The area of a square garden is 72 m2. How long is the diagonal?

Answer:

y = - 2x + 1

Step-by-step explanation:

Substitute an x value from the table into the equation

x = 1 : y = - 2(1) = - 2 ← require to add 1 to obtain y = - 1

x = 4 : y = - 2(4) = - 8 ← require to add 1 yo obtain y = - 7

Then equation describing the relationship is

y = - 2x + 1

Answer:

a and d

Step-by-step explanation:

it is I took the test

Answer:

A. A student's GPA goes down approximately 1 point for every 10 hours spent playing video games.

Step-by-step explanation:

The line shows that the student's GPA goes down 0.5 every 5 hours of video games played. 0.5:5 is equivalent to 1:10. So A is your answer.

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Answer:

937.5

Step-by-step explanation:

150% is equal to 150/100. Therefore, we have to multiply 625 by 150/100. 150/100 is the same as 1.5. Therefore, we have to multiply 625 by 1.5. 625x1.5=937.5.

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Answer:

937.5

Step-by-step explanation:

625×1.50 is 937.5

The probability that a randomly selected light bulb lasts less than 46 hours is 0.1%.

The lifetimes of light bulbs are approximately normally distributed, with a mean of 56 hours and a standard deviation of 3.2 hours. Using this information, we will calculate the proportion of light bulbs that will last more than 62 hours, the proportion of light bulbs that will last 51 hours or less, the proportion of light bulbs that will last between 58 and 61 hours, and the probability that a randomly selected light bulb lasts less than 46 hours. (a) What proportion of light bulbs will last more than 62 hours?z = (x - μ) / σz = (62 - 56) / 3.2 = 1.875From the standard normal distribution table, the proportion of light bulbs that will last more than 62 hours is 0.0301 or 3.01%.Therefore, 3.01% of light bulbs will last more than 62 hours. (b) What proportion of light bulbs will last 51 hours or less?z = (x - μ) / σz = (51 - 56) / 3.2 = -1.5625From the standard normal distribution table, the proportion of light bulbs that will last 51 hours or less is 0.0594 or 5.94%.Therefore, 5.94% of light bulbs will last 51 hours or less. (c) What proportion of light bulbs will last between 58 and 61 hours?z1 = (x1 - μ) / σz1 = (58 - 56) / 3.2 = 0.625z2 = (x2 - μ) / σz2 = (61 - 56) / 3.2 = 1.5625From the standard normal distribution table, the proportion of light bulbs that will last between 58 and 61 hours is the difference between the areas to the left of z2 and z1, which is 0.1371 - 0.2660 = 0.1289 or 12.89%.Therefore, 12.89% of light bulbs will last between 58 and 61 hours. (d) What is the probability that a randomly selected light bulb lasts less than 46 hours?z = (x - μ) / σz = (46 - 56) / 3.2 = -3.125From the standard normal distribution table, the proportion of light bulbs that will last less than 46 hours is 0.0010 or 0.1%.

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Answer: 45

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x^2+8x+36=0

Factor out the GCF: 4

1/4(4x^2+8x+36=0)

x^2+2x+9=0

Solve using the Quadratic formula.

a= 1

b= 2

c= 9

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}\)

\(x = \frac{ -2 \pm \sqrt{2^2 - 4(1)(9)}}{2(1)}\)

\(x = \frac{ -2 \pm \sqrt{4 - 36}}{2}\)

\(x = \frac{ -2 \pm \sqrt{-32}}{2}\)

There are no real solutions because you cannot square root a negative number.

\(x = \frac{ -2 \pm 4\sqrt{2}i}{2}\)

\(x = -1+2\sqrt{2}i\\ x= -1-2\sqrt{2} i\)

For the outer dimensions: length = 35 inches, width = 25 inches, and height = 15 inches.

Step-by-step explanation:

For the interior;

volume = 6000

length, l = 3h

width, w = 2h

height = h

But,

Volume of a cuboid = length x width x height

So that;

6000 = 3h x 2h x h

6000 = 6

Divide through by 6 to have;

1000 =

h =

 = 10

Thus, the height is 10 inches. Thus;

length, l = 3h = 3 x 10 = 30 inches

width, w = 2h = 2 x 10 = 20 inches

For the outer dimension, since the concrete sides and bottom would be 5 inches thick. Then its dimension are;

length, l = 30 + 5 = 35 inches

width, w = 20 + 5 = 25 inches

height = 10 + 5 = 15 inches

The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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Answer:

5. 8(a-5)= -40

8a-40= -40

8a= -40+40

8a=0

a=0/8

a=0

option c is correct.

6. for d,

-1<d<1

I think the answer is option d , which is missing in the attachment.

the 4 question is missing.

so I am not able to answer that

(a) The possible outcomes of this experiment are:

Draw a red marble.

Draw a blue marble.

Draw a green marble.

B)  The probability of each of the outcomes is:

Draw a red marble: 50%

Draw a blue marble: 25%

Draw a green marble: 25%

(c) The outcomes that make up the event drawing a red marble are: 1/3

d) the probability of drawing a green marble is lower than the probability of drawing a red marble.

Given that;

In an experiment, two red marbles, one blue marble, and one green marble, are placed in a bag. A single marble is drawn at random

(a) The possible outcomes of this experiment are:

Draw a red marble.

Draw a blue marble.

Draw a green marble.

(b) The probability of each of the outcomes is:

Draw a red marble: 2/4 = 1/2 = 50%

Draw a blue marble: 1/4 = 25%

Draw a green marble: 1/4 = 25%

(c) The outcomes that make up the event drawing a red marble are:

Draw the first red marble.

Draw the second red marble.

The probability of drawing a red marble is the sum of the probabilities of these two outcomes:

P(Draw a red marble) = P(Draw the first red marble) + P(Draw the second red marble)

P(Draw a red marble) = 2/4 x 1/3 + 2/4 x 1/3

P(Draw a red marble) = 1/3 = 33.3%

(d) The event drawing a green marble is less likely than the event drawing a red marble.

This is because there is only one green marble, whereas there are two red marbles.

Therefore, the probability of drawing a green marble is lower than the probability of drawing a red marble.

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The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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The probability that the mean SAT score for a random sample of 50 freshmen will be anywhere from 1075 to 1110 is approximately 0.7396, or 73.96%.

To solve this problem, we will use the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.

Given:

Population Mean (μ): 1100

Standard Deviation (σ): 95

Sample Size (n): 50

We need to find the probability that the mean SAT score for a random sample of 50 freshmen falls between 1075 and 1110.

First, we calculate the standard error of the mean (SEM) using the formula:

SEM = σ / √n

SEM = 95 / √50 ≈ 13.435

Next, we can calculate the z-scores for the lower and upper limits using the formula:

z = (x - μ) / SEM

For the lower limit:

\(z_{lower\) = (1075 - 1100) / 13.435 ≈ -1.861

For the upper limit:

\(z_{upper\) = (1110 - 1100) / 13.435 ≈ 0.745

Now, we can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

Using the standard normal distribution table, we find the area to the left of -1.861 is approximately 0.0308, and the area to the left of 0.745 is approximately 0.7704.

To find the probability between these two z-scores, we subtract the smaller area from the larger area:

Probability = 0.7704 - 0.0308 ≈ 0.7396

Therefore, the probability that the mean SAT score for a random sample of 50 freshmen will be anywhere from 1075 to 1110 is approximately 0.7396, or 73.96%.

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Answer:

Step-by-step explanation:

Cross multiply. When you have two fractions set equal to each other, you can cross multiply to solve.

5(3y - 8) = 12y and

15y - 40 = 12y and

3y = 40 so

y = 40/3, choice A.

To find the value of x, we need to use the fact that when two lines intersect, the sum of the adjacent angles formed is equal to 180 degrees.

In this case, the angle formed between lines s and t is 23 degrees, and the angle formed between lines r and s is 106 degrees. Let's denote the angle between lines t and r as x.

Using the information given, we can set up the equation:

(106 degrees) + (23 degrees) + x = 180 degrees

Combine the known values:

129 degrees + x = 180 degrees

To isolate x, subtract 129 degrees from both sides of the equation:

x = 180 degrees - 129 degrees

x = 51 degrees

Therefore, the value of x is 51 degrees.

In conclusion, the value of x, the adjacent angles formed between intersecting lines t and r, is 51 degrees.

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Answer:

-4 is the answer

Answer:

-4

Step-by-step explanation:

8+(-12)

+ x - = -

8-12

-4

Answer:

5

Step-by-step explanation:

6x + 4 + 73 + 73 = 180

6x + 150 = 180

6x = 30

x = 5

Those little marks on AB and BC denote congruence. That makes the triangle isoceles. That means the base angles are equal. Both 73.

Triangle Sum Theory states all angles of a triangle add to 180.

Answer:

a ratio compares two numbers by division

Step-by-step explanation:

i just know

Answer:

Ratio

Step-by-step explanation:

Ratio – A comparison of two quantities by division.

The test statistic is at α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

What is p-value?

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, presuming that the null hypothesis is true.

As given,

State the hypothesis,

Ha: μ = 132

Ha: μ ≠ 132 (two failed test)

Test satisfies:

As σ is unknown we will use t-test satisfies

t = (x - μ)/(s/√n)

Substitute values,

t = (137 - 132)/(14.2/√20)

t = 1.57

t satisfies is 1.57.

Critical values,

P(t < tc) = P(t < tc) = 0.05

using t table at df = 19

tc = ±1.729

So value is tc = (-1.729, 1.729)

P-value:

P(t > ItstatI) = p-value

P(t > I1.57I) = p-value

Using t-table

p-value = 0.1329

given

α = 0.10

So, p-value < α

Do not reject Null hypothesis.

Conclusion:

At α = 0.10 we have sufficient evidence that means weight is given by μ = 132 lb.

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Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

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

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

3(n+4)

Step-by-step explanation:

you will take common

3(n+4)

3n + 12 can be factorized to get 3(n+4).

Factorization is the process of writing a number as the product of other numbers known as factors.

3n+12 = 3(n+4)

We have factorized the given expression as 3(n+4).

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Answer:

Step-by-step explanation:

-x=18-6

-x=12

x=-12

Answer:The wavelength of violet light is approximately 0.00000038 meters. In scientific notation, this can be written as 3.8 x 10^-7 meters.

Step-by-step explanation:

Polynomials are algebraic expressions that contain more than two terms. AN example would be: f(x) = x^3 + x^2 + x +1. This equation contains three terms, with the 3rd degree as its highest term. It also means that the graph passed three x-intercepts. This depends in the highest degree. So, the first thing you do is plot the intercepts because for sure, the graph will pass there.

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The percentage of arrests for people who received Multisystemic Therapy (MST) can be calculated by dividing the number of individuals arrested in the MST group (87) by the total number of individuals.

Percentage of arrests for MST group = (87/215) * 100 ≈ 40.47%

To determine if therapy caused significantly fewer arrests at a 0.05 significance level, we need to compare this percentage with the percentage of arrests in the control group.

The percentage of arrests for the control group can be calculated in a similar manner by dividing the number of individuals arrested in the control group (74) by the total number of individuals in the control group (196), and multiplying by 100.

Percentage of arrests for control group = (74/196) * 100 ≈ 37.76%

Comparing the sample percentages, we find that the percentage of arrests for people who received MST (40.47%) is slightly higher than the percentage of arrests for the control group (37.76%).

To determine if this difference is statistically significant at a 0.05 significance level, we would need to perform a hypothesis test, such as a chi-square test, to compare the observed frequencies with the expected frequencies under the assumption that therapy has no effect on reducing arrests.

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The table is filled considering the numeric values of the function, as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The numeric value in this problem is found replacing the lone instance of x by it's value, hence the numeric value at x = -6 is given as follows:

y = 2(-6) - 3

y = -12 - 3

y = -15.

The same procedure is applied for x = -3, x = 0 and x = 3.

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Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

7.4 m it's because toes are yummy

The first step in finding the surface area of the box in terms of only x is to express the height of the box in terms of x. The volume of the box with a square base is given by;V = l × w × hV = x × x × hV = x² × h And, we are told that the volume of the box is 340736 cm³;V = 340736 cm³ .

Substituting x²h in V;340736 cm³ = x²hHence, h = 340736 / x²

Now that we have expressed h in terms of x, we can proceed to find the formula for the surface area of the box.

We know that the box has a square base. Therefore, the surface area of the square is given by the formula;

S₁ = x² . There are four rectangular sides to the box, which all have the same dimensions, x by h.

Therefore, the total surface area for all the rectangular sides can be found by the formula;

S₂ = 4xhReplacing h with 340736 / x²;S₂ = 4x(340736 / x²)S₂ = (1362944 / x) cm²Adding the two surface areas gives the formula for the surface area of the box;

A(x) = x² + (1362944 / x)We can simplify this by taking the common denominator as follows;

A(x) = (x³ + 1362944) / x

Now, to find the derivative A′(x);A(x) = (x³ + 1362944) / xA′(x) = [(3x² × x) - (x³ + 1362944) × 1] / x²A′(x) = (3x² - x³ - 1362944) / x²Setting A′(x) = 0;A′(x) = 0(3x² - x³ - 1362944) / x² = 0.

Solving for x;3x² - x³ - 1362944 = 0x³ - 3x² + 1362944 = 0

This can be solved using the cubic formula;ax³ + bx² + cx + d = 0x = -b ± √(b² - 4ac) / 2a

For our equation, a = 1, b = -3, c = 0 and d = 1362944.

Substituting in the cubic formula; x = -(-3) ± √((-3)² - 4(1)(0)(1362944)) / 2(1)x = 3 ± √(9 - 0) / 2x = 3 ± √9 / 2x = (3 ± 3) / 2x = 6 / 2 or x = 0 / 2x = 3 or x = 0

The value of x is 3 because x cannot be 0, or else there will be no box.

Secondly, we will perform the second derivative test to confirm that this value of x gives a minimum value for the surface area.

To do that, we need to find A′′(x);A′(x) = (3x² - x³ - 1362944) / x²A′′(x) = [(6x × x²) - (2x × (3x² - x³ - 1362944))] / x⁴A′′(x) = (6x³ - 6x³ + 2x⁴ + 2725888) / x⁴A′′(x) = (2x⁴ + 2725888) / x⁴

Evaluating A′′(x) at x = 3;A′′(3) = (2(3)⁴ + 2725888) / (3)⁴A′′(3) = (4374 + 2725888) / 81A′′(3) = 33712.69Since A′′(3) > 0, this means that the graph of A(x) is concave up around that value, so the zero of A′(x) at x = 3 must indicate a local minimum for A(x).

Therefore, the dimensions of the box that minimize the amount of material used are;

Length = x = 3 cm

Width = x = 3 cm

Height = h = 340736 / x² = 12646.67 cm³

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