When the population variance is not known and must be estimated from the data, we use a t-statistic instead of a z-statistic for our hypothesis tests.

This is because the distribution of the sample means follows a t-distribution when the population variance is unknown, whereas it follows a standard normal distribution (z-distribution) when the population variance is known.

The t-distribution has fatter tails than the z-distribution to account for the extra uncertainty introduced by estimating the population variance from the sample.

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The correct numerical expression for the given statement "multiply the sum of 7 and 6 by the sum of 4 and 5" is (7 + 6) x (4 + 5).

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The given statement, "multiply the sum of 7 and 6 by the sum of 4 and 5", can be represented as:

sum of 7 and 6 = (7 + 6)

sum of 4 and 5 = (4 + 5)

multiply: (7 + 6) x (4 + 5)

Hence, the correct numerical expression for the given statement is (7 + 6) x (4 + 5).

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Answer:

(7 + 6) x (4 + 5).

Step-by-step explanation:

hope this helps!

Using the discriminant of the quadratic equation, the temperature will part after 50 minutes

The temperature of the machine part is given by the equation:

T = -0.005x^2 + 0.45x + 125

We need to find out if the temperature will ever reach or exceed 135°F, which means we need to check if there exists a value of x for which T = 135.

Substituting T = 135 in the above equation, we get:

135 = -0.005x^2 + 0.45x + 125

Simplifying the equation, we get:

0.005x^2 - 0.45x + 10 = 0

This is a quadratic equation of the form ax^2 + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.

The discriminant of this quadratic equation is given by:

D = b^2 - 4ac

= (-0.45)^2 - 4(0.005)(10)

= 0.2025 - 0.2

= 0.0025

Since the discriminant is positive, the quadratic equation has two real roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.

We can also find the roots of the quadratic equation using the formula:

[tex]x = (-b \± \sqrt(D)) / 2a[/tex]

Substituting the values of a, b, and D, we get:

[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]

Taking the positive value, we get:

x = 50

Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.

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Mason would save $7,618.32 in interest by paying off $8,500 immediately.

In other terms, compound interest is interest on principle + interest and refers to the addition of interest to the principal amount of a loan or deposit. Reinvesting interest, or adding it to the lent capital rather than paying it out or requesting payment from the borrower, results in interest being generated on the principle amount plus previously accrued interest in the next month. In economics and finance, compound interest is common.

Comparing compound interest to simple interest, which has no effect on previously accrued interest

Given that, Mason has a credit card debt of $15,600.

Using his original payment plan of 60 months we have:

[tex]I = P * (1 + r/n)^{(n*t)} - P[/tex]

Substitute the values we have:

[tex]I = 15,600 * (1 + 0.18/12)^(12*5) - 15,600\\I = 9,316.84[/tex]

For the new plan:

New balance = $15,600 - $8,500 = $7,100

[tex]I = 7,100 * (1 + 0.18/12)^(12*2) - 7,100\\I = $1,698.52[/tex]

Hence, over the course of 24 months, Mason would pay approximately $1,698.52 in interest.

The difference in interest paid between the two scenarios is:

$9,316.84 - $1,698.52 = $7,618.32

Therefore, Mason would save approximately $7,618.32 in interest by paying off $8,500 immediately.

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The distance BC from Tower 2 to the plane is equal to 18,674 feet.

The height of the plane from the ground is equal to 7,595 feet.

In order to determine the distance from Tower 2 to the plane (BC), we would apply the law of sine (sine law) because we have two angles and one side length.

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

[tex]\frac{sin8}{7600} =\frac{sin20}{BC}[/tex]

BCsin8 = 7600sin20

BC = 2599.35/0.1392

Distance, BC = 18,673.50 ≈ 18,674 feet.

Next, we would determine the height of the plane from the ground (CD);

sin24 = CD/18,674

CD = 18,674sin24

Height, CD = 7,595.40 ≈ 7,595 feet.

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Answer:

a)  The length of BC is 15,052 ft to the nearest foot.

b)  The length of CD is 6,122 ft to the nearest foot.

Step-by-step explanation:

Angles on a straight line sum to 180°. Therefore:

[tex]\implies m \angle ABC +24^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle ABC =156^{\circ}[/tex]

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies m \angle BCA+16^{\circ}+156^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle BCA=8^{\circ}[/tex]

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Use the Sine Rule to find the length of BC.

[tex]\implies \dfrac{AB}{\sin BCA}=\dfrac{BC}{\sin CAB}=\dfrac{AC}{\sin ABC}[/tex]

[tex]\implies \dfrac{7600}{\sin 8^{\circ}}=\dfrac{BC}{\sin 16^{\circ}}[/tex]

[tex]\implies BC=\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}[/tex]

[tex]\implies BC=15052.0746...[/tex]

[tex]\implies BC=15052\; \sf ft\;(nearest\;foot)[/tex]

Therefore, the length of BC is 15,052 ft to the nearest foot.

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies m \angle BCD+24^{\circ}+90^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle BCD=66^{\circ}[/tex]

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

To find the length of CD, use the sine trigonometric ratio.

[tex]\implies \sin 24^{\circ}=\dfrac{CD}{BC}[/tex]

[tex]\implies CD=BC\sin 24^{\circ}[/tex]

Substitute the found value of BC into the equation:

[tex]\implies CD=\left(\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}\right)\sin 24^{\circ}[/tex]

[tex]\implies CD=6122.23031...[/tex]

[tex]\implies CD=6122\; \sf ft\;(nearest\;foot)[/tex]

Therefore, the length of CD is 6,122 ft to the nearest foot.

Therefore , the solution of the given problem of standard deviation comes out to be option C with n = 1,000 and p near to 1/2 is the right response.

Statistics uses variance as a way to quantify difference. The image of the result is used to compute the average deviation between the collected data and the mean. Contrary to many other valid measures of variability, it includes those pieces of data on their own by comparing each number to the mean. Variations may be caused by willful mistakes, irrational expectations, or shifting economic or business conditions.

Here,

The following algorithm determines the standard deviation of the sampling distribution of a sample proportion p:

=> √((p*(1-p))/n)

where n is the sample size, and p is the population percentage.

For the sampling distribution of a sample proportion p,

the pair of sample number n and population proportion p that would result in the highest standard deviation is:

=>n =1,000, and p is almost half.

Because p=1/2

yields the highest possible value of the expression (p*(1-p)), a bigger sample size will result in a smaller standard deviation.

The standard deviations will be lower for the other choices, which have smaller sample sizes or extreme values of p.

Therefore, (C) with n = 1,000 and p near to 1/2 is the right response.

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Answer:

14

Step-by-step explanation:

When we round 61.604 to the nearest whole number, we get 62, and when we round 48.44 to the nearest whole number, we get 48.

Therefore, we can estimate 61.604 - 48.44 by subtracting 48 from 62:

62 - 48 = 14

So, the estimated answer is 14.

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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Answer:

a straight line that connects two points on the circumference of a circle

Step-by-step explanation:

Answer: A

y < 2x + 1

y > 1/2x + 2

Answer: 3,600

Step-by-step explanation:

1 kg. = 1000 g.

3.6 X 1000 = 3,600

True. The p-value is a probability value that measures the power of evidence in against to the null hypothesis in a statistical test.

Mainly, it represents the possibility of staring at a test statistic as a minimum as extreme as the one computed, assuming that the null hypothesis is genuine.

If the p-value is small, commonly less than a chosen significance stage (e.g., 0.05), it shows that the determined data is unlikely to have took place by danger alone and provides proof against the null hypothesis. alternatively, a large p-value suggests that the determined information is consistent with the null speculation, and the evidence isn't sturdy enough to reject it.

Consequently, the p-value is an critical tool in statistical inference, permitting researchers to draw conclusions about the population based totally on pattern information and degree the extent of uncertainty in their outcomes.

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Answer:

V=lwh

=2×2×2=8

720÷8=90

90 cubes

Answer: 325

Step-by-step explanation:

65% is more than half of the 500 people. Half of the number of people is 250. 325 is the only answer over 250

The list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.

The sample space for pulling two slips of paper out of the bucket with replacement means that after drawing the first slip of paper, it is returned to the bucket before drawing the second slip. This means that each draw is independent of the previous draw, and the possible outcomes of each draw remain the same for all subsequent draws.

The possible outcomes for each draw are {Red, Blue, Yellow}, and there are three possible outcomes for each draw.

Since we are drawing with replacement, each draw has the same possible outcomes and the same number of outcomes. So, the total number of possible outcomes for two draws is simply the number of outcomes for a single draw raised to the power of 2:

[tex]3^2 = 9[/tex]

Therefore, the list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.

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The new water bill after 5% increase is $126.

The ratio that may be stated as a fraction of 100 is called as a percentage in mathematics. To compute a percentage of a number, divide it by its whole and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given bill of water =$120

Increment in percentage=5%

New water bill= 120+120×5/100

=$126

Hence, The new water bill after 5% increase is $126.

% increase = Increase in bill ÷ Old bill × 100.

5%=Increase in bill/120×100

Increase=5×120/100

=6

New bill=Old bill+ increase=120+6=126

hence, the new water bill after 5% increase is $126.

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This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.

The energy levels in a three-dimensional box are provided by the formula E = (h2/8m) [(n x2/a2) + (n y2/b2) + (n z2/c2)].

where n x, n y, and n z are the quantum numbers for the x, y, and z dimensions, respectively, and h is Planck's constant, m is the particle'smass, a, b, and c are the dimensions of the box.

The amount of various quantum number combinations that result in the same energy is the degeneracy of an energy level.

The degeneracies of the first four energy levels for a three-dimensional box with a=b=1.5c are as follows:

1 degeneracy at first energy level (n=1)

Third degeneracy at second energy level (n=2)

6 degeneracies at third energy level (n=3)

10 degeneracies at energy level four (n = 4)

Hence, This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.

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Answer:

622.04

Step-by-step explanation:

579.99 x 7.25% = 42.049 or 42.05

579.99 + 42.05 = 622.04

The total cost of the camera with sales tax included is $622.04.

A sales tax is a government-imposed consumption tax levied upon that purchase of goods and services. A standard sales tax is assessed at the moment of sale, received by the shop, and paid to the government.

Now according to the question;

The Listed price of the camera is $579.99.

The sales tax rate is 7.25%,

[tex]7.25\% \ \text{of} \ \$579.99 = (7.25\times579.99)\div100[/tex]

Sales tax = $42.04

[tex]\text{Total cost of camera = Listed price + sales tax amount}[/tex]

                                 [tex]= \$579.99 + \$42.04[/tex]

[tex]\text{Total cost of camera} = \$622.04[/tex]

Therefore, the total cost of the camera with sales tax included is $622.04.

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The area of the enlarged logo will be 9 times larger than the original logo.

When an object is enlarged or scaled up how does it area change ?

When an object is enlarged or scaled up by a factor of [tex]k[/tex], both its length and width are multiplied by [tex]k[/tex]. Therefore, the new length is [tex]k[/tex] times the original length, and the new width is [tex]k[/tex] times the original width.

The area of the new object is the product of the new length and width, which is ([tex]k[/tex] times the original length) multiplied by ([tex]k[/tex] times the original width), or [tex]k^2[/tex] times the original area.

Therefore, the area of an object increases by a factor of [tex]k^2[/tex] when the object is enlarged or scaled up by a factor of [tex]k[/tex].

Calculating how many times larger the area of the enlarged logo will be :

The original logo has dimensions of 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches.

Mr. James wants to enlarge the logo so that the dimensions are 3 times larger than the original. This means the new dimensions will be 9 inches by 15 inches.

To determine how many times larger the area of the enlarged logo will be, we need to compare the areas of the original logo and the enlarged logo. The area of the enlarged logo is 9 x 15 = 135 square inches.

To find out how many times larger the area of the enlarged logo is compared to the original logo, we divide the area of the enlarged logo by the area of the original logo:

135 square inches ÷ 15 square inches = 9

Therefore, the area of the enlarged logo will be 9 times larger than the area of the original logo.

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The equation that represents the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

Explanation:

To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).

Therefore, the equation for the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

This can also be written as:

Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)

Therefore, the value of the collection after 5 years is $246.90.

Answer: 254.26

Step-by-step explanation:

The probability of x successes in n independent trials of the experiment is given by the Binomial probability formula, where n is the total number of trials and p is the probability of success in each trial.

Since n = 9 and p = 0.4, we can calculate the probability of x ≤ 3 successes as follows:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (9C0)(0.4)^0(0.6)^9 + (9C1)(0.4)^1(0.6)^8 + (9C2)(0.4)^2(0.6)^7 + (9C3)(0.4)^3(0.6)^6

= 0.17496 + 0.41472 + 0.36608 + 0.04320

= 0.99976

Therefore, the probability of x ≤ 3 successes is 0.99976.

The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²

Area = 1/2(base)(height).

Given the parameters:

If a = 4 and c = 2, then:

Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)

Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)

Area = 1/2(32)(38)

Area = 608 cm²

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a. The number of shares purchased can be calculated as:

Number of Shares = (Investment Amount / Face Value)

= 25,059/ 10 = 2,505.9 = 2,506 (to the nearest whole number)

b. The amount of brokerage paid can be calculated as:

Brokerage = (Investment Amount x Brokerage Rate)

= 2,50,590 x 0.002 = Rs. 501.18

c. The GST paid for the trading can be calculated as:

GST = (Brokerage Amount x GST Rate)

= 501.18 x 0.18 = Rs. 90.22

Answer:

Step-by-step explanation: